Subgroups — C₃₁×#61637 #21518396

Order 7936.

2058 conjugacy classes of subgroups.

The subgroup lattice has 1050 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3539	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3487	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3317	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3309	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3301	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3300	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3287	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3284	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3271	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3269	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3222	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3220	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3198	C₂	1	2	yes	maximal, complemented
14	C₃₁×#3191	C₂	1	2	yes	maximal, complemented
15	C₃₁×#3127	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#3126	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#3013	C₂	1	2	yes	maximal, complemented
18	C₃₁×#3002	C₂	1	2	yes	maximal, complemented
19	C₃₁×#2977	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×C₃₁×2₋¹⁺⁴	C₂²	1	1	yes	characteristic
21	C₂²×#41×C₃₁	C₂²	1	1	yes	characteristic
22	C₂×C₃₁×#137	C₂²	1	2	yes	complemented
23	C₂×C₃₁×#135	C₂²	1	2	yes	—
24	C₂×C₃₁×#135	C₂²	1	2	yes	—
25	C₂×C₃₁×#135	C₂²	1	2	yes	complemented
26	C₃₁×#560	—	2	2	no	—
27	C₃₁×#553	—	2	2	no	—
28	C₃₁×#553	C₂²	1	2	yes	complemented
29	C₃₁×#552	C₂²	1	2	yes	complemented
30	C₃₁×#550	—	2	2	no	—
31	C₃₁×#550	C₂²	1	2	yes	—
32	C₃₁×#550	C₂²	1	2	yes	—
33	C₃₁×#550	C₂²	1	2	yes	complemented
34	C₃₁×#548	—	2	2	no	—
35	C₃₁×#548	C₂²	1	2	yes	—
36	C₃₁×#548	C₂²	1	2	yes	—
37	C₃₁×#547	C₂²	1	2	yes	complemented
38	C₃₁×#541	C₂²	1	1	yes	characteristic
39	C₃₁×#540	—	2	2	no	—
40	C₃₁×#540	C₂²	1	1	yes	characteristic
41	C₃₁×#539	—	2	2	no	—
42	C₃₁×#537	C₂²	1	2	yes	—
43	C₃₁×#535	—	2	2	no	—
44	C₃₁×#535	C₂²	1	1	yes	characteristic
45	C₃₁×#535	C₂²	1	1	yes	characteristic
46	C₃₁×#525	—	2	2	no	—
47	C₃₁×#525	C₂²	1	1	yes	characteristic
48	C₃₁×#525	C₂²	1	2	yes	—
49	C₃₁×#525	C₂²	1	1	yes	characteristic
50	C₃₁×#519	C₂²	1	1	yes	characteristic
51	C₃₁×#497	C₂²	1	1	yes	characteristic, complemented
52	C₃₁×#496	C₂²	1	1	yes	characteristic, complemented
53	C₃₁×#493	C₂²	1	1	yes	characteristic, complemented
54	C₃₁×#492	C₂²	1	1	yes	characteristic, complemented
55	C₃₁×#490	C₂²	1	1	yes	characteristic, complemented
56	C₃₁×#490	C₂²	1	1	yes	characteristic, complemented
57	C₃₁×#488	C₂²	1	1	yes	characteristic, complemented
58	C₃₁×#488	C₂²	1	1	yes	characteristic, complemented
59	C₃₁×#485	C₂²	1	2	yes	—
60	C₃₁×#485	C₂²	1	2	yes	complemented
61	C₃₁×#482	C₂²	1	2	yes	—
62	C₃₁×#482	C₂²	1	2	yes	complemented
63	C₃₁×#481	C₂²	1	2	yes	complemented
64	C₃₁×#480	C₂²	1	2	yes	complemented
65	C₃₁×#479	C₂²	1	2	yes	complemented
66	C₃₁×#479	C₂²	1	2	yes	complemented
67	C₃₁×#469	C₂²	1	2	yes	complemented
68	C₃₁×#468	C₂²	1	2	yes	complemented
69	C₃₁×#467	C₂²	1	2	yes	complemented
70	C₃₁×#466	C₂²	1	2	yes	complemented
71	C₃₁×#466	C₂²	1	2	yes	complemented
72	C₃₁×#465	C₂²	1	2	yes	complemented
73	C₃₁×#465	C₂²	1	2	yes	complemented
74	C₃₁×#465	C₂²	1	2	yes	complemented
75	C₃₁×#464	C₂²	1	2	yes	complemented
76	C₃₁×#463	C₂²	1	2	yes	complemented
77	C₃₁×#462	C₂²	1	2	yes	complemented
78	C₃₁×#460	C₂²	1	2	yes	complemented
79	C₃₁×#460	C₂²	1	2	yes	complemented
80	C₃₁×#459	C₂²	1	2	yes	complemented
81	C₃₁×#452	C₂²	1	2	yes	—
82	C₃₁×#452	C₂²	1	2	yes	—
83	C₃₁×#452	C₂²	1	2	yes	—
84	C₃₁×#452	C₂²	1	2	yes	complemented
85	C₃₁×#452	C₂²	1	2	yes	complemented
86	C₃₁×#451	C₂²	1	2	yes	—
87	C₃₁×#451	C₂²	1	2	yes	complemented
88	C₃₁×#450	C₂²	1	2	yes	—
89	C₃₁×#449	C₂²	1	2	yes	—
90	C₃₁×#449	C₂²	1	2	yes	—
91	C₃₁×#449	C₂²	1	2	yes	—
92	C₃₁×#449	C₂²	1	2	yes	complemented
93	C₃₁×#449	C₂²	1	2	yes	complemented
94	C₃₁×#449	C₂²	1	2	yes	complemented
95	C₃₁×#449	C₂²	1	2	yes	complemented
96	C₃₁×#448	C₂²	1	2	yes	—
97	C₃₁×#448	C₂²	1	2	yes	complemented
98	C₃₁×#447	C₂²	1	2	yes	—
99	C₃₁×#441	C₂²	1	2	yes	complemented
100	C₃₁×#440	C₂²	1	2	yes	complemented
101	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	complemented
102	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
103	C₃₁×#435	C₂²	1	2	yes	complemented
104	C₃₁×#435	C₂²	1	2	yes	complemented
105	C₈×D₄×C₃₁	C₂²	1	2	yes	complemented
106	C₈×D₄×C₃₁	C₂²	1	2	yes	complemented
107	C₃₁×#433	C₂²	1	1	yes	characteristic
108	C₃₁×#433	C₂²	1	1	yes	characteristic
109	C₃₁×#417	C₂²	1	2	yes	complemented
110	C₃₁×#416	C₂²	1	2	yes	—
111	C₃₁×#416	C₂²	1	2	yes	—
112	C₂×C₃₁×#103	C₂²	1	2	yes	complemented
113	C₃₁×#408	C₂²	1	2	yes	—
114	C₂×C₃₁×C₂²⋊C₈	C₂²	1	2	yes	—
115	C₃₁×2₋¹⁺⁴	—	4	4	no	—
116	C₂×#41×C₃₁	—	2	2	no	—
117	C₂×#41×C₃₁	—	2	1	no	—
118	C₂×#41×C₃₁	—	2	2	no	—
119	C₂×#41×C₃₁	—	4	4	no	—
120	C₂×#41×C₃₁	C₂³	1	2	yes	—
121	C₂×#41×C₃₁	C₂³	1	2	yes	—
122	C₂×#41×C₃₁	C₂³	1	2	yes	—
123	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
124	C₂×#41×C₃₁	C₂³	1	2	yes	—
125	C₂×#41×C₃₁	C₂³	1	2	yes	—
126	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
127	C₂²×Q₈×C₃₁	—	2	1	no	—
128	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
129	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
130	C₂²×D₄×C₃₁	—	2	1	no	—
131	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
132	C₂³×C₄×C₃₁	—	2	1	no	—
133	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
134	C₃₁×#137	—	4	4	no	—
135	C₃₁×#135	—	4	4	no	—
136	C₃₁×#135	—	4	4	no	—
137	C₃₁×#135	—	4	4	no	—
138	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
139	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
140	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
141	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
142	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
143	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
144	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
145	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
146	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
147	C₂×D₈×C₃₁	C₂³	1	2	yes	—
148	C₂×D₈×C₃₁	C₂³	1	2	yes	—
149	C₂×D₈×C₃₁	C₂³	1	2	yes	—
150	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
151	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
152	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
153	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
154	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
155	C₃₁×#127	—	2	2	no	—
156	C₃₁×#127	—	2	2	no	—
157	C₃₁×#127	—	2	1	no	—
158	C₃₁×#127	—	2	2	no	—
159	C₃₁×#127	C₂³	1	1	yes	characteristic
160	C₃₁×#127	C₂³	1	1	yes	characteristic
161	C₃₁×#127	C₂³	1	1	yes	characteristic
162	C₃₁×#126	—	2	2	no	—
163	C₃₁×#126	—	2	2	no	—
164	C₃₁×#126	—	2	2	no	—
165	C₃₁×#125	—	2	2	no	—
166	C₃₁×#125	—	2	2	no	—
167	C₃₁×#125	C₂³	1	1	yes	characteristic
168	C₃₁×#125	C₂³	1	1	yes	characteristic
169	C₃₁×#124	—	2	1	no	—
170	C₃₁×#124	—	2	2	no	—
171	C₃₁×#124	—	2	2	no	—
172	C₃₁×#124	C₂³	1	1	yes	characteristic
173	C₃₁×#124	C₂³	1	1	yes	characteristic
174	C₃₁×#123	—	2	2	no	—
175	C₃₁×#123	—	2	1	no	—
176	C₃₁×#123	—	2	2	no	—
177	C₃₁×#123	—	2	2	no	—
178	C₃₁×#123	—	2	2	no	—
179	C₃₁×#123	—	2	2	no	—
180	C₃₁×#123	—	2	2	no	—
181	C₃₁×#123	D₄	1	2	yes	—
182	C₃₁×C₂²⋊Q₈	—	2	2	no	—
183	C₃₁×C₂²⋊Q₈	—	2	2	no	—
184	C₃₁×C₂²⋊Q₈	—	2	2	no	—
185	C₃₁×C₂²⋊Q₈	D₄	1	2	yes	—
186	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
187	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
188	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
189	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
190	C₃₁×#121	—	2	2	no	—
191	C₃₁×#121	—	2	2	no	—
192	C₃₁×#121	—	2	2	no	—
193	C₃₁×#121	—	2	2	no	—
194	C₃₁×#121	—	2	2	no	—
195	C₃₁×#121	—	2	2	no	—
196	C₃₁×#121	—	2	2	no	—
197	C₃₁×#121	—	2	2	no	—
198	C₃₁×#121	—	2	2	no	—
199	C₃₁×#121	—	2	2	no	—
200	C₃₁×#121	—	2	2	no	—
201	C₃₁×#121	—	2	2	no	—
202	C₃₁×#121	—	2	2	no	—
203	C₃₁×#121	—	2	2	no	—
204	C₃₁×#121	—	2	2	no	—
205	C₃₁×#121	D₄	1	2	yes	—
206	C₃₁×#121	C₂³	1	2	yes	—
207	C₃₁×#121	C₂³	1	2	yes	—
208	C₃₁×#121	C₂³	1	2	yes	—
209	C₃₁×#121	C₂³	1	2	yes	—
210	C₃₁×#121	C₂³	1	2	yes	—
211	C₃₁×#121	C₂³	1	2	yes	—
212	C₃₁×#120	—	2	1	no	—
213	C₃₁×#120	—	2	2	no	—
214	C₃₁×#120	—	2	2	no	—
215	C₃₁×#120	—	2	2	no	—
216	C₃₁×#120	D₄	1	2	yes	—
217	C₄×Q₈×C₃₁	—	2	2	no	—
218	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
219	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
220	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
221	C₄×D₄×C₃₁	—	2	2	no	—
222	C₄×D₄×C₃₁	—	2	2	no	—
223	C₄×D₄×C₃₁	—	2	2	no	—
224	C₄×D₄×C₃₁	—	2	2	no	—
225	C₄×D₄×C₃₁	—	2	2	no	—
226	C₄×D₄×C₃₁	—	2	2	no	—
227	C₄×D₄×C₃₁	—	2	2	no	—
228	C₄×D₄×C₃₁	—	2	2	no	—
229	C₄×D₄×C₃₁	—	2	2	no	—
230	C₄×D₄×C₃₁	C₂³	1	2	yes	—
231	C₄×D₄×C₃₁	C₂³	1	2	yes	—
232	C₄×D₄×C₃₁	C₂³	1	2	yes	—
233	C₃₁×#117	—	2	2	no	—
234	C₃₁×#117	—	2	2	no	—
235	C₃₁×#117	C₂³	1	2	yes	—
236	C₃₁×#117	C₂³	1	1	yes	characteristic
237	C₃₁×#117	C₂³	1	1	yes	characteristic
238	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
239	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
240	C₃₁×#107	C₂³	1	2	yes	—
241	C₃₁×#107	C₂³	1	2	yes	—
242	C₃₁×#106	C₂³	1	2	yes	—
243	C₃₁×#106	C₂³	1	2	yes	—
244	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
245	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
246	C₃₁×#103	C₂³	1	2	yes	—
247	C₃₁×#103	C₂³	1	2	yes	—
248	C₃₁×#103	C₂³	1	2	yes	—
249	C₃₁×#103	C₂³	1	2	yes	—
250	C₃₁×#103	C₂³	1	2	yes	—
251	C₃₁×#103	C₂³	1	2	yes	—
252	C₃₁×#103	C₂³	1	2	yes	—
253	C₃₁×#103	C₂³	1	2	yes	—
254	C₃₁×#102	C₂³	1	2	yes	—
255	C₃₁×#102	C₂³	1	2	yes	—
256	C₃₁×#102	C₂³	1	2	yes	—
257	C₃₁×#102	C₂³	1	2	yes	—
258	C₃₁×#102	C₂³	1	2	yes	—
259	C₃₁×#102	C₂³	1	2	yes	—
260	C₃₁×#102	C₂³	1	2	yes	—
261	C₃₁×#102	C₂³	1	2	yes	—
262	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
263	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
264	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
265	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
266	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
267	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
268	C₃₁×#97	C₂³	1	1	yes	characteristic
269	C₃₁×#97	C₂³	1	1	yes	characteristic
270	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
271	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
272	C₂⁴×C₃₁	—	2	1	no	—
273	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
274	#41×C₃₁	—	2	4	no	—
275	#41×C₃₁	—	2	4	no	—
276	#41×C₃₁	—	2	4	no	—
277	#41×C₃₁	—	4	2	no	—
278	#41×C₃₁	—	4	2	no	—
279	#41×C₃₁	—	4	2	no	—
280	#41×C₃₁	—	4	2	no	—
281	#41×C₃₁	—	4	2	no	—
282	#41×C₃₁	—	4	8	no	—
283	#41×C₃₁	—	4	2	no	—
284	#41×C₃₁	—	4	2	no	—
285	#41×C₃₁	—	4	2	no	—
286	#41×C₃₁	—	4	2	no	—
287	#41×C₃₁	—	4	8	no	—
288	#41×C₃₁	—	4	4	no	—
289	C₂×Q₈×C₃₁	—	2	4	no	—
290	C₂×Q₈×C₃₁	—	2	1	no	—
291	C₂×Q₈×C₃₁	—	2	2	no	—
292	C₂×Q₈×C₃₁	—	2	4	no	—
293	C₂×Q₈×C₃₁	—	4	2	no	—
294	C₂×Q₈×C₃₁	—	4	4	no	—
295	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
296	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
297	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
298	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
299	C₂×D₄×C₃₁	—	2	1	no	—
300	C₂×D₄×C₃₁	—	2	2	no	—
301	C₂×D₄×C₃₁	—	2	2	no	—
302	C₂×D₄×C₃₁	—	2	2	no	—
303	C₂×D₄×C₃₁	—	2	2	no	—
304	C₂×D₄×C₃₁	—	2	2	no	—
305	C₂×D₄×C₃₁	—	2	2	no	—
306	C₂×D₄×C₃₁	—	2	2	no	—
307	C₂×D₄×C₃₁	—	2	2	no	—
308	C₂×D₄×C₃₁	—	2	2	no	—
309	C₂×D₄×C₃₁	—	2	2	no	—
310	C₂×D₄×C₃₁	—	2	2	no	—
311	C₂×D₄×C₃₁	—	2	1	no	—
312	C₂×D₄×C₃₁	—	2	2	no	—
313	C₂×D₄×C₃₁	—	2	2	no	—
314	C₂×D₄×C₃₁	—	2	2	no	—
315	C₂×D₄×C₃₁	—	4	2	no	—
316	C₂×D₄×C₃₁	—	4	4	no	—
317	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
318	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
319	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
320	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
321	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
322	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
323	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
324	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
325	C₂²×C₄×C₃₁	—	2	1	no	—
326	C₂²×C₄×C₃₁	—	2	2	no	—
327	C₂²×C₄×C₃₁	—	2	2	no	—
328	C₂²×C₄×C₃₁	—	2	2	no	—
329	C₂²×C₄×C₃₁	—	2	1	no	—
330	C₂²×C₄×C₃₁	—	2	2	no	—
331	C₂²×C₄×C₃₁	—	2	2	no	—
332	C₂²×C₄×C₃₁	—	2	2	no	—
333	C₂²×C₄×C₃₁	—	2	2	no	—
334	C₂²×C₄×C₃₁	—	2	2	no	—
335	C₂²×C₄×C₃₁	—	4	2	no	—
336	C₂²×C₄×C₃₁	—	4	4	no	—
337	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
338	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
339	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
340	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
341	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
342	Q₁₆×C₃₁	—	2	4	no	—
343	Q₁₆×C₃₁	—	2	4	no	—
344	Q₁₆×C₃₁	—	4	2	no	—
345	SD₁₆×C₃₁	—	2	4	no	—
346	SD₁₆×C₃₁	—	2	4	no	—
347	SD₁₆×C₃₁	—	4	2	no	—
348	SD₁₆×C₃₁	—	4	2	no	—
349	SD₁₆×C₃₁	—	4	2	no	—
350	SD₁₆×C₃₁	—	4	2	no	—
351	D₈×C₃₁	—	4	2	no	—
352	D₈×C₃₁	—	4	2	no	—
353	D₈×C₃₁	—	4	2	no	—
354	M₁₆×C₃₁	—	4	2	no	—
355	C₂×C₈×C₃₁	—	4	2	no	—
356	C₂×C₈×C₃₁	—	4	2	no	—
357	C₂×C₈×C₃₁	—	4	2	no	—
358	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
359	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
360	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
361	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
362	C₄⋊C₄×C₃₁	—	2	2	no	—
363	C₄⋊C₄×C₃₁	—	2	2	no	—
364	C₄⋊C₄×C₃₁	—	2	2	no	—
365	C₄⋊C₄×C₃₁	—	2	2	no	—
366	C₄⋊C₄×C₃₁	—	2	2	no	—
367	C₄⋊C₄×C₃₁	—	2	2	no	—
368	C₄⋊C₄×C₃₁	—	2	2	no	—
369	C₄⋊C₄×C₃₁	—	2	2	no	—
370	C₄⋊C₄×C₃₁	—	2	2	no	—
371	C₄⋊C₄×C₃₁	—	2	2	no	—
372	C₄⋊C₄×C₃₁	—	2	2	no	—
373	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
374	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
375	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
376	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
377	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
378	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
379	C₂²⋊C₄×C₃₁	—	2	1	no	—
380	C₂²⋊C₄×C₃₁	—	2	2	no	—
381	C₂²⋊C₄×C₃₁	—	2	2	no	—
382	C₂²⋊C₄×C₃₁	—	2	2	no	—
383	C₂²⋊C₄×C₃₁	—	2	2	no	—
384	C₂²⋊C₄×C₃₁	—	2	2	no	—
385	C₂²⋊C₄×C₃₁	—	2	2	no	—
386	C₂²⋊C₄×C₃₁	—	2	2	no	—
387	C₂²⋊C₄×C₃₁	—	2	2	no	—
388	C₂²⋊C₄×C₃₁	—	2	2	no	—
389	C₂²⋊C₄×C₃₁	—	2	2	no	—
390	C₂²⋊C₄×C₃₁	—	2	2	no	—
391	C₂²⋊C₄×C₃₁	—	2	2	no	—
392	C₂²⋊C₄×C₃₁	—	2	2	no	—
393	C₂²⋊C₄×C₃₁	—	2	2	no	—
394	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
395	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
396	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
397	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
398	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
399	C₄²×C₃₁	—	2	2	no	—
400	C₄²×C₃₁	—	2	2	no	—
401	C₄²×C₃₁	—	2	2	no	—
402	C₄²×C₃₁	—	2	2	no	—
403	C₄²×C₃₁	—	2	1	no	—
404	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
405	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
406	#61637	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
407	C₂³×C₃₁	—	2	2	no	—
408	C₂³×C₃₁	—	2	1	no	—
409	C₂³×C₃₁	—	2	1	no	—
410	C₂³×C₃₁	—	2	1	no	—
411	C₂³×C₃₁	—	4	1	no	—
412	C₂³×C₃₁	—	4	2	no	—
413	C₂³×C₃₁	—	4	2	no	—
414	C₂³×C₃₁	—	8	2	no	—
415	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
416	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
417	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
418	Q₈×C₃₁	—	2	4	no	—
419	Q₈×C₃₁	—	2	2	no	—
420	Q₈×C₃₁	—	2	2	no	—
421	Q₈×C₃₁	—	2	2	no	—
422	Q₈×C₃₁	—	2	2	no	—
423	Q₈×C₃₁	—	4	1	no	—
424	Q₈×C₃₁	—	4	4	no	—
425	Q₈×C₃₁	H(5,𝔽₂)	1	4	yes	—
426	D₄×C₃₁	—	2	2	no	—
427	D₄×C₃₁	—	2	2	no	—
428	D₄×C₃₁	—	2	2	no	—
429	D₄×C₃₁	—	2	2	no	—
430	D₄×C₃₁	—	2	2	no	—
431	D₄×C₃₁	—	4	2	no	—
432	D₄×C₃₁	—	4	2	no	—
433	D₄×C₃₁	—	4	1	no	—
434	D₄×C₃₁	—	4	2	no	—
435	D₄×C₃₁	—	4	4	no	—
436	D₄×C₃₁	—	4	4	no	—
437	D₄×C₃₁	—	4	4	no	—
438	D₄×C₃₁	—	4	2	no	—
439	D₄×C₃₁	—	4	2	no	—
440	D₄×C₃₁	—	8	2	no	—
441	D₄×C₃₁	—	8	2	no	—
442	D₄×C₃₁	—	8	2	no	—
443	D₄×C₃₁	—	8	2	no	—
444	D₄×C₃₁	—	8	2	no	—
445	D₄×C₃₁	—	8	2	no	—
446	D₄×C₃₁	—	8	2	no	—
447	D₄×C₃₁	—	8	2	no	—
448	D₄×C₃₁	—	8	2	no	—
449	D₄×C₃₁	—	8	2	no	—
450	D₄×C₃₁	—	8	2	no	—
451	C₂×C₄×C₃₁	—	2	4	no	—
452	C₂×C₄×C₃₁	—	2	2	no	—
453	C₂×C₄×C₃₁	—	2	2	no	—
454	C₂×C₄×C₃₁	—	2	2	no	—
455	C₂×C₄×C₃₁	—	2	2	no	—
456	C₂×C₄×C₃₁	—	2	2	no	—
457	C₂×C₄×C₃₁	—	2	2	no	—
458	C₂×C₄×C₃₁	—	2	2	no	—
459	C₂×C₄×C₃₁	—	2	2	no	—
460	C₂×C₄×C₃₁	—	2	2	no	—
461	C₂×C₄×C₃₁	—	2	2	no	—
462	C₂×C₄×C₃₁	—	2	1	no	—
463	C₂×C₄×C₃₁	—	4	1	no	—
464	C₂×C₄×C₃₁	—	4	2	no	—
465	C₂×C₄×C₃₁	—	4	4	no	—
466	C₂×C₄×C₃₁	—	4	4	no	—
467	C₂×C₄×C₃₁	—	4	4	no	—
468	C₂×C₄×C₃₁	—	4	4	no	—
469	C₂×C₄×C₃₁	—	4	2	no	—
470	C₂×C₄×C₃₁	—	8	2	no	—
471	C₂×C₄×C₃₁	—	8	2	no	—
472	C₂×C₄×C₃₁	—	8	2	no	—
473	C₂×C₄×C₃₁	—	8	2	no	—
474	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
475	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
476	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
477	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
478	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
479	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
480	C₈×C₃₁	—	2	2	no	—
481	C₈×C₃₁	—	2	2	no	—
482	C₈×C₃₁	—	2	2	no	—
483	C₈×C₃₁	—	2	2	no	—
484	#3539	C₂×C₃₁	1	1	yes	characteristic, complemented
485	#3487	C₂×C₃₁	1	1	yes	characteristic, complemented
486	#3317	C₂×C₃₁	1	2	yes	complemented
487	#3309	C₂×C₃₁	1	2	yes	complemented
488	#3301	C₂×C₃₁	1	2	yes	complemented
489	#3300	C₂×C₃₁	1	2	yes	complemented
490	#3287	C₂×C₃₁	1	2	yes	complemented
491	#3284	C₂×C₃₁	1	2	yes	complemented
492	#3271	C₂×C₃₁	1	2	yes	complemented
493	#3269	C₂×C₃₁	1	2	yes	complemented
494	#3222	C₂×C₃₁	1	1	yes	characteristic, complemented
495	#3220	C₂×C₃₁	1	1	yes	characteristic, complemented
496	#3198	C₂×C₃₁	1	2	yes	complemented
497	#3191	C₂×C₃₁	1	2	yes	complemented
498	#3127	C₂×C₃₁	1	1	yes	characteristic, complemented
499	#3126	C₂×C₃₁	1	1	yes	characteristic, complemented
500	#3013	C₂×C₃₁	1	2	yes	complemented
501	#3002	C₂×C₃₁	1	2	yes	complemented
502	#2977	C₂×C₃₁	1	1	yes	characteristic, complemented
503	C₂²×C₃₁	—	2	2	no	—
504	C₂²×C₃₁	—	2	2	no	—
505	C₂²×C₃₁	—	2	2	no	—
506	C₂²×C₃₁	—	2	2	no	—
507	C₂²×C₃₁	—	2	2	no	—
508	C₂²×C₃₁	—	2	1	no	—
509	C₂²×C₃₁	—	2	2	no	—
510	C₂²×C₃₁	—	2	2	no	—
511	C₂²×C₃₁	—	4	2	no	—
512	C₂²×C₃₁	—	4	2	no	—
513	C₂²×C₃₁	—	4	2	no	—
514	C₂²×C₃₁	—	4	2	no	—
515	C₂²×C₃₁	—	4	2	no	—
516	C₂²×C₃₁	—	4	1	no	—
517	C₂²×C₃₁	—	4	1	no	—
518	C₂²×C₃₁	—	4	1	no	—
519	C₂²×C₃₁	—	4	2	no	—
520	C₂²×C₃₁	—	8	2	no	—
521	C₂²×C₃₁	—	8	4	no	—
522	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
523	C₄×C₃₁	—	2	2	no	—
524	C₄×C₃₁	—	2	2	no	—
525	C₄×C₃₁	—	2	4	no	—
526	C₄×C₃₁	—	2	2	no	—
527	C₄×C₃₁	—	2	1	no	—
528	C₄×C₃₁	—	2	2	no	—
529	C₄×C₃₁	—	4	2	no	—
530	C₄×C₃₁	—	4	2	no	—
531	C₄×C₃₁	—	4	2	no	—
532	C₄×C₃₁	—	4	1	no	—
533	C₄×C₃₁	—	4	2	no	—
534	C₄×C₃₁	C₂×H(5,𝔽₂)	1	2	yes	—
535	C₂×2₋¹⁺⁴	C₂²×C₃₁	1	1	yes	characteristic
536	C₂²×#41	C₂²×C₃₁	1	1	yes	characteristic
537	C₂×#137	C₂²×C₃₁	1	2	yes	complemented
538	C₂×#135	C₂²×C₃₁	1	2	yes	—
539	C₂×#135	C₂²×C₃₁	1	2	yes	—
540	C₂×#135	C₂²×C₃₁	1	2	yes	complemented
541	#560	—	2	2	no	—
542	#553	—	2	2	no	—
543	#553	C₂²×C₃₁	1	2	yes	complemented
544	#552	C₂²×C₃₁	1	2	yes	complemented
545	#550	—	2	2	no	—
546	#550	C₂²×C₃₁	1	2	yes	—
547	#550	C₂²×C₃₁	1	2	yes	—
548	#550	C₂²×C₃₁	1	2	yes	complemented
549	#548	—	2	2	no	—
550	#548	C₂²×C₃₁	1	2	yes	—
551	#548	C₂²×C₃₁	1	2	yes	—
552	#547	C₂²×C₃₁	1	2	yes	complemented
553	#541	C₂²×C₃₁	1	1	yes	characteristic
554	#540	—	2	2	no	—
555	#540	C₂²×C₃₁	1	1	yes	characteristic
556	#539	—	2	2	no	—
557	#537	C₂²×C₃₁	1	2	yes	—
558	#535	—	2	2	no	—
559	#535	C₂²×C₃₁	1	1	yes	characteristic
560	#535	C₂²×C₃₁	1	1	yes	characteristic
561	#525	—	2	2	no	—
562	#525	C₂²×C₃₁	1	1	yes	characteristic
563	#525	C₂²×C₃₁	1	2	yes	—
564	#525	C₂²×C₃₁	1	1	yes	characteristic
565	#519	C₂²×C₃₁	1	1	yes	characteristic
566	#497	C₂²×C₃₁	1	1	yes	characteristic, complemented
567	#496	C₂²×C₃₁	1	1	yes	characteristic, complemented
568	#493	C₂²×C₃₁	1	1	yes	characteristic, complemented
569	#492	C₂²×C₃₁	1	1	yes	characteristic, complemented
570	#490	C₂²×C₃₁	1	1	yes	characteristic, complemented
571	#490	C₂²×C₃₁	1	1	yes	characteristic, complemented
572	#488	C₂²×C₃₁	1	1	yes	characteristic, complemented
573	#488	C₂²×C₃₁	1	1	yes	characteristic, complemented
574	#485	C₂²×C₃₁	1	2	yes	—
575	#485	C₂²×C₃₁	1	2	yes	complemented
576	#482	C₂²×C₃₁	1	2	yes	—
577	#482	C₂²×C₃₁	1	2	yes	complemented
578	#481	C₂²×C₃₁	1	2	yes	complemented
579	#480	C₂²×C₃₁	1	2	yes	complemented
580	#479	C₂²×C₃₁	1	2	yes	complemented
581	#479	C₂²×C₃₁	1	2	yes	complemented
582	#469	C₂²×C₃₁	1	2	yes	complemented
583	#468	C₂²×C₃₁	1	2	yes	complemented
584	#467	C₂²×C₃₁	1	2	yes	complemented
585	#466	C₂²×C₃₁	1	2	yes	complemented
586	#466	C₂²×C₃₁	1	2	yes	complemented
587	#465	C₂²×C₃₁	1	2	yes	complemented
588	#465	C₂²×C₃₁	1	2	yes	complemented
589	#465	C₂²×C₃₁	1	2	yes	complemented
590	#464	C₂²×C₃₁	1	2	yes	complemented
591	#463	C₂²×C₃₁	1	2	yes	complemented
592	#462	C₂²×C₃₁	1	2	yes	complemented
593	#460	C₂²×C₃₁	1	2	yes	complemented
594	#460	C₂²×C₃₁	1	2	yes	complemented
595	#459	C₂²×C₃₁	1	2	yes	complemented
596	#452	C₂²×C₃₁	1	2	yes	—
597	#452	C₂²×C₃₁	1	2	yes	—
598	#452	C₂²×C₃₁	1	2	yes	—
599	#452	C₂²×C₃₁	1	2	yes	complemented
600	#452	C₂²×C₃₁	1	2	yes	complemented
601	#451	C₂²×C₃₁	1	2	yes	—
602	#451	C₂²×C₃₁	1	2	yes	complemented
603	#450	C₂²×C₃₁	1	2	yes	—
604	#449	C₂²×C₃₁	1	2	yes	—
605	#449	C₂²×C₃₁	1	2	yes	—
606	#449	C₂²×C₃₁	1	2	yes	—
607	#449	C₂²×C₃₁	1	2	yes	complemented
608	#449	C₂²×C₃₁	1	2	yes	complemented
609	#449	C₂²×C₃₁	1	2	yes	complemented
610	#449	C₂²×C₃₁	1	2	yes	complemented
611	#448	C₂²×C₃₁	1	2	yes	—
612	#448	C₂²×C₃₁	1	2	yes	complemented
613	#447	C₂²×C₃₁	1	2	yes	—
614	#441	C₂²×C₃₁	1	2	yes	complemented
615	#440	C₂²×C₃₁	1	2	yes	complemented
616	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	complemented
617	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
618	#435	C₂²×C₃₁	1	2	yes	complemented
619	#435	C₂²×C₃₁	1	2	yes	complemented
620	C₈×D₄	C₂²×C₃₁	1	2	yes	complemented
621	C₈×D₄	C₂²×C₃₁	1	2	yes	complemented
622	#433	C₂²×C₃₁	1	1	yes	characteristic
623	#433	C₂²×C₃₁	1	1	yes	characteristic
624	#417	C₂²×C₃₁	1	2	yes	complemented
625	#416	C₂²×C₃₁	1	2	yes	—
626	#416	C₂²×C₃₁	1	2	yes	—
627	C₂×#103	C₂²×C₃₁	1	2	yes	complemented
628	#408	C₂²×C₃₁	1	2	yes	—
629	C₂×C₂²⋊C₈	C₂²×C₃₁	1	2	yes	—
630	C₂×C₃₁	—	4	2	no	—
631	C₂×C₃₁	—	4	2	no	—
632	C₂×C₃₁	—	4	1	no	—
633	C₂×C₃₁	—	8	2	no	—
634	C₂×C₃₁	—	8	1	no	—
635	C₂×C₃₁	—	8	1	no	—
636	C₂×C₃₁	—	8	1	no	—
637	C₂×C₃₁	#3484	1	1	yes	characteristic
638	C₂×C₃₁	#3584	1	2	yes	—
639	2₋¹⁺⁴	—	4	4	no	—
640	C₂×#41	—	2	2	no	—
641	C₂×#41	—	2	1	no	—
642	C₂×#41	—	2	2	no	—
643	C₂×#41	—	4	4	no	—
644	C₂×#41	C₂³×C₃₁	1	2	yes	—
645	C₂×#41	C₂³×C₃₁	1	2	yes	—
646	C₂×#41	C₂³×C₃₁	1	2	yes	—
647	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
648	C₂×#41	C₂³×C₃₁	1	2	yes	—
649	C₂×#41	C₂³×C₃₁	1	2	yes	—
650	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
651	C₂²×Q₈	—	2	1	no	—
652	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
653	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
654	C₂²×D₄	—	2	1	no	—
655	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
656	C₂³×C₄	—	2	1	no	—
657	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
658	#137	—	4	4	no	—
659	#135	—	4	4	no	—
660	#135	—	4	4	no	—
661	#135	—	4	4	no	—
662	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
663	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
664	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
665	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
666	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
667	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
668	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
669	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
670	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
671	C₂×D₈	C₂³×C₃₁	1	2	yes	—
672	C₂×D₈	C₂³×C₃₁	1	2	yes	—
673	C₂×D₈	C₂³×C₃₁	1	2	yes	—
674	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
675	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
676	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
677	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
678	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
679	#127	—	2	2	no	—
680	#127	—	2	2	no	—
681	#127	—	2	1	no	—
682	#127	—	2	2	no	—
683	#127	C₂³×C₃₁	1	1	yes	characteristic
684	#127	C₂³×C₃₁	1	1	yes	characteristic
685	#127	C₂³×C₃₁	1	1	yes	characteristic
686	#126	—	2	2	no	—
687	#126	—	2	2	no	—
688	#126	—	2	2	no	—
689	#125	—	2	2	no	—
690	#125	—	2	2	no	—
691	#125	C₂³×C₃₁	1	1	yes	characteristic
692	#125	C₂³×C₃₁	1	1	yes	characteristic
693	#124	—	2	1	no	—
694	#124	—	2	2	no	—
695	#124	—	2	2	no	—
696	#124	C₂³×C₃₁	1	1	yes	characteristic
697	#124	C₂³×C₃₁	1	1	yes	characteristic
698	#123	—	2	2	no	—
699	#123	—	2	1	no	—
700	#123	—	2	2	no	—
701	#123	—	2	2	no	—
702	#123	—	2	2	no	—
703	#123	—	2	2	no	—
704	#123	—	2	2	no	—
705	#123	D₄×C₃₁	1	2	yes	—
706	C₂²⋊Q₈	—	2	2	no	—
707	C₂²⋊Q₈	—	2	2	no	—
708	C₂²⋊Q₈	—	2	2	no	—
709	C₂²⋊Q₈	D₄×C₃₁	1	2	yes	—
710	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
711	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
712	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
713	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
714	#121	—	2	2	no	—
715	#121	—	2	2	no	—
716	#121	—	2	2	no	—
717	#121	—	2	2	no	—
718	#121	—	2	2	no	—
719	#121	—	2	2	no	—
720	#121	—	2	2	no	—
721	#121	—	2	2	no	—
722	#121	—	2	2	no	—
723	#121	—	2	2	no	—
724	#121	—	2	2	no	—
725	#121	—	2	2	no	—
726	#121	—	2	2	no	—
727	#121	—	2	2	no	—
728	#121	—	2	2	no	—
729	#121	D₄×C₃₁	1	2	yes	—
730	#121	C₂³×C₃₁	1	2	yes	—
731	#121	C₂³×C₃₁	1	2	yes	—
732	#121	C₂³×C₃₁	1	2	yes	—
733	#121	C₂³×C₃₁	1	2	yes	—
734	#121	C₂³×C₃₁	1	2	yes	—
735	#121	C₂³×C₃₁	1	2	yes	—
736	#120	—	2	1	no	—
737	#120	—	2	2	no	—
738	#120	—	2	2	no	—
739	#120	—	2	2	no	—
740	#120	D₄×C₃₁	1	2	yes	—
741	C₄×Q₈	—	2	2	no	—
742	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
743	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
744	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
745	C₄×D₄	—	2	2	no	—
746	C₄×D₄	—	2	2	no	—
747	C₄×D₄	—	2	2	no	—
748	C₄×D₄	—	2	2	no	—
749	C₄×D₄	—	2	2	no	—
750	C₄×D₄	—	2	2	no	—
751	C₄×D₄	—	2	2	no	—
752	C₄×D₄	—	2	2	no	—
753	C₄×D₄	—	2	2	no	—
754	C₄×D₄	C₂³×C₃₁	1	2	yes	—
755	C₄×D₄	C₂³×C₃₁	1	2	yes	—
756	C₄×D₄	C₂³×C₃₁	1	2	yes	—
757	#117	—	2	2	no	—
758	#117	—	2	2	no	—
759	#117	C₂³×C₃₁	1	1	yes	characteristic
760	#117	C₂³×C₃₁	1	2	yes	—
761	#117	C₂³×C₃₁	1	1	yes	characteristic
762	C₂×C₄⋊C₄	—	2	2	no	—
763	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
764	#107	C₂³×C₃₁	1	2	yes	—
765	#107	C₂³×C₃₁	1	2	yes	—
766	#106	C₂³×C₃₁	1	2	yes	—
767	#106	C₂³×C₃₁	1	2	yes	—
768	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
769	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
770	#103	C₂³×C₃₁	1	2	yes	—
771	#103	C₂³×C₃₁	1	2	yes	—
772	#103	C₂³×C₃₁	1	2	yes	—
773	#103	C₂³×C₃₁	1	2	yes	—
774	#103	C₂³×C₃₁	1	2	yes	—
775	#103	C₂³×C₃₁	1	2	yes	—
776	#103	C₂³×C₃₁	1	2	yes	—
777	#103	C₂³×C₃₁	1	2	yes	—
778	#102	C₂³×C₃₁	1	2	yes	—
779	#102	C₂³×C₃₁	1	2	yes	—
780	#102	C₂³×C₃₁	1	2	yes	—
781	#102	C₂³×C₃₁	1	2	yes	—
782	#102	C₂³×C₃₁	1	2	yes	—
783	#102	C₂³×C₃₁	1	2	yes	—
784	#102	C₂³×C₃₁	1	2	yes	—
785	#102	C₂³×C₃₁	1	2	yes	—
786	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
787	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
788	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
789	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
790	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
791	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
792	#97	C₂³×C₃₁	1	1	yes	characteristic
793	#97	C₂³×C₃₁	1	1	yes	characteristic
794	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
795	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
796	C₃₁	#61637	1	1	yes	characteristic, direct product factor, Sylow
797	C₂⁴	—	2	1	no	—
798	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
799	#41	—	2	4	no	—
800	#41	—	2	4	no	—
801	#41	—	2	4	no	—
802	#41	—	4	2	no	—
803	#41	—	4	2	no	—
804	#41	—	4	2	no	—
805	#41	—	4	2	no	—
806	#41	—	4	2	no	—
807	#41	—	4	8	no	—
808	#41	—	4	2	no	—
809	#41	—	4	2	no	—
810	#41	—	4	2	no	—
811	#41	—	4	2	no	—
812	#41	—	4	8	no	—
813	#41	—	4	4	no	—
814	C₂×Q₈	—	2	4	no	—
815	C₂×Q₈	—	2	1	no	—
816	C₂×Q₈	—	2	2	no	—
817	C₂×Q₈	—	2	4	no	—
818	C₂×Q₈	—	4	2	no	—
819	C₂×Q₈	—	4	4	no	—
820	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
821	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
822	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
823	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
824	C₂×D₄	—	2	1	no	—
825	C₂×D₄	—	2	2	no	—
826	C₂×D₄	—	2	2	no	—
827	C₂×D₄	—	2	2	no	—
828	C₂×D₄	—	2	2	no	—
829	C₂×D₄	—	2	2	no	—
830	C₂×D₄	—	2	2	no	—
831	C₂×D₄	—	2	2	no	—
832	C₂×D₄	—	2	2	no	—
833	C₂×D₄	—	2	2	no	—
834	C₂×D₄	—	2	2	no	—
835	C₂×D₄	—	2	2	no	—
836	C₂×D₄	—	2	1	no	—
837	C₂×D₄	—	2	2	no	—
838	C₂×D₄	—	2	2	no	—
839	C₂×D₄	—	2	2	no	—
840	C₂×D₄	—	4	2	no	—
841	C₂×D₄	—	4	4	no	—
842	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
843	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
844	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
845	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
846	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
847	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
848	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
849	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
850	C₂²×C₄	—	2	1	no	—
851	C₂²×C₄	—	2	2	no	—
852	C₂²×C₄	—	2	2	no	—
853	C₂²×C₄	—	2	2	no	—
854	C₂²×C₄	—	2	1	no	—
855	C₂²×C₄	—	2	2	no	—
856	C₂²×C₄	—	2	2	no	—
857	C₂²×C₄	—	2	2	no	—
858	C₂²×C₄	—	2	2	no	—
859	C₂²×C₄	—	2	2	no	—
860	C₂²×C₄	—	4	2	no	—
861	C₂²×C₄	—	4	4	no	—
862	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
863	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
864	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
865	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
866	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
867	Q₁₆	—	2	4	no	—
868	Q₁₆	—	2	4	no	—
869	Q₁₆	—	4	2	no	—
870	SD₁₆	—	2	4	no	—
871	SD₁₆	—	2	4	no	—
872	SD₁₆	—	4	2	no	—
873	SD₁₆	—	4	2	no	—
874	SD₁₆	—	4	2	no	—
875	SD₁₆	—	4	2	no	—
876	D₈	—	4	2	no	—
877	D₈	—	4	2	no	—
878	D₈	—	4	2	no	—
879	M₁₆	—	4	2	no	—
880	C₂×C₈	—	4	2	no	—
881	C₂×C₈	—	4	2	no	—
882	C₂×C₈	—	4	2	no	—
883	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
884	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
885	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
886	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
887	C₄⋊C₄	—	2	2	no	—
888	C₄⋊C₄	—	2	2	no	—
889	C₄⋊C₄	—	2	2	no	—
890	C₄⋊C₄	—	2	2	no	—
891	C₄⋊C₄	—	2	2	no	—
892	C₄⋊C₄	—	2	2	no	—
893	C₄⋊C₄	—	2	2	no	—
894	C₄⋊C₄	—	2	2	no	—
895	C₄⋊C₄	—	2	2	no	—
896	C₄⋊C₄	—	2	2	no	—
897	C₄⋊C₄	—	2	2	no	—
898	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
899	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
900	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
901	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
902	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
903	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
904	C₂²⋊C₄	—	2	1	no	—
905	C₂²⋊C₄	—	2	2	no	—
906	C₂²⋊C₄	—	2	2	no	—
907	C₂²⋊C₄	—	2	2	no	—
908	C₂²⋊C₄	—	2	2	no	—
909	C₂²⋊C₄	—	2	2	no	—
910	C₂²⋊C₄	—	2	2	no	—
911	C₂²⋊C₄	—	2	2	no	—
912	C₂²⋊C₄	—	2	2	no	—
913	C₂²⋊C₄	—	2	2	no	—
914	C₂²⋊C₄	—	2	2	no	—
915	C₂²⋊C₄	—	2	2	no	—
916	C₂²⋊C₄	—	2	2	no	—
917	C₂²⋊C₄	—	2	2	no	—
918	C₂²⋊C₄	—	2	2	no	—
919	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
920	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
921	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
922	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
923	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
924	C₄²	—	2	2	no	—
925	C₄²	—	2	2	no	—
926	C₄²	—	2	2	no	—
927	C₄²	—	2	2	no	—
928	C₄²	—	2	1	no	—
929	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
930	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
931	C₂³	—	2	2	no	—
932	C₂³	—	2	1	no	—
933	C₂³	—	2	1	no	—
934	C₂³	—	2	1	no	—
935	C₂³	—	4	1	no	—
936	C₂³	—	4	2	no	—
937	C₂³	—	4	2	no	—
938	C₂³	—	8	2	no	—
939	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
940	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
941	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
942	Q₈	—	2	4	no	—
943	Q₈	—	2	2	no	—
944	Q₈	—	2	2	no	—
945	Q₈	—	2	2	no	—
946	Q₈	—	2	2	no	—
947	Q₈	—	4	1	no	—
948	Q₈	—	4	4	no	—
949	Q₈	C₃₁×H(5,𝔽₂)	1	4	yes	—
950	D₄	—	2	2	no	—
951	D₄	—	2	2	no	—
952	D₄	—	2	2	no	—
953	D₄	—	2	2	no	—
954	D₄	—	2	2	no	—
955	D₄	—	4	2	no	—
956	D₄	—	4	2	no	—
957	D₄	—	4	1	no	—
958	D₄	—	4	2	no	—
959	D₄	—	4	4	no	—
960	D₄	—	4	4	no	—
961	D₄	—	4	4	no	—
962	D₄	—	4	2	no	—
963	D₄	—	4	2	no	—
964	D₄	—	8	2	no	—
965	D₄	—	8	2	no	—
966	D₄	—	8	2	no	—
967	D₄	—	8	2	no	—
968	D₄	—	8	2	no	—
969	D₄	—	8	2	no	—
970	D₄	—	8	2	no	—
971	D₄	—	8	2	no	—
972	D₄	—	8	2	no	—
973	D₄	—	8	2	no	—
974	D₄	—	8	2	no	—
975	C₂×C₄	—	2	4	no	—
976	C₂×C₄	—	2	2	no	—
977	C₂×C₄	—	2	2	no	—
978	C₂×C₄	—	2	2	no	—
979	C₂×C₄	—	2	2	no	—
980	C₂×C₄	—	2	2	no	—
981	C₂×C₄	—	2	2	no	—
982	C₂×C₄	—	2	2	no	—
983	C₂×C₄	—	2	2	no	—
984	C₂×C₄	—	2	2	no	—
985	C₂×C₄	—	2	2	no	—
986	C₂×C₄	—	2	1	no	—
987	C₂×C₄	—	4	1	no	—
988	C₂×C₄	—	4	2	no	—
989	C₂×C₄	—	4	4	no	—
990	C₂×C₄	—	4	4	no	—
991	C₂×C₄	—	4	4	no	—
992	C₂×C₄	—	4	4	no	—
993	C₂×C₄	—	4	2	no	—
994	C₂×C₄	—	8	2	no	—
995	C₂×C₄	—	8	2	no	—
996	C₂×C₄	—	8	2	no	—
997	C₂×C₄	—	8	2	no	—
998	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
999	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1000	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1001	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1002	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1003	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1004	C₈	—	2	2	no	—
1005	C₈	—	2	2	no	—
1006	C₈	—	2	2	no	—
1007	C₈	—	2	2	no	—
1008	C₂²	—	2	1	no	—
1009	C₂²	—	2	2	no	—
1010	C₂²	—	2	2	no	—
1011	C₂²	—	2	2	no	—
1012	C₂²	—	2	2	no	—
1013	C₂²	—	2	2	no	—
1014	C₂²	—	2	2	no	—
1015	C₂²	—	2	2	no	—
1016	C₂²	—	4	1	no	—
1017	C₂²	—	4	1	no	—
1018	C₂²	—	4	1	no	—
1019	C₂²	—	4	2	no	—
1020	C₂²	—	4	2	no	—
1021	C₂²	—	4	2	no	—
1022	C₂²	—	4	2	no	—
1023	C₂²	—	4	2	no	—
1024	C₂²	—	4	2	no	—
1025	C₂²	—	8	2	no	—
1026	C₂²	—	8	4	no	—
1027	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1028	C₄	—	2	4	no	—
1029	C₄	—	2	2	no	—
1030	C₄	—	2	1	no	—
1031	C₄	—	2	2	no	—
1032	C₄	—	2	2	no	—
1033	C₄	—	2	2	no	—
1034	C₄	—	4	1	no	—
1035	C₄	—	4	2	no	—
1036	C₄	—	4	2	no	—
1037	C₄	—	4	2	no	—
1038	C₄	—	4	2	no	—
1039	C₄	C₂×C₃₁×H(5,𝔽₂)	1	2	yes	—
1040	C₂	—	4	1	no	—
1041	C₂	—	4	2	no	—
1042	C₂	—	4	2	no	—
1043	C₂	—	8	1	no	—
1044	C₂	—	8	1	no	—
1045	C₂	—	8	1	no	—
1046	C₂	—	8	2	no	—
1047	C₂	C₃₁×#3484	1	1	yes	characteristic
1048	C₂	C₃₁×#3584	1	2	yes	—

	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 ◁ C₃₁×#525 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3539	C₂	semidirect
2. C₃₁×#3487	C₂	semidirect
3. C₃₁×#3317	C₂	semidirect
4. C₃₁×#3309	C₂	semidirect
5. C₃₁×#3301	C₂	semidirect
6. C₃₁×#3300	C₂	semidirect
7. C₃₁×#3287	C₂	semidirect
8. C₃₁×#3284	C₂	semidirect
9. C₃₁×#3271	C₂	semidirect
10. C₃₁×#3269	C₂	semidirect
11. C₃₁×#3222	C₂	semidirect
12. C₃₁×#3220	C₂	semidirect
13. C₃₁×#3198	C₂	semidirect
14. C₃₁×#3191	C₂	semidirect
15. C₃₁×#3127	C₂	semidirect
16. C₃₁×#3126	C₂	semidirect
17. C₃₁×#3013	C₂	semidirect
18. C₃₁×#3002	C₂	semidirect
19. C₃₁×#2977	C₂	semidirect
22. C₂×C₃₁×#137	C₂²	semidirect
25. C₂×C₃₁×#135	C₂²	semidirect
28. C₃₁×#553	C₂²	semidirect
29. C₃₁×#552	C₂²	semidirect
33. C₃₁×#550	C₂²	semidirect
37. C₃₁×#547	C₂²	semidirect
51. C₃₁×#497	C₂²	semidirect
52. C₃₁×#496	C₂²	semidirect
53. C₃₁×#493	C₂²	semidirect
54. C₃₁×#492	C₂²	semidirect
55. C₃₁×#490	C₂²	semidirect
56. C₃₁×#490	C₂²	semidirect
57. C₃₁×#488	C₂²	semidirect
58. C₃₁×#488	C₂²	semidirect
60. C₃₁×#485	C₂²	semidirect
62. C₃₁×#482	C₂²	semidirect
63. C₃₁×#481	C₂²	semidirect
64. C₃₁×#480	C₂²	semidirect
65. C₃₁×#479	C₂²	semidirect
66. C₃₁×#479	C₂²	semidirect
67. C₃₁×#469	C₂²	semidirect
68. C₃₁×#468	C₂²	semidirect
69. C₃₁×#467	C₂²	semidirect
70. C₃₁×#466	C₂²	semidirect
71. C₃₁×#466	C₂²	semidirect
72. C₃₁×#465	C₂²	semidirect
73. C₃₁×#465	C₂²	semidirect
74. C₃₁×#465	C₂²	semidirect
75. C₃₁×#464	C₂²	semidirect
76. C₃₁×#463	C₂²	semidirect
77. C₃₁×#462	C₂²	semidirect
78. C₃₁×#460	C₂²	semidirect
79. C₃₁×#460	C₂²	semidirect
80. C₃₁×#459	C₂²	semidirect
84. C₃₁×#452	C₂²	semidirect
85. C₃₁×#452	C₂²	semidirect
87. C₃₁×#451	C₂²	semidirect
92. C₃₁×#449	C₂²	semidirect
93. C₃₁×#449	C₂²	semidirect
94. C₃₁×#449	C₂²	semidirect
95. C₃₁×#449	C₂²	semidirect
97. C₃₁×#448	C₂²	semidirect
99. C₃₁×#441	C₂²	semidirect
100. C₃₁×#440	C₂²	semidirect
101. C₄×Q₁₆×C₃₁	C₂²	semidirect
102. C₄×SD₁₆×C₃₁	C₂²	semidirect
103. C₃₁×#435	C₂²	semidirect
104. C₃₁×#435	C₂²	semidirect
105. C₈×D₄×C₃₁	C₂²	semidirect
106. C₈×D₄×C₃₁	C₂²	semidirect
109. C₃₁×#417	C₂²	semidirect
112. C₂×C₃₁×#103	C₂²	semidirect
406. #61637	C₃₁	direct (N × H)
484. #3539	C₂×C₃₁	semidirect
485. #3487	C₂×C₃₁	semidirect
486. #3317	C₂×C₃₁	semidirect
487. #3309	C₂×C₃₁	semidirect
488. #3301	C₂×C₃₁	semidirect
489. #3300	C₂×C₃₁	semidirect
490. #3287	C₂×C₃₁	semidirect
491. #3284	C₂×C₃₁	semidirect
492. #3271	C₂×C₃₁	semidirect
493. #3269	C₂×C₃₁	semidirect
494. #3222	C₂×C₃₁	semidirect
495. #3220	C₂×C₃₁	semidirect
496. #3198	C₂×C₃₁	semidirect
497. #3191	C₂×C₃₁	semidirect
498. #3127	C₂×C₃₁	semidirect
499. #3126	C₂×C₃₁	semidirect
500. #3013	C₂×C₃₁	semidirect
501. #3002	C₂×C₃₁	semidirect
502. #2977	C₂×C₃₁	semidirect
537. C₂×#137	C₂²×C₃₁	semidirect
540. C₂×#135	C₂²×C₃₁	semidirect
543. #553	C₂²×C₃₁	semidirect
544. #552	C₂²×C₃₁	semidirect
548. #550	C₂²×C₃₁	semidirect
552. #547	C₂²×C₃₁	semidirect
566. #497	C₂²×C₃₁	semidirect
567. #496	C₂²×C₃₁	semidirect
568. #493	C₂²×C₃₁	semidirect
569. #492	C₂²×C₃₁	semidirect
570. #490	C₂²×C₃₁	semidirect
571. #490	C₂²×C₃₁	semidirect
572. #488	C₂²×C₃₁	semidirect
573. #488	C₂²×C₃₁	semidirect
575. #485	C₂²×C₃₁	semidirect
577. #482	C₂²×C₃₁	semidirect
578. #481	C₂²×C₃₁	semidirect
579. #480	C₂²×C₃₁	semidirect
580. #479	C₂²×C₃₁	semidirect
581. #479	C₂²×C₃₁	semidirect
582. #469	C₂²×C₃₁	semidirect
583. #468	C₂²×C₃₁	semidirect
584. #467	C₂²×C₃₁	semidirect
585. #466	C₂²×C₃₁	semidirect
586. #466	C₂²×C₃₁	semidirect
587. #465	C₂²×C₃₁	semidirect
588. #465	C₂²×C₃₁	semidirect
589. #465	C₂²×C₃₁	semidirect
590. #464	C₂²×C₃₁	semidirect
591. #463	C₂²×C₃₁	semidirect
592. #462	C₂²×C₃₁	semidirect
593. #460	C₂²×C₃₁	semidirect
594. #460	C₂²×C₃₁	semidirect
595. #459	C₂²×C₃₁	semidirect
599. #452	C₂²×C₃₁	semidirect
600. #452	C₂²×C₃₁	semidirect
602. #451	C₂²×C₃₁	semidirect
607. #449	C₂²×C₃₁	semidirect
608. #449	C₂²×C₃₁	semidirect
609. #449	C₂²×C₃₁	semidirect
610. #449	C₂²×C₃₁	semidirect
612. #448	C₂²×C₃₁	semidirect
614. #441	C₂²×C₃₁	semidirect
615. #440	C₂²×C₃₁	semidirect
616. C₄×Q₁₆	C₂²×C₃₁	semidirect
617. C₄×SD₁₆	C₂²×C₃₁	semidirect
618. #435	C₂²×C₃₁	semidirect
619. #435	C₂²×C₃₁	semidirect
620. C₈×D₄	C₂²×C₃₁	semidirect
621. C₈×D₄	C₂²×C₃₁	semidirect
624. #417	C₂²×C₃₁	semidirect
627. C₂×#103	C₂²×C₃₁	semidirect
796. C₃₁	#61637	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×#3539	2
C₃₁×#3487	2
C₃₁×#3317	2
C₃₁×#3309	2
C₃₁×#3301	2
C₃₁×#3300	2
C₃₁×#3287	2
C₃₁×#3284	2
C₃₁×#3271	2
C₃₁×#3269	2
C₃₁×#3222	2
C₃₁×#3220	2
C₃₁×#3198	2
C₃₁×#3191	2
C₃₁×#3127	2
C₃₁×#3126	2
C₃₁×#3013	2
C₃₁×#3002	2
C₃₁×#2977	2
#61637	31

Subgroups — C31×#61637 #21518396

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61637 #21518396