Subgroups — C₃₁×#60721 #21517480

Order 7936.

1898 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×#3512	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3511	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3181	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3180	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3179	C₂	1	4	yes	maximal, complemented
6	C₃₁×#3178	C₂	1	4	yes	maximal, complemented
7	C₃₁×#3172	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3171	C₂	1	2	yes	maximal, complemented
9	C₂×C₃₁×#501	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#3150	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#3142	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3141	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3061	C₂	1	2	yes	maximal, complemented
14	C₃₁×#3060	C₂	1	2	yes	maximal, complemented
15	C₃₁×#2952	C₂	1	2	yes	maximal, complemented
16	C₃₁×#2951	C₂	1	2	yes	maximal, complemented
17	C₃₁×#2875	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₃₁×#135	C₂²	1	2	yes	—
19	C₂×C₃₁×#135	C₂²	1	2	yes	—
20	C₂×C₃₁×#131	C₂²	1	2	yes	—
21	C₃₁×#556	—	2	1	no	—
22	C₃₁×#555	—	2	1	no	—
23	C₃₁×#554	—	2	1	no	—
24	C₃₁×#553	—	2	2	no	—
25	C₃₁×#553	—	2	2	no	—
26	C₃₁×#553	—	2	2	no	—
27	C₃₁×#553	—	2	1	no	—
28	C₃₁×#553	—	2	1	no	—
29	C₃₁×#552	—	2	1	no	—
30	C₃₁×#552	—	2	1	no	—
31	C₃₁×#548	—	2	2	no	—
32	C₃₁×#547	—	2	1	no	—
33	C₃₁×#542	C₂²	1	4	yes	—
34	C₃₁×#541	C₂²	1	2	yes	—
35	C₃₁×#540	C₂²	1	2	yes	—
36	C₃₁×#537	C₂²	1	2	yes	—
37	C₃₁×#537	C₂²	1	1	yes	characteristic
38	C₃₁×#537	C₂²	1	1	yes	characteristic
39	C₃₁×#533	C₂²	1	2	yes	—
40	C₃₁×#532	C₂²	1	1	yes	characteristic
41	C₃₁×#532	C₂²	1	1	yes	characteristic
42	C₃₁×#532	C₂²	1	2	yes	—
43	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
44	C₃₁×#529	C₂²	1	2	yes	—
45	C₃₁×#529	C₂²	1	2	yes	—
46	C₂×C₃₁×#125	C₂²	1	1	yes	characteristic
47	C₃₁×#520	C₂²	1	1	yes	characteristic
48	C₃₁×#520	C₂²	1	2	yes	—
49	C₃₁×#520	C₂²	1	1	yes	characteristic
50	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
51	C₃₁×#501	C₂²	1	2	yes	—
52	C₃₁×#501	C₂²	1	4	yes	—
53	C₃₁×#501	C₂²	1	2	yes	—
54	C₃₁×#497	C₂²	1	1	yes	characteristic
55	C₃₁×#497	C₂²	1	2	yes	—
56	C₃₁×#497	C₂²	1	1	yes	characteristic
57	C₃₁×#496	C₂²	1	1	yes	characteristic
58	C₃₁×#496	C₂²	1	2	yes	—
59	C₃₁×#496	C₂²	1	1	yes	characteristic
60	C₃₁×#491	C₂²	1	2	yes	—
61	C₃₁×#490	C₂²	1	2	yes	—
62	C₃₁×#489	C₂²	1	2	yes	—
63	C₃₁×#489	C₂²	1	2	yes	—
64	C₃₁×#488	C₂²	1	4	yes	—
65	C₃₁×#487	C₂²	1	2	yes	—
66	C₃₁×#486	C₂²	1	2	yes	—
67	C₃₁×#470	C₂²	1	4	yes	—
68	C₃₁×#469	C₂²	1	4	yes	—
69	C₃₁×#468	C₂²	1	4	yes	—
70	C₃₁×#468	C₂²	1	4	yes	—
71	C₃₁×#467	C₂²	1	4	yes	—
72	C₃₁×#466	C₂²	1	4	yes	—
73	C₃₁×#465	C₂²	1	4	yes	—
74	C₃₁×#465	C₂²	1	4	yes	—
75	C₃₁×#442	C₂²	1	4	yes	—
76	C₃₁×#441	C₂²	1	4	yes	—
77	C₃₁×#440	C₂²	1	4	yes	—
78	C₃₁×#440	C₂²	1	4	yes	—
79	C₄×Q₁₆×C₃₁	C₂²	1	4	yes	—
80	C₄×SD₁₆×C₃₁	C₂²	1	4	yes	—
81	C₄×SD₁₆×C₃₁	C₂²	1	4	yes	—
82	C₄×D₈×C₃₁	C₂²	1	4	yes	—
83	C₂×C₃₁×#107	C₂²	1	2	yes	—
84	C₂×C₃₁×#106	C₂²	1	2	yes	—
85	C₃₁×#417	C₂²	1	2	yes	—
86	C₃₁×#417	C₂²	1	2	yes	—
87	C₃₁×#417	C₂²	1	2	yes	—
88	C₃₁×#417	C₂²	1	2	yes	—
89	C₃₁×#405	C₂²	1	4	yes	—
90	C₃₁×#405	C₂²	1	2	yes	—
91	C₄×M₁₆×C₃₁	C₂²	1	1	yes	characteristic
92	C₄×M₁₆×C₃₁	C₂²	1	2	yes	—
93	C₂×C₃₁×#97	C₂²	1	1	yes	characteristic
94	C₂×C₃₁×#97	C₂²	1	2	yes	—
95	C₂×#41×C₃₁	—	2	2	no	—
96	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
97	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
98	C₂×#41×C₃₁	C₂³	1	2	yes	—
99	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
100	C₂²×Q₈×C₃₁	—	2	1	no	—
101	C₃₁×#135	—	2	8	no	—
102	C₃₁×#135	—	2	8	no	—
103	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
104	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
105	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
106	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
107	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
108	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
109	C₂×D₈×C₃₁	C₂³	1	2	yes	—
110	C₂×D₈×C₃₁	C₂³	1	2	yes	—
111	C₃₁×#131	—	2	8	no	—
112	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
113	C₂×M₁₆×C₃₁	C₂³	1	4	yes	—
114	C₂²×C₈×C₃₁	C₂³	1	4	yes	—
115	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
116	C₃₁×C₄⋊Q₈	—	2	1	no	—
117	C₃₁×C₄⋊Q₈	—	2	1	no	—
118	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
119	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
120	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
121	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
122	C₃₁×#127	C₂³	1	1	yes	characteristic
123	C₃₁×#127	C₂³	1	1	yes	characteristic
124	C₃₁×#126	—	2	4	no	—
125	C₃₁×#126	—	2	2	no	—
126	C₃₁×#126	—	2	2	no	—
127	C₃₁×#126	—	2	2	no	—
128	C₃₁×#126	—	2	2	no	—
129	C₃₁×#125	—	2	2	no	—
130	C₃₁×#125	—	2	2	no	—
131	C₃₁×#125	—	2	1	no	—
132	C₃₁×#125	—	2	1	no	—
133	C₃₁×#125	—	2	2	no	—
134	C₃₁×#125	C₂³	1	2	yes	—
135	C₃₁×#125	C₂³	1	2	yes	—
136	C₃₁×#124	—	2	4	no	—
137	C₃₁×#124	—	2	2	no	—
138	C₃₁×#124	C₂³	1	2	yes	—
139	C₃₁×#124	C₂³	1	1	yes	characteristic
140	C₃₁×#124	C₂³	1	1	yes	characteristic
141	C₃₁×#123	—	2	2	no	—
142	C₃₁×#123	—	2	2	no	—
143	C₃₁×#123	—	2	2	no	—
144	C₃₁×#123	—	2	2	no	—
145	C₃₁×#123	—	2	4	no	—
146	C₃₁×C₂²⋊Q₈	—	2	1	no	—
147	C₃₁×C₂²⋊Q₈	—	2	1	no	—
148	C₃₁×C₂²⋊Q₈	—	2	2	no	—
149	C₃₁×C₂²⋊Q₈	—	2	2	no	—
150	C₃₁×C₂²⋊Q₈	—	2	4	no	—
151	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
152	C₃₁×C₂²⋊Q₈	C₂³	1	4	yes	—
153	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
154	C₃₁×#121	—	2	2	no	—
155	C₃₁×#121	—	2	4	no	—
156	C₃₁×#121	—	2	1	no	—
157	C₃₁×#121	—	2	1	no	—
158	C₃₁×#121	—	2	2	no	—
159	C₃₁×#121	—	2	2	no	—
160	C₃₁×#121	—	2	1	no	—
161	C₃₁×#121	—	2	1	no	—
162	C₃₁×#121	—	2	1	no	—
163	C₃₁×#121	—	2	1	no	—
164	C₃₁×#121	—	2	2	no	—
165	C₃₁×#121	—	2	2	no	—
166	C₃₁×#121	—	2	2	no	—
167	C₃₁×#121	C₂³	1	2	yes	—
168	C₃₁×#121	C₂³	1	4	yes	—
169	C₃₁×#121	C₂³	1	2	yes	—
170	C₄×Q₈×C₃₁	—	2	2	no	—
171	C₄×Q₈×C₃₁	D₄	1	1	yes	characteristic
172	C₄×Q₈×C₃₁	D₄	1	1	yes	characteristic
173	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
174	C₄×Q₈×C₃₁	C₂³	1	4	yes	—
175	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
176	C₄×D₄×C₃₁	—	2	2	no	—
177	C₄×D₄×C₃₁	—	2	2	no	—
178	C₄×D₄×C₃₁	—	2	4	no	—
179	C₄×D₄×C₃₁	—	2	2	no	—
180	C₄×D₄×C₃₁	—	2	2	no	—
181	C₄×D₄×C₃₁	—	2	1	no	—
182	C₄×D₄×C₃₁	—	2	1	no	—
183	C₄×D₄×C₃₁	—	2	1	no	—
184	C₄×D₄×C₃₁	—	2	2	no	—
185	C₄×D₄×C₃₁	—	2	1	no	—
186	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
187	C₄×D₄×C₃₁	D₄	1	2	yes	—
188	C₄×D₄×C₃₁	D₄	1	2	yes	—
189	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
190	C₄×D₄×C₃₁	C₂³	1	2	yes	—
191	C₄×D₄×C₃₁	C₂³	1	4	yes	—
192	C₄×D₄×C₃₁	C₂³	1	2	yes	—
193	C₃₁×#117	—	2	2	no	—
194	C₃₁×#117	—	2	1	no	—
195	C₃₁×#117	—	2	1	no	—
196	C₃₁×#117	—	2	2	no	—
197	C₃₁×#117	—	2	2	no	—
198	C₃₁×#117	—	2	2	no	—
199	C₃₁×#117	C₂³	1	1	yes	characteristic
200	C₃₁×#117	C₂³	1	2	yes	—
201	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
202	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
203	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
204	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
205	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
206	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
207	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
208	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
209	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
210	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
211	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
212	C₃₁×#107	C₂³	1	4	yes	—
213	C₃₁×#107	C₂³	1	4	yes	—
214	C₃₁×#106	C₂³	1	4	yes	—
215	C₃₁×#106	C₂³	1	4	yes	—
216	C₃₁×#103	C₂³	1	4	yes	—
217	C₃₁×#103	C₂³	1	4	yes	—
218	C₃₁×#103	C₂³	1	4	yes	—
219	C₃₁×#103	C₂³	1	4	yes	—
220	C₃₁×#102	C₂³	1	4	yes	—
221	C₃₁×#102	C₂³	1	4	yes	—
222	C₃₁×#102	C₂³	1	4	yes	—
223	C₃₁×#102	C₂³	1	4	yes	—
224	C₃₁×#97	C₂³	1	1	yes	characteristic
225	C₃₁×#97	C₂³	1	2	yes	—
226	C₃₁×#97	C₂³	1	1	yes	characteristic
227	C₃₁×#97	C₂³	1	4	yes	—
228	C₃₁×#97	C₂³	1	2	yes	—
229	C₄×C₈×C₃₁	C₂³	1	4	yes	—
230	C₄×C₈×C₃₁	C₂³	1	2	yes	—
231	#41×C₃₁	—	2	4	no	—
232	#41×C₃₁	—	2	4	no	—
233	#41×C₃₁	—	2	4	no	—
234	#41×C₃₁	—	2	4	no	—
235	#41×C₃₁	—	2	4	no	—
236	#41×C₃₁	—	8	4	no	—
237	C₂×Q₈×C₃₁	—	2	2	no	—
238	C₂×Q₈×C₃₁	—	2	2	no	—
239	C₂×Q₈×C₃₁	—	8	2	no	—
240	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
241	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
242	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
243	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
244	C₂×D₄×C₃₁	—	2	2	no	—
245	C₂×D₄×C₃₁	—	2	1	no	—
246	C₂×D₄×C₃₁	—	2	1	no	—
247	C₂×D₄×C₃₁	—	2	2	no	—
248	C₂×D₄×C₃₁	—	2	2	no	—
249	C₂×D₄×C₃₁	—	2	4	no	—
250	C₂×D₄×C₃₁	—	2	1	no	—
251	C₂×D₄×C₃₁	—	2	1	no	—
252	C₂×D₄×C₃₁	—	2	1	no	—
253	C₂×D₄×C₃₁	—	2	1	no	—
254	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
255	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
256	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
257	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
258	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
259	C₂²×C₄×C₃₁	—	2	1	no	—
260	C₂²×C₄×C₃₁	—	2	1	no	—
261	C₂²×C₄×C₃₁	—	2	2	no	—
262	C₂²×C₄×C₃₁	—	2	2	no	—
263	C₂²×C₄×C₃₁	—	2	1	no	—
264	C₂²×C₄×C₃₁	—	2	1	no	—
265	C₂²×C₄×C₃₁	—	2	2	no	—
266	C₂²×C₄×C₃₁	—	2	2	no	—
267	C₂²×C₄×C₃₁	—	2	4	no	—
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	2	yes	—
271	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
272	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
273	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
274	Q₁₆×C₃₁	—	2	4	no	—
275	Q₁₆×C₃₁	—	2	4	no	—
276	SD₁₆×C₃₁	—	2	4	no	—
277	SD₁₆×C₃₁	—	2	4	no	—
278	SD₁₆×C₃₁	—	2	4	no	—
279	SD₁₆×C₃₁	—	2	4	no	—
280	D₈×C₃₁	—	2	4	no	—
281	D₈×C₃₁	—	2	4	no	—
282	M₁₆×C₃₁	—	2	4	no	—
283	M₁₆×C₃₁	—	2	8	no	—
284	C₂×C₈×C₃₁	—	2	8	no	—
285	C₂×C₈×C₃₁	#41	1	8	yes	complemented
286	C₂×C₈×C₃₁	C₂⁴	1	4	yes	—
287	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
288	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
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	2	no	—
293	C₄⋊C₄×C₃₁	—	2	2	no	—
294	C₄⋊C₄×C₃₁	—	2	2	no	—
295	C₄⋊C₄×C₃₁	—	2	4	no	—
296	C₄⋊C₄×C₃₁	—	2	2	no	—
297	C₄⋊C₄×C₃₁	—	2	2	no	—
298	C₄⋊C₄×C₃₁	—	2	2	no	—
299	C₄⋊C₄×C₃₁	—	2	2	no	—
300	C₄⋊C₄×C₃₁	—	2	2	no	—
301	C₄⋊C₄×C₃₁	—	2	1	no	—
302	C₄⋊C₄×C₃₁	—	2	2	no	—
303	C₄⋊C₄×C₃₁	—	2	2	no	—
304	C₄⋊C₄×C₃₁	—	2	1	no	—
305	C₄⋊C₄×C₃₁	—	2	1	no	—
306	C₄⋊C₄×C₃₁	—	2	1	no	—
307	C₄⋊C₄×C₃₁	—	2	4	no	—
308	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
309	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
310	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
311	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
312	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
313	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
314	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
315	C₂²⋊C₄×C₃₁	—	2	4	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	—	2	1	no	—
320	C₂²⋊C₄×C₃₁	—	2	2	no	—
321	C₂²⋊C₄×C₃₁	—	2	2	no	—
322	C₂²⋊C₄×C₃₁	—	2	4	no	—
323	C₂²⋊C₄×C₃₁	—	2	2	no	—
324	C₂²⋊C₄×C₃₁	—	2	2	no	—
325	C₂²⋊C₄×C₃₁	—	2	1	no	—
326	C₂²⋊C₄×C₃₁	—	2	1	no	—
327	C₂²⋊C₄×C₃₁	—	2	4	no	—
328	C₂²⋊C₄×C₃₁	—	2	2	no	—
329	C₂²⋊C₄×C₃₁	—	2	2	no	—
330	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
331	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
332	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
333	C₄²×C₃₁	—	2	2	no	—
334	C₄²×C₃₁	—	2	2	no	—
335	C₄²×C₃₁	—	2	4	no	—
336	C₄²×C₃₁	C₂×D₄	1	2	yes	—
337	C₄²×C₃₁	C₂×D₄	1	2	yes	—
338	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
339	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
340	C₄²×C₃₁	C₂⁴	1	2	yes	—
341	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
342	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
343	#60721	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
344	C₂³×C₃₁	—	2	2	no	—
345	C₂³×C₃₁	—	2	1	no	—
346	C₂³×C₃₁	—	2	1	no	—
347	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
348	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
349	Q₈×C₃₁	—	2	2	no	—
350	Q₈×C₃₁	—	2	2	no	—
351	Q₈×C₃₁	—	2	2	no	—
352	Q₈×C₃₁	—	2	2	no	—
353	Q₈×C₃₁	—	2	2	no	—
354	Q₈×C₃₁	—	4	4	no	—
355	Q₈×C₃₁	—	8	2	no	—
356	D₄×C₃₁	—	2	4	no	—
357	D₄×C₃₁	—	2	2	no	—
358	D₄×C₃₁	—	2	2	no	—
359	D₄×C₃₁	—	2	2	no	—
360	D₄×C₃₁	—	2	2	no	—
361	D₄×C₃₁	—	2	2	no	—
362	D₄×C₃₁	—	4	2	no	—
363	D₄×C₃₁	—	4	2	no	—
364	D₄×C₃₁	—	4	4	no	—
365	D₄×C₃₁	—	4	2	no	—
366	D₄×C₃₁	—	4	2	no	—
367	D₄×C₃₁	—	8	1	no	—
368	D₄×C₃₁	—	8	1	no	—
369	D₄×C₃₁	—	8	2	no	—
370	D₄×C₃₁	—	8	2	no	—
371	D₄×C₃₁	—	8	4	no	—
372	C₂×C₄×C₃₁	—	2	4	no	—
373	C₂×C₄×C₃₁	—	2	1	no	—
374	C₂×C₄×C₃₁	—	2	1	no	—
375	C₂×C₄×C₃₁	—	2	2	no	—
376	C₂×C₄×C₃₁	—	2	2	no	—
377	C₂×C₄×C₃₁	—	2	2	no	—
378	C₂×C₄×C₃₁	—	2	4	no	—
379	C₂×C₄×C₃₁	—	4	2	no	—
380	C₂×C₄×C₃₁	—	4	1	no	—
381	C₂×C₄×C₃₁	—	4	1	no	—
382	C₂×C₄×C₃₁	—	4	2	no	—
383	C₂×C₄×C₃₁	—	4	4	no	—
384	C₂×C₄×C₃₁	—	4	2	no	—
385	C₂×C₄×C₃₁	—	4	2	no	—
386	C₂×C₄×C₃₁	—	8	2	no	—
387	C₂×C₄×C₃₁	—	8	2	no	—
388	C₂×C₄×C₃₁	—	8	4	no	—
389	C₂×C₄×C₃₁	—	8	1	no	—
390	C₂×C₄×C₃₁	—	8	1	no	—
391	C₂×C₄×C₃₁	—	8	2	no	—
392	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
393	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
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	2	yes	—
397	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
398	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
399	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
400	C₂×C₄×C₃₁	C₂×#41	1	4	yes	—
401	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
402	C₈×C₃₁	—	2	4	no	—
403	C₈×C₃₁	C₂×#41	1	4	yes	—
404	C₈×C₃₁	C₂×#41	1	4	yes	—
405	#3512	C₂×C₃₁	1	1	yes	characteristic, complemented
406	#3511	C₂×C₃₁	1	1	yes	characteristic, complemented
407	#3181	C₂×C₃₁	1	2	yes	complemented
408	#3180	C₂×C₃₁	1	2	yes	complemented
409	#3179	C₂×C₃₁	1	4	yes	complemented
410	#3178	C₂×C₃₁	1	4	yes	complemented
411	#3172	C₂×C₃₁	1	2	yes	complemented
412	#3171	C₂×C₃₁	1	2	yes	complemented
413	C₂×#501	C₂×C₃₁	1	1	yes	characteristic, complemented
414	#3150	C₂×C₃₁	1	1	yes	characteristic, complemented
415	#3142	C₂×C₃₁	1	1	yes	characteristic, complemented
416	#3141	C₂×C₃₁	1	1	yes	characteristic, complemented
417	#3061	C₂×C₃₁	1	2	yes	complemented
418	#3060	C₂×C₃₁	1	2	yes	complemented
419	#2952	C₂×C₃₁	1	2	yes	complemented
420	#2951	C₂×C₃₁	1	2	yes	complemented
421	#2875	C₂×C₃₁	1	1	yes	characteristic, complemented
422	C₂²×C₃₁	—	2	1	no	—
423	C₂²×C₃₁	—	2	1	no	—
424	C₂²×C₃₁	—	2	2	no	—
425	C₂²×C₃₁	—	2	2	no	—
426	C₂²×C₃₁	—	2	2	no	—
427	C₂²×C₃₁	—	4	2	no	—
428	C₂²×C₃₁	—	4	1	no	—
429	C₂²×C₃₁	—	4	1	no	—
430	C₂²×C₃₁	—	4	1	no	—
431	C₂²×C₃₁	—	4	2	no	—
432	C₂²×C₃₁	—	4	1	no	—
433	C₂²×C₃₁	—	4	2	no	—
434	C₂²×C₃₁	—	4	1	no	—
435	C₂²×C₃₁	—	4	1	no	—
436	C₂²×C₃₁	#532	1	2	yes	—
437	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
438	C₄×C₃₁	—	2	1	no	—
439	C₄×C₃₁	—	2	2	no	—
440	C₄×C₃₁	—	2	1	no	—
441	C₄×C₃₁	—	2	1	no	—
442	C₄×C₃₁	—	2	2	no	—
443	C₄×C₃₁	—	2	1	no	—
444	C₄×C₃₁	—	2	2	no	—
445	C₄×C₃₁	—	4	2	no	—
446	C₄×C₃₁	—	4	4	no	—
447	C₄×C₃₁	—	4	2	no	—
448	C₄×C₃₁	—	4	1	no	—
449	C₄×C₃₁	—	4	1	no	—
450	C₄×C₃₁	—	4	2	no	—
451	C₄×C₃₁	#532	1	2	yes	—
452	C₄×C₃₁	C₂²×#41	1	2	yes	—
453	C₂×#135	C₂²×C₃₁	1	2	yes	—
454	C₂×#135	C₂²×C₃₁	1	2	yes	—
455	C₂×#131	C₂²×C₃₁	1	2	yes	—
456	#556	—	2	1	no	—
457	#555	—	2	1	no	—
458	#554	—	2	1	no	—
459	#553	—	2	2	no	—
460	#553	—	2	2	no	—
461	#553	—	2	2	no	—
462	#553	—	2	1	no	—
463	#553	—	2	1	no	—
464	#552	—	2	1	no	—
465	#552	—	2	1	no	—
466	#548	—	2	2	no	—
467	#547	—	2	1	no	—
468	#542	C₂²×C₃₁	1	4	yes	—
469	#541	C₂²×C₃₁	1	2	yes	—
470	#540	C₂²×C₃₁	1	2	yes	—
471	#537	C₂²×C₃₁	1	2	yes	—
472	#537	C₂²×C₃₁	1	1	yes	characteristic
473	#537	C₂²×C₃₁	1	1	yes	characteristic
474	#533	C₂²×C₃₁	1	2	yes	—
475	#532	C₂²×C₃₁	1	1	yes	characteristic
476	#532	C₂²×C₃₁	1	1	yes	characteristic
477	#532	C₂²×C₃₁	1	2	yes	—
478	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
479	#529	C₂²×C₃₁	1	2	yes	—
480	#529	C₂²×C₃₁	1	2	yes	—
481	C₂×#125	C₂²×C₃₁	1	1	yes	characteristic
482	#520	C₂²×C₃₁	1	1	yes	characteristic
483	#520	C₂²×C₃₁	1	2	yes	—
484	#520	C₂²×C₃₁	1	1	yes	characteristic
485	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
486	#501	C₂²×C₃₁	1	2	yes	—
487	#501	C₂²×C₃₁	1	4	yes	—
488	#501	C₂²×C₃₁	1	2	yes	—
489	#497	C₂²×C₃₁	1	1	yes	characteristic
490	#497	C₂²×C₃₁	1	2	yes	—
491	#497	C₂²×C₃₁	1	1	yes	characteristic
492	#496	C₂²×C₃₁	1	1	yes	characteristic
493	#496	C₂²×C₃₁	1	2	yes	—
494	#496	C₂²×C₃₁	1	1	yes	characteristic
495	#491	C₂²×C₃₁	1	2	yes	—
496	#490	C₂²×C₃₁	1	2	yes	—
497	#489	C₂²×C₃₁	1	2	yes	—
498	#489	C₂²×C₃₁	1	2	yes	—
499	#488	C₂²×C₃₁	1	4	yes	—
500	#487	C₂²×C₃₁	1	2	yes	—
501	#486	C₂²×C₃₁	1	2	yes	—
502	#470	C₂²×C₃₁	1	4	yes	—
503	#469	C₂²×C₃₁	1	4	yes	—
504	#468	C₂²×C₃₁	1	4	yes	—
505	#468	C₂²×C₃₁	1	4	yes	—
506	#467	C₂²×C₃₁	1	4	yes	—
507	#466	C₂²×C₃₁	1	4	yes	—
508	#465	C₂²×C₃₁	1	4	yes	—
509	#465	C₂²×C₃₁	1	4	yes	—
510	#442	C₂²×C₃₁	1	4	yes	—
511	#441	C₂²×C₃₁	1	4	yes	—
512	#440	C₂²×C₃₁	1	4	yes	—
513	#440	C₂²×C₃₁	1	4	yes	—
514	C₄×Q₁₆	C₂²×C₃₁	1	4	yes	—
515	C₄×SD₁₆	C₂²×C₃₁	1	4	yes	—
516	C₄×SD₁₆	C₂²×C₃₁	1	4	yes	—
517	C₄×D₈	C₂²×C₃₁	1	4	yes	—
518	C₂×#107	C₂²×C₃₁	1	2	yes	—
519	C₂×#106	C₂²×C₃₁	1	2	yes	—
520	#417	C₂²×C₃₁	1	2	yes	—
521	#417	C₂²×C₃₁	1	2	yes	—
522	#417	C₂²×C₃₁	1	2	yes	—
523	#417	C₂²×C₃₁	1	2	yes	—
524	#405	C₂²×C₃₁	1	4	yes	—
525	#405	C₂²×C₃₁	1	2	yes	—
526	C₄×M₁₆	C₂²×C₃₁	1	1	yes	characteristic
527	C₄×M₁₆	C₂²×C₃₁	1	2	yes	—
528	C₂×#97	C₂²×C₃₁	1	1	yes	characteristic
529	C₂×#97	C₂²×C₃₁	1	2	yes	—
530	C₂×C₃₁	—	2	2	no	—
531	C₂×C₃₁	—	4	2	no	—
532	C₂×C₃₁	—	8	2	no	—
533	C₂×C₃₁	—	8	1	no	—
534	C₂×C₃₁	—	8	1	no	—
535	C₂×C₃₁	C₂×#532	1	1	yes	characteristic
536	C₂×C₃₁	#3585	1	1	yes	characteristic
537	C₂×C₃₁	#3586	1	1	yes	characteristic
538	C₂×#41	—	2	2	no	—
539	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
540	C₂×#41	C₂³×C₃₁	1	2	yes	—
541	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
542	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
543	C₂²×Q₈	—	2	1	no	—
544	#135	—	2	8	no	—
545	#135	—	2	8	no	—
546	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
547	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
548	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
549	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
550	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
551	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
552	C₂×D₈	C₂³×C₃₁	1	2	yes	—
553	C₂×D₈	C₂³×C₃₁	1	2	yes	—
554	#131	—	2	8	no	—
555	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
556	C₂×M₁₆	C₂³×C₃₁	1	4	yes	—
557	C₂²×C₈	C₂³×C₃₁	1	4	yes	—
558	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
559	C₄⋊Q₈	—	2	1	no	—
560	C₄⋊Q₈	—	2	1	no	—
561	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
562	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
563	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
564	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
565	#127	C₂³×C₃₁	1	1	yes	characteristic
566	#127	C₂³×C₃₁	1	1	yes	characteristic
567	#126	—	2	4	no	—
568	#126	—	2	2	no	—
569	#126	—	2	2	no	—
570	#126	—	2	2	no	—
571	#126	—	2	2	no	—
572	#125	—	2	2	no	—
573	#125	—	2	2	no	—
574	#125	—	2	1	no	—
575	#125	—	2	1	no	—
576	#125	—	2	2	no	—
577	#125	C₂³×C₃₁	1	2	yes	—
578	#125	C₂³×C₃₁	1	2	yes	—
579	#124	—	2	4	no	—
580	#124	—	2	2	no	—
581	#124	C₂³×C₃₁	1	1	yes	characteristic
582	#124	C₂³×C₃₁	1	1	yes	characteristic
583	#124	C₂³×C₃₁	1	2	yes	—
584	#123	—	2	2	no	—
585	#123	—	2	2	no	—
586	#123	—	2	2	no	—
587	#123	—	2	2	no	—
588	#123	—	2	4	no	—
589	C₂²⋊Q₈	—	2	1	no	—
590	C₂²⋊Q₈	—	2	1	no	—
591	C₂²⋊Q₈	—	2	2	no	—
592	C₂²⋊Q₈	—	2	2	no	—
593	C₂²⋊Q₈	—	2	4	no	—
594	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
595	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
596	C₂²⋊Q₈	C₂³×C₃₁	1	4	yes	—
597	#121	—	2	2	no	—
598	#121	—	2	4	no	—
599	#121	—	2	1	no	—
600	#121	—	2	1	no	—
601	#121	—	2	2	no	—
602	#121	—	2	2	no	—
603	#121	—	2	1	no	—
604	#121	—	2	1	no	—
605	#121	—	2	1	no	—
606	#121	—	2	1	no	—
607	#121	—	2	2	no	—
608	#121	—	2	2	no	—
609	#121	—	2	2	no	—
610	#121	C₂³×C₃₁	1	2	yes	—
611	#121	C₂³×C₃₁	1	2	yes	—
612	#121	C₂³×C₃₁	1	4	yes	—
613	C₄×Q₈	—	2	2	no	—
614	C₄×Q₈	D₄×C₃₁	1	1	yes	characteristic
615	C₄×Q₈	D₄×C₃₁	1	1	yes	characteristic
616	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
617	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
618	C₄×Q₈	C₂³×C₃₁	1	4	yes	—
619	C₄×D₄	—	2	2	no	—
620	C₄×D₄	—	2	2	no	—
621	C₄×D₄	—	2	4	no	—
622	C₄×D₄	—	2	2	no	—
623	C₄×D₄	—	2	2	no	—
624	C₄×D₄	—	2	1	no	—
625	C₄×D₄	—	2	1	no	—
626	C₄×D₄	—	2	1	no	—
627	C₄×D₄	—	2	2	no	—
628	C₄×D₄	—	2	1	no	—
629	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
630	C₄×D₄	D₄×C₃₁	1	2	yes	—
631	C₄×D₄	D₄×C₃₁	1	2	yes	—
632	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
633	C₄×D₄	C₂³×C₃₁	1	2	yes	—
634	C₄×D₄	C₂³×C₃₁	1	2	yes	—
635	C₄×D₄	C₂³×C₃₁	1	4	yes	—
636	#117	—	2	2	no	—
637	#117	—	2	1	no	—
638	#117	—	2	1	no	—
639	#117	—	2	2	no	—
640	#117	—	2	2	no	—
641	#117	—	2	2	no	—
642	#117	C₂³×C₃₁	1	1	yes	characteristic
643	#117	C₂³×C₃₁	1	2	yes	—
644	C₂×C₄⋊C₄	—	2	1	no	—
645	C₂×C₄⋊C₄	—	2	1	no	—
646	C₂×C₄⋊C₄	—	2	1	no	—
647	C₂×C₄⋊C₄	—	2	2	no	—
648	C₂×C₄⋊C₄	—	2	1	no	—
649	C₂×C₄⋊C₄	—	2	1	no	—
650	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
651	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
652	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
653	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
654	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
655	#107	C₂³×C₃₁	1	4	yes	—
656	#107	C₂³×C₃₁	1	4	yes	—
657	#106	C₂³×C₃₁	1	4	yes	—
658	#106	C₂³×C₃₁	1	4	yes	—
659	#103	C₂³×C₃₁	1	4	yes	—
660	#103	C₂³×C₃₁	1	4	yes	—
661	#103	C₂³×C₃₁	1	4	yes	—
662	#103	C₂³×C₃₁	1	4	yes	—
663	#102	C₂³×C₃₁	1	4	yes	—
664	#102	C₂³×C₃₁	1	4	yes	—
665	#102	C₂³×C₃₁	1	4	yes	—
666	#102	C₂³×C₃₁	1	4	yes	—
667	#97	C₂³×C₃₁	1	1	yes	characteristic
668	#97	C₂³×C₃₁	1	2	yes	—
669	#97	C₂³×C₃₁	1	1	yes	characteristic
670	#97	C₂³×C₃₁	1	4	yes	—
671	#97	C₂³×C₃₁	1	2	yes	—
672	C₄×C₈	C₂³×C₃₁	1	4	yes	—
673	C₄×C₈	C₂³×C₃₁	1	2	yes	—
674	C₃₁	#60721	1	1	yes	characteristic, direct product factor, Sylow
675	#41	—	2	4	no	—
676	#41	—	2	4	no	—
677	#41	—	2	4	no	—
678	#41	—	2	4	no	—
679	#41	—	2	4	no	—
680	#41	—	8	4	no	—
681	C₂×Q₈	—	2	2	no	—
682	C₂×Q₈	—	2	2	no	—
683	C₂×Q₈	—	8	2	no	—
684	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
685	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
686	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
687	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
688	C₂×D₄	—	2	2	no	—
689	C₂×D₄	—	2	1	no	—
690	C₂×D₄	—	2	1	no	—
691	C₂×D₄	—	2	2	no	—
692	C₂×D₄	—	2	2	no	—
693	C₂×D₄	—	2	4	no	—
694	C₂×D₄	—	2	1	no	—
695	C₂×D₄	—	2	1	no	—
696	C₂×D₄	—	2	1	no	—
697	C₂×D₄	—	2	1	no	—
698	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
699	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
700	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
701	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
702	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
703	C₂²×C₄	—	2	1	no	—
704	C₂²×C₄	—	2	1	no	—
705	C₂²×C₄	—	2	2	no	—
706	C₂²×C₄	—	2	2	no	—
707	C₂²×C₄	—	2	1	no	—
708	C₂²×C₄	—	2	1	no	—
709	C₂²×C₄	—	2	2	no	—
710	C₂²×C₄	—	2	2	no	—
711	C₂²×C₄	—	2	4	no	—
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	2	yes	—
715	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
716	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
717	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
718	Q₁₆	—	2	4	no	—
719	Q₁₆	—	2	4	no	—
720	SD₁₆	—	2	4	no	—
721	SD₁₆	—	2	4	no	—
722	SD₁₆	—	2	4	no	—
723	SD₁₆	—	2	4	no	—
724	D₈	—	2	4	no	—
725	D₈	—	2	4	no	—
726	M₁₆	—	2	4	no	—
727	M₁₆	—	2	8	no	—
728	C₂×C₈	—	2	8	no	—
729	C₂×C₈	#41×C₃₁	1	8	yes	complemented
730	C₂×C₈	C₂⁴×C₃₁	1	4	yes	—
731	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
732	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
733	C₄⋊C₄	—	2	1	no	—
734	C₄⋊C₄	—	2	1	no	—
735	C₄⋊C₄	—	2	2	no	—
736	C₄⋊C₄	—	2	2	no	—
737	C₄⋊C₄	—	2	2	no	—
738	C₄⋊C₄	—	2	2	no	—
739	C₄⋊C₄	—	2	4	no	—
740	C₄⋊C₄	—	2	2	no	—
741	C₄⋊C₄	—	2	2	no	—
742	C₄⋊C₄	—	2	2	no	—
743	C₄⋊C₄	—	2	2	no	—
744	C₄⋊C₄	—	2	2	no	—
745	C₄⋊C₄	—	2	1	no	—
746	C₄⋊C₄	—	2	2	no	—
747	C₄⋊C₄	—	2	2	no	—
748	C₄⋊C₄	—	2	1	no	—
749	C₄⋊C₄	—	2	1	no	—
750	C₄⋊C₄	—	2	1	no	—
751	C₄⋊C₄	—	2	4	no	—
752	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
753	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
754	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
755	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
756	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
757	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
758	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
759	C₂²⋊C₄	—	2	4	no	—
760	C₂²⋊C₄	—	2	2	no	—
761	C₂²⋊C₄	—	2	2	no	—
762	C₂²⋊C₄	—	2	1	no	—
763	C₂²⋊C₄	—	2	1	no	—
764	C₂²⋊C₄	—	2	2	no	—
765	C₂²⋊C₄	—	2	2	no	—
766	C₂²⋊C₄	—	2	4	no	—
767	C₂²⋊C₄	—	2	2	no	—
768	C₂²⋊C₄	—	2	2	no	—
769	C₂²⋊C₄	—	2	1	no	—
770	C₂²⋊C₄	—	2	1	no	—
771	C₂²⋊C₄	—	2	4	no	—
772	C₂²⋊C₄	—	2	2	no	—
773	C₂²⋊C₄	—	2	2	no	—
774	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
775	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
776	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
777	C₄²	—	2	2	no	—
778	C₄²	—	2	2	no	—
779	C₄²	—	2	4	no	—
780	C₄²	C₂×D₄×C₃₁	1	2	yes	—
781	C₄²	C₂×D₄×C₃₁	1	2	yes	—
782	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
783	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
784	C₄²	C₂⁴×C₃₁	1	2	yes	—
785	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
786	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
787	C₂³	—	2	2	no	—
788	C₂³	—	2	1	no	—
789	C₂³	—	2	1	no	—
790	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
791	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
792	Q₈	—	2	2	no	—
793	Q₈	—	2	2	no	—
794	Q₈	—	2	2	no	—
795	Q₈	—	2	2	no	—
796	Q₈	—	2	2	no	—
797	Q₈	—	4	4	no	—
798	Q₈	—	8	2	no	—
799	D₄	—	2	4	no	—
800	D₄	—	2	2	no	—
801	D₄	—	2	2	no	—
802	D₄	—	2	2	no	—
803	D₄	—	2	2	no	—
804	D₄	—	2	2	no	—
805	D₄	—	4	2	no	—
806	D₄	—	4	2	no	—
807	D₄	—	4	4	no	—
808	D₄	—	4	2	no	—
809	D₄	—	4	2	no	—
810	D₄	—	8	1	no	—
811	D₄	—	8	1	no	—
812	D₄	—	8	2	no	—
813	D₄	—	8	2	no	—
814	D₄	—	8	4	no	—
815	C₂×C₄	—	2	4	no	—
816	C₂×C₄	—	2	1	no	—
817	C₂×C₄	—	2	1	no	—
818	C₂×C₄	—	2	2	no	—
819	C₂×C₄	—	2	2	no	—
820	C₂×C₄	—	2	2	no	—
821	C₂×C₄	—	2	4	no	—
822	C₂×C₄	—	4	2	no	—
823	C₂×C₄	—	4	1	no	—
824	C₂×C₄	—	4	1	no	—
825	C₂×C₄	—	4	2	no	—
826	C₂×C₄	—	4	4	no	—
827	C₂×C₄	—	4	2	no	—
828	C₂×C₄	—	4	2	no	—
829	C₂×C₄	—	8	2	no	—
830	C₂×C₄	—	8	2	no	—
831	C₂×C₄	—	8	4	no	—
832	C₂×C₄	—	8	1	no	—
833	C₂×C₄	—	8	1	no	—
834	C₂×C₄	—	8	2	no	—
835	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
836	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
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	2	yes	—
840	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
841	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
842	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
843	C₂×C₄	C₂×#41×C₃₁	1	4	yes	—
844	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
845	C₈	—	2	4	no	—
846	C₈	C₂×#41×C₃₁	1	4	yes	—
847	C₈	C₂×#41×C₃₁	1	4	yes	—
848	C₂²	—	2	1	no	—
849	C₂²	—	2	1	no	—
850	C₂²	—	2	2	no	—
851	C₂²	—	2	2	no	—
852	C₂²	—	2	2	no	—
853	C₂²	—	4	2	no	—
854	C₂²	—	4	1	no	—
855	C₂²	—	4	1	no	—
856	C₂²	—	4	2	no	—
857	C₂²	—	4	1	no	—
858	C₂²	—	4	1	no	—
859	C₂²	—	4	1	no	—
860	C₂²	—	4	2	no	—
861	C₂²	—	4	1	no	—
862	C₂²	C₃₁×#532	1	2	yes	—
863	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
864	C₄	—	2	2	no	—
865	C₄	—	2	1	no	—
866	C₄	—	2	2	no	—
867	C₄	—	2	1	no	—
868	C₄	—	2	1	no	—
869	C₄	—	2	2	no	—
870	C₄	—	2	1	no	—
871	C₄	—	4	1	no	—
872	C₄	—	4	1	no	—
873	C₄	—	4	2	no	—
874	C₄	—	4	4	no	—
875	C₄	—	4	2	no	—
876	C₄	—	4	2	no	—
877	C₄	C₃₁×#532	1	2	yes	—
878	C₄	C₂²×#41×C₃₁	1	2	yes	—
879	C₂	—	2	2	no	—
880	C₂	—	4	2	no	—
881	C₂	—	8	2	no	—
882	C₂	—	8	1	no	—
883	C₂	—	8	1	no	—
884	C₂	C₂×C₃₁×#532	1	1	yes	characteristic
885	C₂	C₃₁×#3585	1	1	yes	characteristic
886	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×#3512	C₂	semidirect
2. C₃₁×#3511	C₂	semidirect
3. C₃₁×#3181	C₂	semidirect
4. C₃₁×#3180	C₂	semidirect
5. C₃₁×#3179	C₂	semidirect
6. C₃₁×#3178	C₂	semidirect
7. C₃₁×#3172	C₂	semidirect
8. C₃₁×#3171	C₂	semidirect
9. C₂×C₃₁×#501	C₂	semidirect
10. C₃₁×#3150	C₂	semidirect
11. C₃₁×#3142	C₂	semidirect
12. C₃₁×#3141	C₂	semidirect
13. C₃₁×#3061	C₂	semidirect
14. C₃₁×#3060	C₂	semidirect
15. C₃₁×#2952	C₂	semidirect
16. C₃₁×#2951	C₂	semidirect
17. C₃₁×#2875	C₂	semidirect
285. C₂×C₈×C₃₁	#41	semidirect
343. #60721	C₃₁	direct (N × H)
405. #3512	C₂×C₃₁	semidirect
406. #3511	C₂×C₃₁	semidirect
407. #3181	C₂×C₃₁	semidirect
408. #3180	C₂×C₃₁	semidirect
409. #3179	C₂×C₃₁	semidirect
410. #3178	C₂×C₃₁	semidirect
411. #3172	C₂×C₃₁	semidirect
412. #3171	C₂×C₃₁	semidirect
413. C₂×#501	C₂×C₃₁	semidirect
414. #3150	C₂×C₃₁	semidirect
415. #3142	C₂×C₃₁	semidirect
416. #3141	C₂×C₃₁	semidirect
417. #3061	C₂×C₃₁	semidirect
418. #3060	C₂×C₃₁	semidirect
419. #2952	C₂×C₃₁	semidirect
420. #2951	C₂×C₃₁	semidirect
421. #2875	C₂×C₃₁	semidirect
674. C₃₁	#60721	direct (N × H)
729. C₂×C₈	#41×C₃₁	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃₁×#3512	2
C₃₁×#3511	2
C₃₁×#3181	2
C₃₁×#3180	2
C₃₁×#3179	2
C₃₁×#3178	2
C₃₁×#3172	2
C₃₁×#3171	2
C₂×C₃₁×#501	2
C₃₁×#3150	2
C₃₁×#3142	2
C₃₁×#3141	2
C₃₁×#3061	2
C₃₁×#3060	2
C₃₁×#2952	2
C₃₁×#2951	2
C₃₁×#2875	2
#60721	31

Subgroups — C31×#60721 #21517480

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#60721 #21517480