Subgroups — C₃₁×#62591 #21519350

Order 7936.

1726 conjugacy classes of subgroups.

The subgroup lattice has 850 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3515	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3511	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3364	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3360	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3331	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3330	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3327	C₂	1	4	yes	maximal, complemented
8	C₃₁×#3326	C₂	1	4	yes	maximal, complemented
9	C₃₁×#3236	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3235	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#3219	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3218	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3172	C₂	1	2	yes	maximal, complemented
14	C₃₁×#3171	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3142	C₂	1	2	yes	maximal, complemented
16	C₃₁×#3139	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#2971	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃₁×#557	C₂²	1	1	yes	characteristic
19	C₃₁×#556	C₂²	1	2	yes	—
20	C₃₁×#555	—	2	1	no	—
21	C₃₁×#554	—	2	1	no	—
22	C₃₁×#554	C₂²	1	1	yes	characteristic
23	C₃₁×#554	C₂²	1	1	yes	characteristic
24	C₃₁×#553	—	2	2	no	—
25	C₃₁×#553	C₂²	1	2	yes	—
26	C₃₁×#552	—	2	2	no	—
27	C₃₁×#552	—	2	1	no	—
28	C₃₁×#552	C₂²	1	2	yes	—
29	C₃₁×#548	C₂²	1	4	yes	—
30	C₃₁×#547	—	2	1	no	—
31	C₃₁×#547	C₂²	1	2	yes	—
32	C₃₁×#547	C₂²	1	1	yes	characteristic
33	C₃₁×#542	—	2	2	no	—
34	C₃₁×#541	—	2	1	no	—
35	C₃₁×#539	—	2	2	no	—
36	C₃₁×#537	—	2	1	no	—
37	C₃₁×#533	C₂²	1	2	yes	—
38	C₃₁×#533	C₂²	1	1	yes	characteristic
39	C₃₁×#532	C₂²	1	2	yes	—
40	C₃₁×#532	C₂²	1	1	yes	characteristic
41	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
42	C₃₁×#529	C₂²	1	1	yes	characteristic
43	C₃₁×#529	C₂²	1	2	yes	—
44	C₂×C₃₁×#125	C₂²	1	2	yes	—
45	C₃₁×#520	—	2	1	no	—
46	C₃₁×#520	—	2	1	no	—
47	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
48	C₃₁×#501	C₂²	1	1	yes	characteristic
49	C₃₁×#501	C₂²	1	2	yes	—
50	C₃₁×#497	C₂²	1	2	yes	—
51	C₃₁×#496	C₂²	1	1	yes	characteristic
52	C₃₁×#491	C₂²	1	2	yes	—
53	C₃₁×#491	C₂²	1	2	yes	—
54	C₃₁×#491	C₂²	1	2	yes	—
55	C₃₁×#490	C₂²	1	1	yes	characteristic
56	C₃₁×#490	C₂²	1	2	yes	—
57	C₃₁×#489	C₂²	1	1	yes	characteristic
58	C₃₁×#488	C₂²	1	4	yes	—
59	C₃₁×#488	C₂²	1	4	yes	—
60	C₃₁×#487	C₂²	1	2	yes	—
61	C₃₁×#487	C₂²	1	2	yes	—
62	C₃₁×#484	C₂²	1	4	yes	—
63	C₃₁×#483	C₂²	1	4	yes	—
64	C₃₁×#482	C₂²	1	4	yes	—
65	C₃₁×#479	C₂²	1	4	yes	—
66	C₃₁×#479	C₂²	1	4	yes	—
67	C₃₁×#476	C₂²	1	2	yes	—
68	C₃₁×#474	C₂²	1	2	yes	—
69	C₃₁×#470	C₂²	1	4	yes	—
70	C₃₁×#469	C₂²	1	2	yes	—
71	C₃₁×#468	C₂²	1	2	yes	—
72	C₃₁×#468	C₂²	1	4	yes	—
73	C₃₁×#464	C₂²	1	4	yes	—
74	C₃₁×#463	C₂²	1	4	yes	—
75	C₃₁×#462	C₂²	1	2	yes	—
76	C₃₁×#461	C₂²	1	2	yes	—
77	C₃₁×#452	C₂²	1	4	yes	—
78	C₃₁×#451	C₂²	1	2	yes	—
79	C₃₁×#449	C₂²	1	4	yes	—
80	C₃₁×#448	C₂²	1	2	yes	—
81	C₈×Q₈×C₃₁	C₂²	1	2	yes	—
82	C₄×Q₁₆×C₃₁	C₂²	1	4	yes	—
83	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	—
84	C₄×SD₁₆×C₃₁	C₂²	1	4	yes	—
85	C₄×D₈×C₃₁	C₂²	1	2	yes	—
86	C₃₁×#436	C₂²	1	2	yes	—
87	C₃₁×#436	C₂²	1	4	yes	—
88	C₃₁×#432	C₂²	1	1	yes	characteristic
89	C₃₁×#432	C₂²	1	2	yes	—
90	C₃₁×#419	C₂²	1	4	yes	—
91	C₃₁×#417	C₂²	1	4	yes	—
92	C₃₁×#417	C₂²	1	4	yes	—
93	C₄×M₁₆×C₃₁	C₂²	1	1	yes	characteristic
94	C₄×M₁₆×C₃₁	C₂²	1	2	yes	—
95	C₂×#41×C₃₁	—	2	1	no	—
96	C₂×#41×C₃₁	—	2	1	no	—
97	C₂×#41×C₃₁	D₄	1	1	yes	characteristic
98	C₂×#41×C₃₁	C₂³	1	4	yes	—
99	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
100	C₂×Q₁₆×C₃₁	C₂³	1	4	yes	—
101	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
102	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
103	C₂×D₈×C₃₁	C₂³	1	2	yes	—
104	C₂×M₁₆×C₃₁	C₂³	1	4	yes	—
105	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
106	C₃₁×C₄⋊Q₈	—	2	1	no	—
107	C₃₁×C₄⋊Q₈	—	2	1	no	—
108	C₃₁×C₄⋊Q₈	—	2	1	no	—
109	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
110	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
111	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
112	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
113	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
114	C₃₁×#127	C₂³	1	1	yes	characteristic
115	C₃₁×#126	—	2	2	no	—
116	C₃₁×#126	—	2	4	no	—
117	C₃₁×#126	—	2	2	no	—
118	C₃₁×#126	—	2	2	no	—
119	C₃₁×#126	—	2	1	no	—
120	C₃₁×#125	—	2	2	no	—
121	C₃₁×#125	—	2	2	no	—
122	C₃₁×#125	—	2	1	no	—
123	C₃₁×#125	—	2	2	no	—
124	C₃₁×#125	—	2	2	no	—
125	C₃₁×#125	—	2	2	no	—
126	C₃₁×#125	C₂³	1	2	yes	—
127	C₃₁×#125	C₂³	1	2	yes	—
128	C₃₁×#125	C₂³	1	1	yes	characteristic
129	C₃₁×#125	C₂³	1	2	yes	—
130	C₃₁×#124	—	2	4	no	—
131	C₃₁×#124	—	2	1	no	—
132	C₃₁×#124	C₂³	1	4	yes	—
133	C₃₁×#124	C₂³	1	1	yes	characteristic
134	C₃₁×#123	—	2	2	no	—
135	C₃₁×#123	—	2	1	no	—
136	C₃₁×#123	—	2	2	no	—
137	C₃₁×#123	—	2	2	no	—
138	C₃₁×#123	—	2	2	no	—
139	C₃₁×#123	—	2	4	no	—
140	C₃₁×C₂²⋊Q₈	—	2	2	no	—
141	C₃₁×C₂²⋊Q₈	—	2	1	no	—
142	C₃₁×C₂²⋊Q₈	—	2	2	no	—
143	C₃₁×C₂²⋊Q₈	—	2	1	no	—
144	C₃₁×C₂²⋊Q₈	—	2	1	no	—
145	C₃₁×C₂²⋊Q₈	—	2	2	no	—
146	C₃₁×C₂²⋊Q₈	—	2	1	no	—
147	C₃₁×C₂²⋊Q₈	—	2	4	no	—
148	C₃₁×C₂²⋊Q₈	—	2	2	no	—
149	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
150	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
151	C₃₁×C₂²⋊Q₈	C₂³	1	4	yes	—
152	C₃₁×#121	—	2	2	no	—
153	C₃₁×#121	—	2	4	no	—
154	C₃₁×#121	—	2	2	no	—
155	C₃₁×#121	—	2	2	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×#121	C₂³	1	2	yes	—
161	C₄×Q₈×C₃₁	—	2	1	no	—
162	C₄×Q₈×C₃₁	—	2	1	no	—
163	C₄×Q₈×C₃₁	—	2	2	no	—
164	C₄×Q₈×C₃₁	—	2	1	no	—
165	C₄×Q₈×C₃₁	D₄	1	1	yes	characteristic
166	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
167	C₄×Q₈×C₃₁	C₂³	1	4	yes	—
168	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
169	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
170	C₄×D₄×C₃₁	—	2	1	no	—
171	C₄×D₄×C₃₁	—	2	2	no	—
172	C₄×D₄×C₃₁	—	2	1	no	—
173	C₄×D₄×C₃₁	—	2	4	no	—
174	C₄×D₄×C₃₁	—	2	2	no	—
175	C₄×D₄×C₃₁	—	2	2	no	—
176	C₄×D₄×C₃₁	—	2	2	no	—
177	C₄×D₄×C₃₁	—	2	1	no	—
178	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
179	C₄×D₄×C₃₁	D₄	1	2	yes	—
180	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
181	C₄×D₄×C₃₁	C₂³	1	2	yes	—
182	C₄×D₄×C₃₁	C₂³	1	2	yes	—
183	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
184	C₄×D₄×C₃₁	C₂³	1	2	yes	—
185	C₃₁×#117	—	2	2	no	—
186	C₃₁×#117	—	2	2	no	—
187	C₃₁×#117	—	2	2	no	—
188	C₃₁×#117	—	2	1	no	—
189	C₃₁×#117	—	2	2	no	—
190	C₃₁×#117	D₄	1	1	yes	characteristic
191	C₃₁×#117	D₄	1	2	yes	—
192	C₃₁×#117	C₂³	1	2	yes	—
193	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
194	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
195	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
196	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
197	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
198	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
199	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
200	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
201	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
202	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
203	C₃₁×#107	C₂³	1	2	yes	—
204	C₃₁×#107	C₂³	1	4	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	4	yes	—
212	C₃₁×#103	C₂³	1	4	yes	—
213	C₃₁×#103	C₂³	1	4	yes	—
214	C₃₁×#103	C₂³	1	4	yes	—
215	C₃₁×#103	C₂³	1	2	yes	—
216	C₃₁×#102	C₂³	1	2	yes	—
217	C₃₁×#102	C₂³	1	2	yes	—
218	C₃₁×#102	C₂³	1	4	yes	—
219	C₃₁×#102	C₂³	1	4	yes	—
220	C₃₁×#102	C₂³	1	2	yes	—
221	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
222	C₃₁×C₂²⋊C₈	C₂³	1	4	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	#41×C₃₁	—	4	2	no	—
229	#41×C₃₁	—	4	4	no	—
230	#41×C₃₁	—	4	4	no	—
231	#41×C₃₁	—	4	4	no	—
232	#41×C₃₁	—	4	4	no	—
233	C₂×Q₈×C₃₁	—	2	1	no	—
234	C₂×Q₈×C₃₁	—	2	1	no	—
235	C₂×Q₈×C₃₁	—	2	1	no	—
236	C₂×Q₈×C₃₁	—	2	2	no	—
237	C₂×Q₈×C₃₁	—	4	4	no	—
238	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
239	C₂×Q₈×C₃₁	C₂⁴	1	4	yes	—
240	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
241	C₂×D₄×C₃₁	—	2	2	no	—
242	C₂×D₄×C₃₁	—	2	2	no	—
243	C₂×D₄×C₃₁	—	2	1	no	—
244	C₂×D₄×C₃₁	—	2	4	no	—
245	C₂×D₄×C₃₁	—	2	1	no	—
246	C₂×D₄×C₃₁	—	2	1	no	—
247	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
248	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
249	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
250	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
251	C₂²×C₄×C₃₁	—	2	2	no	—
252	C₂²×C₄×C₃₁	—	2	2	no	—
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	4	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	2	yes	—
263	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
264	Q₁₆×C₃₁	—	4	4	no	—
265	SD₁₆×C₃₁	—	4	2	no	—
266	SD₁₆×C₃₁	—	4	4	no	—
267	D₈×C₃₁	—	4	2	no	—
268	M₁₆×C₃₁	—	4	2	no	—
269	M₁₆×C₃₁	—	4	4	no	—
270	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
271	C₂×C₈×C₃₁	C₂⁴	1	4	yes	—
272	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
273	C₄⋊C₄×C₃₁	—	2	2	no	—
274	C₄⋊C₄×C₃₁	—	2	2	no	—
275	C₄⋊C₄×C₃₁	—	2	1	no	—
276	C₄⋊C₄×C₃₁	—	2	1	no	—
277	C₄⋊C₄×C₃₁	—	2	2	no	—
278	C₄⋊C₄×C₃₁	—	2	2	no	—
279	C₄⋊C₄×C₃₁	—	2	2	no	—
280	C₄⋊C₄×C₃₁	—	2	1	no	—
281	C₄⋊C₄×C₃₁	—	2	4	no	—
282	C₄⋊C₄×C₃₁	—	2	2	no	—
283	C₄⋊C₄×C₃₁	—	2	2	no	—
284	C₄⋊C₄×C₃₁	—	2	2	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	—	2	2	no	—
292	C₄⋊C₄×C₃₁	—	2	1	no	—
293	C₄⋊C₄×C₃₁	—	2	4	no	—
294	C₄⋊C₄×C₃₁	—	2	1	no	—
295	C₄⋊C₄×C₃₁	—	2	2	no	—
296	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
297	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
298	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
299	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
300	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
301	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
302	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
303	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
304	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
305	C₂²⋊C₄×C₃₁	—	2	2	no	—
306	C₂²⋊C₄×C₃₁	—	2	4	no	—
307	C₂²⋊C₄×C₃₁	—	2	2	no	—
308	C₂²⋊C₄×C₃₁	—	2	1	no	—
309	C₂²⋊C₄×C₃₁	—	2	1	no	—
310	C₂²⋊C₄×C₃₁	—	2	4	no	—
311	C₂²⋊C₄×C₃₁	—	2	1	no	—
312	C₂²⋊C₄×C₃₁	—	2	1	no	—
313	C₂²⋊C₄×C₃₁	—	2	2	no	—
314	C₂²⋊C₄×C₃₁	—	2	4	no	—
315	C₂²⋊C₄×C₃₁	—	2	2	no	—
316	C₂²⋊C₄×C₃₁	—	2	2	no	—
317	C₂²⋊C₄×C₃₁	—	2	2	no	—
318	C₂²⋊C₄×C₃₁	—	2	1	no	—
319	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
320	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
321	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
322	C₄²×C₃₁	—	2	4	no	—
323	C₄²×C₃₁	—	2	2	no	—
324	C₄²×C₃₁	—	2	2	no	—
325	C₄²×C₃₁	—	2	1	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	1	yes	characteristic
331	C₄²×C₃₁	C₂⁴	1	2	yes	—
332	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
333	#62591	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	C₂²×D₄	1	2	yes	—
337	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
338	Q₈×C₃₁	—	2	2	no	—
339	Q₈×C₃₁	—	2	2	no	—
340	Q₈×C₃₁	—	2	4	no	—
341	Q₈×C₃₁	—	2	4	no	—
342	Q₈×C₃₁	—	4	2	no	—
343	Q₈×C₃₁	—	4	2	no	—
344	Q₈×C₃₁	—	8	1	no	—
345	Q₈×C₃₁	—	8	2	no	—
346	D₄×C₃₁	—	2	2	no	—
347	D₄×C₃₁	—	2	2	no	—
348	D₄×C₃₁	—	2	2	no	—
349	D₄×C₃₁	—	2	2	no	—
350	D₄×C₃₁	—	4	2	no	—
351	D₄×C₃₁	—	4	2	no	—
352	D₄×C₃₁	—	4	2	no	—
353	D₄×C₃₁	—	4	4	no	—
354	D₄×C₃₁	—	4	4	no	—
355	D₄×C₃₁	—	8	1	no	—
356	D₄×C₃₁	—	8	4	no	—
357	C₂×C₄×C₃₁	—	2	2	no	—
358	C₂×C₄×C₃₁	—	2	2	no	—
359	C₂×C₄×C₃₁	—	2	4	no	—
360	C₂×C₄×C₃₁	—	2	1	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	4	no	—
365	C₂×C₄×C₃₁	—	2	1	no	—
366	C₂×C₄×C₃₁	—	2	1	no	—
367	C₂×C₄×C₃₁	—	4	2	no	—
368	C₂×C₄×C₃₁	—	4	1	no	—
369	C₂×C₄×C₃₁	—	4	2	no	—
370	C₂×C₄×C₃₁	—	4	4	no	—
371	C₂×C₄×C₃₁	—	4	2	no	—
372	C₂×C₄×C₃₁	—	4	4	no	—
373	C₂×C₄×C₃₁	—	8	2	no	—
374	C₂×C₄×C₃₁	—	8	4	no	—
375	C₂×C₄×C₃₁	—	8	2	no	—
376	C₂×C₄×C₃₁	—	8	2	no	—
377	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
378	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
379	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
380	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
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	2	yes	—
384	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
385	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
386	C₈×C₃₁	—	2	2	no	—
387	C₈×C₃₁	—	2	2	no	—
388	C₈×C₃₁	—	2	4	no	—
389	#3515	C₂×C₃₁	1	1	yes	characteristic, complemented
390	#3511	C₂×C₃₁	1	1	yes	characteristic, complemented
391	#3364	C₂×C₃₁	1	2	yes	complemented
392	#3360	C₂×C₃₁	1	2	yes	complemented
393	#3331	C₂×C₃₁	1	2	yes	complemented
394	#3330	C₂×C₃₁	1	2	yes	complemented
395	#3327	C₂×C₃₁	1	4	yes	complemented
396	#3326	C₂×C₃₁	1	4	yes	complemented
397	#3236	C₂×C₃₁	1	2	yes	complemented
398	#3235	C₂×C₃₁	1	1	yes	characteristic, complemented
399	#3219	C₂×C₃₁	1	2	yes	complemented
400	#3218	C₂×C₃₁	1	1	yes	characteristic, complemented
401	#3172	C₂×C₃₁	1	2	yes	complemented
402	#3171	C₂×C₃₁	1	1	yes	characteristic, complemented
403	#3142	C₂×C₃₁	1	2	yes	complemented
404	#3139	C₂×C₃₁	1	1	yes	characteristic, complemented
405	#2971	C₂×C₃₁	1	1	yes	characteristic, complemented
406	C₂²×C₃₁	—	2	2	no	—
407	C₂²×C₃₁	—	2	1	no	—
408	C₂²×C₃₁	—	2	1	no	—
409	C₂²×C₃₁	—	2	2	no	—
410	C₂²×C₃₁	—	2	1	no	—
411	C₂²×C₃₁	—	2	2	no	—
412	C₂²×C₃₁	—	4	1	no	—
413	C₂²×C₃₁	—	4	2	no	—
414	C₂²×C₃₁	—	4	2	no	—
415	C₂²×C₃₁	—	4	1	no	—
416	C₂²×C₃₁	—	4	2	no	—
417	C₂²×C₃₁	—	4	1	no	—
418	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
419	C₄×C₃₁	—	2	1	no	—
420	C₄×C₃₁	—	2	2	no	—
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	—	4	1	no	—
427	C₄×C₃₁	—	4	2	no	—
428	C₄×C₃₁	—	4	4	no	—
429	C₄×C₃₁	—	4	1	no	—
430	C₄×C₃₁	—	4	1	no	—
431	C₄×C₃₁	—	4	2	no	—
432	C₄×C₃₁	—	4	2	no	—
433	C₄×C₃₁	#575	1	2	yes	—
434	C₄×C₃₁	#585	1	2	yes	—
435	#557	C₂²×C₃₁	1	1	yes	characteristic
436	#556	C₂²×C₃₁	1	2	yes	—
437	#555	—	2	1	no	—
438	#554	—	2	1	no	—
439	#554	C₂²×C₃₁	1	1	yes	characteristic
440	#554	C₂²×C₃₁	1	1	yes	characteristic
441	#553	—	2	2	no	—
442	#553	C₂²×C₃₁	1	2	yes	—
443	#552	—	2	2	no	—
444	#552	—	2	1	no	—
445	#552	C₂²×C₃₁	1	2	yes	—
446	#548	C₂²×C₃₁	1	4	yes	—
447	#547	—	2	1	no	—
448	#547	C₂²×C₃₁	1	2	yes	—
449	#547	C₂²×C₃₁	1	1	yes	characteristic
450	#542	—	2	2	no	—
451	#541	—	2	1	no	—
452	#539	—	2	2	no	—
453	#537	—	2	1	no	—
454	#533	C₂²×C₃₁	1	2	yes	—
455	#533	C₂²×C₃₁	1	1	yes	characteristic
456	#532	C₂²×C₃₁	1	2	yes	—
457	#532	C₂²×C₃₁	1	1	yes	characteristic
458	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
459	#529	C₂²×C₃₁	1	1	yes	characteristic
460	#529	C₂²×C₃₁	1	2	yes	—
461	C₂×#125	C₂²×C₃₁	1	2	yes	—
462	#520	—	2	1	no	—
463	#520	—	2	1	no	—
464	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
465	#501	C₂²×C₃₁	1	1	yes	characteristic
466	#501	C₂²×C₃₁	1	2	yes	—
467	#497	C₂²×C₃₁	1	2	yes	—
468	#496	C₂²×C₃₁	1	1	yes	characteristic
469	#491	C₂²×C₃₁	1	2	yes	—
470	#491	C₂²×C₃₁	1	2	yes	—
471	#491	C₂²×C₃₁	1	2	yes	—
472	#490	C₂²×C₃₁	1	1	yes	characteristic
473	#490	C₂²×C₃₁	1	2	yes	—
474	#489	C₂²×C₃₁	1	1	yes	characteristic
475	#488	C₂²×C₃₁	1	4	yes	—
476	#488	C₂²×C₃₁	1	4	yes	—
477	#487	C₂²×C₃₁	1	2	yes	—
478	#487	C₂²×C₃₁	1	2	yes	—
479	#484	C₂²×C₃₁	1	4	yes	—
480	#483	C₂²×C₃₁	1	4	yes	—
481	#482	C₂²×C₃₁	1	4	yes	—
482	#479	C₂²×C₃₁	1	4	yes	—
483	#479	C₂²×C₃₁	1	4	yes	—
484	#476	C₂²×C₃₁	1	2	yes	—
485	#474	C₂²×C₃₁	1	2	yes	—
486	#470	C₂²×C₃₁	1	4	yes	—
487	#469	C₂²×C₃₁	1	2	yes	—
488	#468	C₂²×C₃₁	1	4	yes	—
489	#468	C₂²×C₃₁	1	2	yes	—
490	#464	C₂²×C₃₁	1	4	yes	—
491	#463	C₂²×C₃₁	1	4	yes	—
492	#462	C₂²×C₃₁	1	2	yes	—
493	#461	C₂²×C₃₁	1	2	yes	—
494	#452	C₂²×C₃₁	1	4	yes	—
495	#451	C₂²×C₃₁	1	2	yes	—
496	#449	C₂²×C₃₁	1	4	yes	—
497	#448	C₂²×C₃₁	1	2	yes	—
498	C₈×Q₈	C₂²×C₃₁	1	2	yes	—
499	C₄×Q₁₆	C₂²×C₃₁	1	4	yes	—
500	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	—
501	C₄×SD₁₆	C₂²×C₃₁	1	4	yes	—
502	C₄×D₈	C₂²×C₃₁	1	2	yes	—
503	#436	C₂²×C₃₁	1	2	yes	—
504	#436	C₂²×C₃₁	1	4	yes	—
505	#432	C₂²×C₃₁	1	1	yes	characteristic
506	#432	C₂²×C₃₁	1	2	yes	—
507	#419	C₂²×C₃₁	1	4	yes	—
508	#417	C₂²×C₃₁	1	4	yes	—
509	#417	C₂²×C₃₁	1	4	yes	—
510	C₄×M₁₆	C₂²×C₃₁	1	1	yes	characteristic
511	C₄×M₁₆	C₂²×C₃₁	1	2	yes	—
512	C₂×C₃₁	—	4	2	no	—
513	C₂×C₃₁	—	4	1	no	—
514	C₂×C₃₁	—	8	1	no	—
515	C₂×C₃₁	—	8	2	no	—
516	C₂×C₃₁	#3500	1	1	yes	characteristic
517	C₂×C₃₁	C₂×#575	1	1	yes	characteristic
518	C₂×C₃₁	#3586	1	1	yes	characteristic
519	C₂×#41	—	2	1	no	—
520	C₂×#41	—	2	1	no	—
521	C₂×#41	D₄×C₃₁	1	1	yes	characteristic
522	C₂×#41	C₂³×C₃₁	1	4	yes	—
523	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
524	C₂×Q₁₆	C₂³×C₃₁	1	4	yes	—
525	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
526	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
527	C₂×D₈	C₂³×C₃₁	1	2	yes	—
528	C₂×M₁₆	C₂³×C₃₁	1	4	yes	—
529	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
530	C₄⋊Q₈	—	2	1	no	—
531	C₄⋊Q₈	—	2	1	no	—
532	C₄⋊Q₈	—	2	1	no	—
533	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
534	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
535	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
536	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
537	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
538	#127	C₂³×C₃₁	1	1	yes	characteristic
539	#126	—	2	2	no	—
540	#126	—	2	4	no	—
541	#126	—	2	2	no	—
542	#126	—	2	2	no	—
543	#126	—	2	1	no	—
544	#125	—	2	2	no	—
545	#125	—	2	2	no	—
546	#125	—	2	1	no	—
547	#125	—	2	2	no	—
548	#125	—	2	2	no	—
549	#125	—	2	2	no	—
550	#125	C₂³×C₃₁	1	1	yes	characteristic
551	#125	C₂³×C₃₁	1	2	yes	—
552	#125	C₂³×C₃₁	1	2	yes	—
553	#125	C₂³×C₃₁	1	2	yes	—
554	#124	—	2	4	no	—
555	#124	—	2	1	no	—
556	#124	C₂³×C₃₁	1	1	yes	characteristic
557	#124	C₂³×C₃₁	1	4	yes	—
558	#123	—	2	2	no	—
559	#123	—	2	1	no	—
560	#123	—	2	2	no	—
561	#123	—	2	2	no	—
562	#123	—	2	2	no	—
563	#123	—	2	4	no	—
564	C₂²⋊Q₈	—	2	2	no	—
565	C₂²⋊Q₈	—	2	1	no	—
566	C₂²⋊Q₈	—	2	2	no	—
567	C₂²⋊Q₈	—	2	1	no	—
568	C₂²⋊Q₈	—	2	1	no	—
569	C₂²⋊Q₈	—	2	2	no	—
570	C₂²⋊Q₈	—	2	1	no	—
571	C₂²⋊Q₈	—	2	4	no	—
572	C₂²⋊Q₈	—	2	2	no	—
573	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
574	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
575	C₂²⋊Q₈	C₂³×C₃₁	1	4	yes	—
576	#121	—	2	2	no	—
577	#121	—	2	4	no	—
578	#121	—	2	2	no	—
579	#121	—	2	2	no	—
580	#121	—	2	1	no	—
581	#121	—	2	2	no	—
582	#121	C₂³×C₃₁	1	2	yes	—
583	#121	C₂³×C₃₁	1	1	yes	characteristic
584	#121	C₂³×C₃₁	1	2	yes	—
585	C₄×Q₈	—	2	1	no	—
586	C₄×Q₈	—	2	1	no	—
587	C₄×Q₈	—	2	2	no	—
588	C₄×Q₈	—	2	1	no	—
589	C₄×Q₈	D₄×C₃₁	1	1	yes	characteristic
590	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
591	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
592	C₄×Q₈	C₂³×C₃₁	1	4	yes	—
593	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
594	C₄×D₄	—	2	1	no	—
595	C₄×D₄	—	2	2	no	—
596	C₄×D₄	—	2	1	no	—
597	C₄×D₄	—	2	4	no	—
598	C₄×D₄	—	2	2	no	—
599	C₄×D₄	—	2	2	no	—
600	C₄×D₄	—	2	2	no	—
601	C₄×D₄	—	2	1	no	—
602	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
603	C₄×D₄	D₄×C₃₁	1	2	yes	—
604	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
605	C₄×D₄	C₂³×C₃₁	1	2	yes	—
606	C₄×D₄	C₂³×C₃₁	1	2	yes	—
607	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
608	C₄×D₄	C₂³×C₃₁	1	2	yes	—
609	#117	—	2	2	no	—
610	#117	—	2	2	no	—
611	#117	—	2	2	no	—
612	#117	—	2	1	no	—
613	#117	—	2	2	no	—
614	#117	D₄×C₃₁	1	1	yes	characteristic
615	#117	D₄×C₃₁	1	2	yes	—
616	#117	C₂³×C₃₁	1	2	yes	—
617	C₂×C₄⋊C₄	—	2	2	no	—
618	C₂×C₄⋊C₄	—	2	1	no	—
619	C₂×C₄⋊C₄	—	2	2	no	—
620	C₂×C₄⋊C₄	—	2	1	no	—
621	C₂×C₄⋊C₄	—	2	2	no	—
622	C₂×C₄⋊C₄	—	2	1	no	—
623	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
624	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
625	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
626	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
627	#107	C₂³×C₃₁	1	2	yes	—
628	#107	C₂³×C₃₁	1	4	yes	—
629	#106	C₂³×C₃₁	1	2	yes	—
630	#106	C₂³×C₃₁	1	4	yes	—
631	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
632	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
633	#103	C₂³×C₃₁	1	4	yes	—
634	#103	C₂³×C₃₁	1	4	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	#103	C₂³×C₃₁	1	2	yes	—
640	#102	C₂³×C₃₁	1	2	yes	—
641	#102	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	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
646	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
647	#97	C₂³×C₃₁	1	1	yes	characteristic
648	#97	C₂³×C₃₁	1	2	yes	—
649	#97	C₂³×C₃₁	1	1	yes	characteristic
650	C₄×C₈	C₂³×C₃₁	1	2	yes	—
651	C₄×C₈	C₂³×C₃₁	1	4	yes	—
652	C₃₁	#62591	1	1	yes	characteristic, direct product factor, Sylow
653	#41	—	4	2	no	—
654	#41	—	4	4	no	—
655	#41	—	4	4	no	—
656	#41	—	4	4	no	—
657	#41	—	4	4	no	—
658	C₂×Q₈	—	2	1	no	—
659	C₂×Q₈	—	2	1	no	—
660	C₂×Q₈	—	2	1	no	—
661	C₂×Q₈	—	2	2	no	—
662	C₂×Q₈	—	4	4	no	—
663	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
664	C₂×Q₈	C₂⁴×C₃₁	1	4	yes	—
665	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
666	C₂×D₄	—	2	2	no	—
667	C₂×D₄	—	2	2	no	—
668	C₂×D₄	—	2	1	no	—
669	C₂×D₄	—	2	4	no	—
670	C₂×D₄	—	2	1	no	—
671	C₂×D₄	—	2	1	no	—
672	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
673	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
674	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
675	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
676	C₂²×C₄	—	2	2	no	—
677	C₂²×C₄	—	2	2	no	—
678	C₂²×C₄	—	2	2	no	—
679	C₂²×C₄	—	2	2	no	—
680	C₂²×C₄	—	2	1	no	—
681	C₂²×C₄	—	2	2	no	—
682	C₂²×C₄	—	2	4	no	—
683	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
684	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
685	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
686	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
687	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
688	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
689	Q₁₆	—	4	4	no	—
690	SD₁₆	—	4	2	no	—
691	SD₁₆	—	4	4	no	—
692	D₈	—	4	2	no	—
693	M₁₆	—	4	2	no	—
694	M₁₆	—	4	4	no	—
695	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
696	C₂×C₈	C₂⁴×C₃₁	1	4	yes	—
697	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
698	C₄⋊C₄	—	2	2	no	—
699	C₄⋊C₄	—	2	2	no	—
700	C₄⋊C₄	—	2	1	no	—
701	C₄⋊C₄	—	2	1	no	—
702	C₄⋊C₄	—	2	2	no	—
703	C₄⋊C₄	—	2	2	no	—
704	C₄⋊C₄	—	2	2	no	—
705	C₄⋊C₄	—	2	1	no	—
706	C₄⋊C₄	—	2	4	no	—
707	C₄⋊C₄	—	2	2	no	—
708	C₄⋊C₄	—	2	2	no	—
709	C₄⋊C₄	—	2	2	no	—
710	C₄⋊C₄	—	2	2	no	—
711	C₄⋊C₄	—	2	2	no	—
712	C₄⋊C₄	—	2	2	no	—
713	C₄⋊C₄	—	2	2	no	—
714	C₄⋊C₄	—	2	1	no	—
715	C₄⋊C₄	—	2	1	no	—
716	C₄⋊C₄	—	2	2	no	—
717	C₄⋊C₄	—	2	1	no	—
718	C₄⋊C₄	—	2	4	no	—
719	C₄⋊C₄	—	2	1	no	—
720	C₄⋊C₄	—	2	2	no	—
721	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
722	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
723	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
724	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
725	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
726	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
727	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
728	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
729	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
730	C₂²⋊C₄	—	2	2	no	—
731	C₂²⋊C₄	—	2	4	no	—
732	C₂²⋊C₄	—	2	2	no	—
733	C₂²⋊C₄	—	2	1	no	—
734	C₂²⋊C₄	—	2	1	no	—
735	C₂²⋊C₄	—	2	4	no	—
736	C₂²⋊C₄	—	2	1	no	—
737	C₂²⋊C₄	—	2	1	no	—
738	C₂²⋊C₄	—	2	2	no	—
739	C₂²⋊C₄	—	2	4	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	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	1	no	—
751	C₄²	C₂×D₄×C₃₁	1	2	yes	—
752	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
753	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
754	C₄²	C₂×D₄×C₃₁	1	2	yes	—
755	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
756	C₄²	C₂⁴×C₃₁	1	2	yes	—
757	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
758	C₂³	—	2	1	no	—
759	C₂³	—	2	2	no	—
760	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
761	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
762	Q₈	—	2	2	no	—
763	Q₈	—	2	2	no	—
764	Q₈	—	2	4	no	—
765	Q₈	—	2	4	no	—
766	Q₈	—	4	2	no	—
767	Q₈	—	4	2	no	—
768	Q₈	—	8	1	no	—
769	Q₈	—	8	2	no	—
770	D₄	—	2	2	no	—
771	D₄	—	2	2	no	—
772	D₄	—	2	2	no	—
773	D₄	—	2	2	no	—
774	D₄	—	4	2	no	—
775	D₄	—	4	2	no	—
776	D₄	—	4	2	no	—
777	D₄	—	4	4	no	—
778	D₄	—	4	4	no	—
779	D₄	—	8	1	no	—
780	D₄	—	8	4	no	—
781	C₂×C₄	—	2	2	no	—
782	C₂×C₄	—	2	2	no	—
783	C₂×C₄	—	2	4	no	—
784	C₂×C₄	—	2	1	no	—
785	C₂×C₄	—	2	2	no	—
786	C₂×C₄	—	2	2	no	—
787	C₂×C₄	—	2	2	no	—
788	C₂×C₄	—	2	4	no	—
789	C₂×C₄	—	2	1	no	—
790	C₂×C₄	—	2	1	no	—
791	C₂×C₄	—	4	2	no	—
792	C₂×C₄	—	4	1	no	—
793	C₂×C₄	—	4	2	no	—
794	C₂×C₄	—	4	4	no	—
795	C₂×C₄	—	4	2	no	—
796	C₂×C₄	—	4	4	no	—
797	C₂×C₄	—	8	2	no	—
798	C₂×C₄	—	8	4	no	—
799	C₂×C₄	—	8	2	no	—
800	C₂×C₄	—	8	2	no	—
801	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
802	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
803	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
804	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
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	2	yes	—
808	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
809	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
810	C₈	—	2	2	no	—
811	C₈	—	2	2	no	—
812	C₈	—	2	4	no	—
813	C₂²	—	2	1	no	—
814	C₂²	—	2	2	no	—
815	C₂²	—	2	1	no	—
816	C₂²	—	2	2	no	—
817	C₂²	—	2	2	no	—
818	C₂²	—	2	1	no	—
819	C₂²	—	4	2	no	—
820	C₂²	—	4	1	no	—
821	C₂²	—	4	2	no	—
822	C₂²	—	4	1	no	—
823	C₂²	—	4	1	no	—
824	C₂²	—	4	2	no	—
825	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
826	C₄	—	2	2	no	—
827	C₄	—	2	1	no	—
828	C₄	—	2	1	no	—
829	C₄	—	2	2	no	—
830	C₄	—	2	1	no	—
831	C₄	—	2	2	no	—
832	C₄	—	2	1	no	—
833	C₄	—	4	4	no	—
834	C₄	—	4	1	no	—
835	C₄	—	4	1	no	—
836	C₄	—	4	2	no	—
837	C₄	—	4	2	no	—
838	C₄	—	4	1	no	—
839	C₄	—	4	2	no	—
840	C₄	C₃₁×#575	1	2	yes	—
841	C₄	C₃₁×#585	1	2	yes	—
842	C₂	—	4	1	no	—
843	C₂	—	4	2	no	—
844	C₂	—	8	2	no	—
845	C₂	—	8	1	no	—
846	C₂	C₃₁×#3500	1	1	yes	characteristic
847	C₂	C₂×C₃₁×#575	1	1	yes	characteristic
848	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 ◁ C₄×#41×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3515	C₂	semidirect
2. C₃₁×#3511	C₂	semidirect
3. C₃₁×#3364	C₂	semidirect
4. C₃₁×#3360	C₂	semidirect
5. C₃₁×#3331	C₂	semidirect
6. C₃₁×#3330	C₂	semidirect
7. C₃₁×#3327	C₂	semidirect
8. C₃₁×#3326	C₂	semidirect
9. C₃₁×#3236	C₂	semidirect
10. C₃₁×#3235	C₂	semidirect
11. C₃₁×#3219	C₂	semidirect
12. C₃₁×#3218	C₂	semidirect
13. C₃₁×#3172	C₂	semidirect
14. C₃₁×#3171	C₂	semidirect
15. C₃₁×#3142	C₂	semidirect
16. C₃₁×#3139	C₂	semidirect
17. C₃₁×#2971	C₂	semidirect
333. #62591	C₃₁	direct (N × H)
389. #3515	C₂×C₃₁	semidirect
390. #3511	C₂×C₃₁	semidirect
391. #3364	C₂×C₃₁	semidirect
392. #3360	C₂×C₃₁	semidirect
393. #3331	C₂×C₃₁	semidirect
394. #3330	C₂×C₃₁	semidirect
395. #3327	C₂×C₃₁	semidirect
396. #3326	C₂×C₃₁	semidirect
397. #3236	C₂×C₃₁	semidirect
398. #3235	C₂×C₃₁	semidirect
399. #3219	C₂×C₃₁	semidirect
400. #3218	C₂×C₃₁	semidirect
401. #3172	C₂×C₃₁	semidirect
402. #3171	C₂×C₃₁	semidirect
403. #3142	C₂×C₃₁	semidirect
404. #3139	C₂×C₃₁	semidirect
405. #2971	C₂×C₃₁	semidirect
652. C₃₁	#62591	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×#3515	2
C₃₁×#3511	2
C₃₁×#3364	2
C₃₁×#3360	2
C₃₁×#3331	2
C₃₁×#3330	2
C₃₁×#3327	2
C₃₁×#3326	2
C₃₁×#3236	2
C₃₁×#3235	2
C₃₁×#3219	2
C₃₁×#3218	2
C₃₁×#3172	2
C₃₁×#3171	2
C₃₁×#3142	2
C₃₁×#3139	2
C₃₁×#2971	2
#62591	31

Subgroups — C31×#62591 #21519350

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#62591 #21519350