Subgroups — C₃₁×#61064 #21517823

Order 7936.

2682 conjugacy classes of subgroups.

The subgroup lattice has 834 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#578	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃₁×#575	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3489	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3276	C₂	1	4	yes	maximal, complemented
5	C₃₁×#3275	C₂	1	4	yes	maximal, complemented
6	C₃₁×#3270	C₂	1	4	yes	maximal, complemented
7	C₃₁×#3267	C₂	1	4	yes	maximal, complemented
8	C₃₁×#3156	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#3060	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₃₁×#470	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#3046	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3013	C₂	1	2	yes	maximal, complemented
13	C₃₁×#3007	C₂	1	2	yes	maximal, complemented
14	C₃₁×#2952	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#2930	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₃₁×2₋¹⁺⁴	C₂²	1	2	yes	complemented
17	C₂²×#41×C₃₁	C₂²	1	2	yes	—
18	C₃₁×#578	—	2	8	no	—
19	C₃₁×#575	—	2	8	no	—
20	C₂×C₃₁×#137	C₂²	1	2	yes	—
21	C₂×C₃₁×#137	C₂²	1	2	yes	—
22	C₂×C₃₁×#137	C₂²	1	2	yes	complemented
23	C₂×C₃₁×#137	C₂²	1	4	yes	complemented
24	C₂×C₃₁×#137	C₂²	1	2	yes	complemented
25	C₂×C₃₁×AGL(1,ℤ/8)	C₂²	1	2	yes	—
26	C₂×C₃₁×AGL(1,ℤ/8)	C₂²	1	2	yes	—
27	C₂×C₃₁×#135	C₂²	1	1	yes	characteristic
28	C₂×C₃₁×#135	C₂²	1	2	yes	—
29	C₂×C₃₁×#135	C₂²	1	1	yes	characteristic
30	C₂×C₃₁×#135	C₂²	1	2	yes	complemented
31	C₂²×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
32	C₂²×Q₁₆×C₃₁	C₂²	1	2	yes	complemented
33	C₂×C₃₁×#131	C₂²	1	1	yes	characteristic, complemented
34	C₂²×M₁₆×C₃₁	C₂²	1	1	yes	characteristic
35	D₄×Q₈×C₃₁	C₂²	1	4	yes	complemented
36	C₃₁×#548	C₂²	1	4	yes	—
37	C₃₁×#547	—	2	4	no	—
38	C₃₁×#547	C₂²	1	4	yes	—
39	C₃₁×#546	—	2	4	no	—
40	C₃₁×#546	C₂²	1	4	yes	complemented
41	C₃₁×#537	—	2	2	no	—
42	C₃₁×#537	C₂²	1	2	yes	complemented
43	C₃₁×#536	—	2	2	no	—
44	C₃₁×#536	C₂²	1	2	yes	complemented
45	C₃₁×#525	—	2	2	no	—
46	C₃₁×#525	C₂²	1	1	yes	characteristic
47	C₂×C₃₁×C₂²⋊Q₈	—	2	2	no	—
48	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	—
49	C₃₁×#520	C₂²	1	2	yes	complemented
50	C₃₁×#497	C₂²	1	4	yes	complemented
51	C₃₁×#495	C₂²	1	2	yes	complemented
52	C₃₁×#494	C₂²	1	2	yes	complemented
53	C₃₁×#470	C₂²	1	4	yes	complemented
54	C₃₁×#470	C₂²	1	4	yes	complemented
55	C₃₁×#470	C₂²	1	2	yes	complemented
56	C₃₁×#469	C₂²	1	2	yes	complemented
57	C₃₁×#465	C₂²	1	4	yes	complemented
58	C₃₁×#464	C₂²	1	4	yes	complemented
59	C₃₁×#463	C₂²	1	4	yes	complemented
60	C₃₁×#462	C₂²	1	4	yes	complemented
61	C₃₁×#461	C₂²	1	4	yes	complemented
62	C₃₁×#452	C₂²	1	4	yes	—
63	C₃₁×#452	C₂²	1	4	yes	—
64	C₃₁×#452	C₂²	1	4	yes	complemented
65	C₃₁×#451	C₂²	1	4	yes	complemented
66	C₃₁×#451	C₂²	1	4	yes	complemented
67	C₃₁×#450	C₂²	1	4	yes	complemented
68	C₃₁×#449	C₂²	1	4	yes	complemented
69	C₃₁×#448	C₂²	1	4	yes	complemented
70	C₃₁×#442	C₂²	1	2	yes	complemented
71	C₃₁×#441	C₂²	1	2	yes	complemented
72	C₄×SD₁₆×C₃₁	C₂²	1	4	yes	complemented
73	C₃₁×#436	C₂²	1	4	yes	complemented
74	C₃₁×#435	C₂²	1	4	yes	complemented
75	C₂×C₃₁×#106	C₂²	1	1	yes	characteristic, complemented
76	C₃₁×#424	C₂²	1	1	yes	characteristic, complemented
77	C₃₁×#417	C₂²	1	2	yes	complemented
78	C₃₁×#417	C₂²	1	2	yes	complemented
79	C₂×C₃₁×#103	C₂²	1	2	yes	complemented
80	C₃₁×#408	C₂²	1	1	yes	characteristic, complemented
81	C₃₁×#407	C₂²	1	1	yes	characteristic
82	C₃₁×#405	C₂²	1	1	yes	characteristic, complemented
83	C₃₁×2₋¹⁺⁴	—	2	8	no	—
84	C₃₁×2₋¹⁺⁴	—	4	4	no	—
85	C₂×#41×C₃₁	—	2	2	no	—
86	C₂×#41×C₃₁	—	2	4	no	—
87	C₂×#41×C₃₁	—	2	2	no	—
88	C₂×#41×C₃₁	—	2	2	no	—
89	C₂×#41×C₃₁	—	2	8	no	—
90	C₂×#41×C₃₁	—	4	4	no	—
91	C₂×#41×C₃₁	C₂³	1	2	yes	—
92	C₂×#41×C₃₁	C₂³	1	4	yes	—
93	C₂×#41×C₃₁	C₂³	1	2	yes	—
94	C₂×#41×C₃₁	C₂³	1	2	yes	—
95	C₂×#41×C₃₁	C₂³	1	2	yes	—
96	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
97	C₂²×Q₈×C₃₁	—	2	2	no	—
98	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
99	C₂²×Q₈×C₃₁	C₂³	1	4	yes	—
100	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
101	C₂²×D₄×C₃₁	—	2	2	no	—
102	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
103	C₂³×C₄×C₃₁	—	2	2	no	—
104	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
105	C₃₁×#137	—	2	8	no	—
106	C₃₁×#137	—	2	8	no	—
107	C₃₁×#137	—	2	8	no	—
108	C₃₁×#137	—	2	16	no	—
109	C₃₁×#137	—	4	4	no	—
110	C₃₁×AGL(1,ℤ/8)	—	2	8	no	—
111	C₃₁×AGL(1,ℤ/8)	—	2	8	no	—
112	C₃₁×#135	—	2	8	no	—
113	C₃₁×#135	—	2	8	no	—
114	C₃₁×#135	—	2	4	no	—
115	C₃₁×#135	D₄	1	8	yes	complemented
116	C₂×Q₁₆×C₃₁	—	2	8	no	—
117	C₂×Q₁₆×C₃₁	—	2	4	no	—
118	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
119	C₂×Q₁₆×C₃₁	C₂³	1	4	yes	—
120	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
121	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
122	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
123	C₂×Q₁₆×C₃₁	C₂³	1	4	yes	—
124	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
125	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
126	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
127	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
128	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
129	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
130	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
131	C₂×D₈×C₃₁	C₂³	1	2	yes	—
132	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
133	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
134	C₃₁×#131	—	2	4	no	—
135	C₂×M₁₆×C₃₁	—	2	4	no	—
136	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
137	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
138	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
139	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
140	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
141	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
142	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
143	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
144	C₃₁×C₄⋊Q₈	—	2	4	no	—
145	C₃₁×C₄⋊Q₈	C₂³	1	4	yes	—
146	C₃₁×#124	—	2	4	no	—
147	C₃₁×#124	C₂³	1	4	yes	—
148	C₃₁×#123	—	2	4	no	—
149	C₃₁×#123	—	2	4	no	—
150	C₃₁×#123	—	2	4	no	—
151	C₃₁×#123	—	2	4	no	—
152	C₃₁×#123	D₄	1	2	yes	—
153	C₃₁×C₂²⋊Q₈	—	2	2	no	—
154	C₃₁×C₂²⋊Q₈	—	2	2	no	—
155	C₃₁×C₂²⋊Q₈	—	2	2	no	—
156	C₃₁×C₂²⋊Q₈	—	2	2	no	—
157	C₃₁×C₂²⋊Q₈	—	2	4	no	—
158	C₃₁×C₂²⋊Q₈	—	2	2	no	—
159	C₃₁×C₂²⋊Q₈	—	2	4	no	—
160	C₃₁×C₂²⋊Q₈	—	2	4	no	—
161	C₃₁×C₂²⋊Q₈	D₄	1	2	yes	—
162	C₃₁×C₂²⋊Q₈	C₂³	1	4	yes	—
163	C₃₁×C₂²⋊Q₈	C₂³	1	4	yes	—
164	C₃₁×C₂²⋊Q₈	C₂³	1	4	yes	—
165	C₃₁×#121	—	2	2	no	—
166	C₃₁×#121	—	2	4	no	—
167	C₃₁×#121	—	2	4	no	—
168	C₃₁×#121	—	2	4	no	—
169	C₃₁×#121	—	2	4	no	—
170	C₃₁×#121	D₄	1	2	yes	—
171	C₃₁×#121	C₂³	1	4	yes	—
172	C₃₁×#120	—	2	4	no	—
173	C₃₁×#120	D₄	1	2	yes	—
174	C₄×Q₈×C₃₁	C₂³	1	4	yes	—
175	C₄×D₄×C₃₁	—	2	4	no	—
176	C₄×D₄×C₃₁	—	2	4	no	—
177	C₄×D₄×C₃₁	—	2	4	no	—
178	C₄×D₄×C₃₁	C₂³	1	4	yes	—
179	C₄×D₄×C₃₁	C₂³	1	4	yes	—
180	C₃₁×#117	—	2	2	no	—
181	C₃₁×#117	C₂³	1	1	yes	characteristic
182	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
183	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
184	C₂×C₄⋊C₄×C₃₁	—	2	4	no	—
185	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
186	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
187	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
188	C₃₁×#106	C₂³	1	2	yes	—
189	C₃₁×#106	C₂³	1	2	yes	—
190	C₃₁×C₄⋊C₈	C₂³	1	4	yes	—
191	C₃₁×#103	C₂³	1	4	yes	—
192	C₃₁×#103	C₂³	1	4	yes	—
193	C₃₁×#103	C₂³	1	4	yes	—
194	C₃₁×#103	C₂³	1	4	yes	—
195	C₃₁×#102	C₂³	1	4	yes	—
196	C₃₁×#102	C₂³	1	4	yes	—
197	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
198	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
199	C₃₁×#97	C₂³	1	2	yes	—
200	C₄×C₈×C₃₁	C₂³	1	2	yes	—
201	C₂⁴×C₃₁	—	2	2	no	—
202	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
203	#41×C₃₁	—	2	2	no	—
204	#41×C₃₁	—	2	4	no	—
205	#41×C₃₁	—	2	2	no	—
206	#41×C₃₁	—	2	4	no	—
207	#41×C₃₁	—	2	8	no	—
208	#41×C₃₁	—	2	4	no	—
209	#41×C₃₁	—	2	4	no	—
210	#41×C₃₁	—	2	4	no	—
211	#41×C₃₁	—	4	8	no	—
212	#41×C₃₁	—	4	2	no	—
213	#41×C₃₁	—	4	2	no	—
214	#41×C₃₁	—	4	4	no	—
215	#41×C₃₁	—	4	8	no	—
216	#41×C₃₁	—	4	8	no	—
217	#41×C₃₁	—	4	16	no	—
218	#41×C₃₁	C₂×D₄	1	8	yes	—
219	C₂×Q₈×C₃₁	—	2	2	no	—
220	C₂×Q₈×C₃₁	—	2	4	no	—
221	C₂×Q₈×C₃₁	—	2	2	no	—
222	C₂×Q₈×C₃₁	—	2	8	no	—
223	C₂×Q₈×C₃₁	—	2	4	no	—
224	C₂×Q₈×C₃₁	—	2	4	no	—
225	C₂×Q₈×C₃₁	—	2	4	no	—
226	C₂×Q₈×C₃₁	—	4	2	no	—
227	C₂×Q₈×C₃₁	—	4	4	no	—
228	C₂×Q₈×C₃₁	—	4	8	no	—
229	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
230	C₂×Q₈×C₃₁	C₂⁴	1	4	yes	—
231	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
232	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
233	C₂×D₄×C₃₁	—	2	2	no	—
234	C₂×D₄×C₃₁	—	2	4	no	—
235	C₂×D₄×C₃₁	—	2	4	no	—
236	C₂×D₄×C₃₁	—	2	2	no	—
237	C₂×D₄×C₃₁	—	2	2	no	—
238	C₂×D₄×C₃₁	—	2	2	no	—
239	C₂×D₄×C₃₁	—	2	4	no	—
240	C₂×D₄×C₃₁	—	2	2	no	—
241	C₂×D₄×C₃₁	—	4	2	no	—
242	C₂×D₄×C₃₁	—	4	8	no	—
243	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
244	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
245	C₂×D₄×C₃₁	C₂×D₄	1	4	yes	—
246	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
247	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
248	C₂²×C₄×C₃₁	—	2	2	no	—
249	C₂²×C₄×C₃₁	—	2	2	no	—
250	C₂²×C₄×C₃₁	—	2	2	no	—
251	C₂²×C₄×C₃₁	—	2	2	no	—
252	C₂²×C₄×C₃₁	—	2	4	no	—
253	C₂²×C₄×C₃₁	—	2	2	no	—
254	C₂²×C₄×C₃₁	—	2	2	no	—
255	C₂²×C₄×C₃₁	—	2	4	no	—
256	C₂²×C₄×C₃₁	—	2	2	no	—
257	C₂²×C₄×C₃₁	—	2	2	no	—
258	C₂²×C₄×C₃₁	—	2	2	no	—
259	C₂²×C₄×C₃₁	—	2	4	no	—
260	C₂²×C₄×C₃₁	—	4	8	no	—
261	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
262	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
263	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
264	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
265	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
266	Q₁₆×C₃₁	—	2	8	no	—
267	Q₁₆×C₃₁	—	2	4	no	—
268	Q₁₆×C₃₁	—	2	4	no	—
269	Q₁₆×C₃₁	—	2	4	no	—
270	Q₁₆×C₃₁	—	2	2	no	—
271	Q₁₆×C₃₁	—	4	4	no	—
272	Q₁₆×C₃₁	C₂×D₄	1	4	yes	—
273	SD₁₆×C₃₁	—	2	4	no	—
274	SD₁₆×C₃₁	—	2	4	no	—
275	SD₁₆×C₃₁	—	2	8	no	—
276	SD₁₆×C₃₁	—	2	4	no	—
277	SD₁₆×C₃₁	—	4	4	no	—
278	SD₁₆×C₃₁	C₂×D₄	1	8	yes	—
279	D₈×C₃₁	—	2	4	no	—
280	D₈×C₃₁	—	2	2	no	—
281	D₈×C₃₁	C₂×D₄	1	4	yes	—
282	M₁₆×C₃₁	—	2	2	no	—
283	M₁₆×C₃₁	—	2	2	no	—
284	M₁₆×C₃₁	—	2	4	no	—
285	M₁₆×C₃₁	—	2	4	no	—
286	M₁₆×C₃₁	—	2	4	no	—
287	C₂×C₈×C₃₁	—	2	2	no	—
288	C₂×C₈×C₃₁	—	2	4	no	—
289	C₂×C₈×C₃₁	C₂×D₄	1	4	yes	—
290	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
291	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
292	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
293	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
294	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
295	C₄⋊C₄×C₃₁	—	2	4	no	—
296	C₄⋊C₄×C₃₁	—	2	2	no	—
297	C₄⋊C₄×C₃₁	—	2	4	no	—
298	C₄⋊C₄×C₃₁	—	2	4	no	—
299	C₄⋊C₄×C₃₁	—	2	4	no	—
300	C₄⋊C₄×C₃₁	—	2	4	no	—
301	C₄⋊C₄×C₃₁	—	2	4	no	—
302	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
303	C₄⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
304	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
305	C₂²⋊C₄×C₃₁	—	2	4	no	—
306	C₂²⋊C₄×C₃₁	—	2	4	no	—
307	C₂²⋊C₄×C₃₁	—	2	4	no	—
308	C₂²⋊C₄×C₃₁	—	2	4	no	—
309	C₂²⋊C₄×C₃₁	—	2	4	no	—
310	C₂²⋊C₄×C₃₁	—	2	4	no	—
311	C₂²⋊C₄×C₃₁	—	2	4	no	—
312	C₂²⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
313	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
314	C₂²⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
315	C₄²×C₃₁	—	2	4	no	—
316	C₄²×C₃₁	C₂⁴	1	2	yes	—
317	#61064	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
318	C₂³×C₃₁	—	2	2	no	—
319	C₂³×C₃₁	—	2	2	no	—
320	C₂³×C₃₁	—	2	2	no	—
321	C₂³×C₃₁	—	4	2	no	—
322	C₂³×C₃₁	—	4	4	no	—
323	C₂³×C₃₁	—	4	4	no	—
324	C₂³×C₃₁	—	8	2	no	—
325	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
326	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
327	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
328	Q₈×C₃₁	—	2	2	no	—
329	Q₈×C₃₁	—	2	2	no	—
330	Q₈×C₃₁	—	2	2	no	—
331	Q₈×C₃₁	—	2	4	no	—
332	Q₈×C₃₁	—	2	4	no	—
333	Q₈×C₃₁	—	2	2	no	—
334	Q₈×C₃₁	—	4	8	no	—
335	Q₈×C₃₁	—	4	4	no	—
336	Q₈×C₃₁	—	4	4	no	—
337	Q₈×C₃₁	C₂²×D₄	1	4	yes	—
338	D₄×C₃₁	—	2	8	no	—
339	D₄×C₃₁	—	2	4	no	—
340	D₄×C₃₁	—	2	2	no	—
341	D₄×C₃₁	—	2	2	no	—
342	D₄×C₃₁	—	2	2	no	—
343	D₄×C₃₁	—	2	2	no	—
344	D₄×C₃₁	—	4	4	no	—
345	D₄×C₃₁	—	4	4	no	—
346	D₄×C₃₁	—	4	4	no	—
347	D₄×C₃₁	—	4	4	no	—
348	D₄×C₃₁	—	4	8	no	—
349	D₄×C₃₁	—	4	4	no	—
350	D₄×C₃₁	—	8	4	no	—
351	D₄×C₃₁	C₂²×D₄	1	4	yes	—
352	C₂×C₄×C₃₁	—	2	2	no	—
353	C₂×C₄×C₃₁	—	2	2	no	—
354	C₂×C₄×C₃₁	—	2	4	no	—
355	C₂×C₄×C₃₁	—	2	8	no	—
356	C₂×C₄×C₃₁	—	2	2	no	—
357	C₂×C₄×C₃₁	—	2	2	no	—
358	C₂×C₄×C₃₁	—	2	2	no	—
359	C₂×C₄×C₃₁	—	2	2	no	—
360	C₂×C₄×C₃₁	—	2	4	no	—
361	C₂×C₄×C₃₁	—	2	4	no	—
362	C₂×C₄×C₃₁	—	2	2	no	—
363	C₂×C₄×C₃₁	—	4	4	no	—
364	C₂×C₄×C₃₁	—	4	4	no	—
365	C₂×C₄×C₃₁	—	4	4	no	—
366	C₂×C₄×C₃₁	—	4	8	no	—
367	C₂×C₄×C₃₁	—	4	8	no	—
368	C₂×C₄×C₃₁	—	4	4	no	—
369	C₂×C₄×C₃₁	—	4	4	no	—
370	C₂×C₄×C₃₁	—	8	4	no	—
371	C₂×C₄×C₃₁	—	8	2	no	—
372	C₂×C₄×C₃₁	C₂²×D₄	1	4	yes	—
373	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
374	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
375	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
376	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
377	C₂×C₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
378	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
379	C₈×C₃₁	—	2	2	no	—
380	C₈×C₃₁	—	2	2	no	—
381	C₈×C₃₁	—	2	2	no	—
382	C₈×C₃₁	C₂²×D₄	1	2	yes	—
383	C₈×C₃₁	C₂²×D₄	1	2	yes	—
384	C₂×#578	C₂×C₃₁	1	1	yes	characteristic, complemented
385	C₂×#575	C₂×C₃₁	1	1	yes	characteristic, complemented
386	#3489	C₂×C₃₁	1	2	yes	complemented
387	#3276	C₂×C₃₁	1	4	yes	complemented
388	#3275	C₂×C₃₁	1	4	yes	complemented
389	#3270	C₂×C₃₁	1	4	yes	complemented
390	#3267	C₂×C₃₁	1	4	yes	complemented
391	#3156	C₂×C₃₁	1	1	yes	characteristic, complemented
392	#3060	C₂×C₃₁	1	1	yes	characteristic, complemented
393	C₂×#470	C₂×C₃₁	1	1	yes	characteristic, complemented
394	#3046	C₂×C₃₁	1	2	yes	complemented
395	#3013	C₂×C₃₁	1	2	yes	complemented
396	#3007	C₂×C₃₁	1	2	yes	complemented
397	#2952	C₂×C₃₁	1	1	yes	characteristic, complemented
398	#2930	C₂×C₃₁	1	1	yes	characteristic, complemented
399	C₂²×C₃₁	—	2	2	no	—
400	C₂²×C₃₁	—	2	2	no	—
401	C₂²×C₃₁	—	2	4	no	—
402	C₂²×C₃₁	—	2	2	no	—
403	C₂²×C₃₁	—	2	2	no	—
404	C₂²×C₃₁	—	2	2	no	—
405	C₂²×C₃₁	—	2	4	no	—
406	C₂²×C₃₁	—	4	2	no	—
407	C₂²×C₃₁	—	4	2	no	—
408	C₂²×C₃₁	—	4	2	no	—
409	C₂²×C₃₁	—	4	2	no	—
410	C₂²×C₃₁	—	4	2	no	—
411	C₂²×C₃₁	—	8	2	no	—
412	C₂²×C₃₁	—	8	8	no	—
413	C₂²×C₃₁	D₄²	1	2	yes	—
414	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
415	C₄×C₃₁	—	2	4	no	—
416	C₄×C₃₁	—	2	2	no	—
417	C₄×C₃₁	—	2	4	no	—
418	C₄×C₃₁	—	2	2	no	—
419	C₄×C₃₁	—	4	4	no	—
420	C₄×C₃₁	—	4	2	no	—
421	C₄×C₃₁	—	4	4	no	—
422	C₄×C₃₁	D₄²	1	2	yes	—
423	C₄×C₃₁	C₂³×D₄	1	1	yes	characteristic
424	C₄×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
425	C₂×2₋¹⁺⁴	C₂²×C₃₁	1	2	yes	complemented
426	C₂²×#41	C₂²×C₃₁	1	2	yes	—
427	#578	—	2	8	no	—
428	#575	—	2	8	no	—
429	C₂×#137	C₂²×C₃₁	1	2	yes	—
430	C₂×#137	C₂²×C₃₁	1	2	yes	—
431	C₂×#137	C₂²×C₃₁	1	2	yes	complemented
432	C₂×#137	C₂²×C₃₁	1	4	yes	complemented
433	C₂×#137	C₂²×C₃₁	1	2	yes	complemented
434	C₂×AGL(1,ℤ/8)	C₂²×C₃₁	1	2	yes	—
435	C₂×AGL(1,ℤ/8)	C₂²×C₃₁	1	2	yes	—
436	C₂×#135	C₂²×C₃₁	1	1	yes	characteristic
437	C₂×#135	C₂²×C₃₁	1	2	yes	—
438	C₂×#135	C₂²×C₃₁	1	1	yes	characteristic
439	C₂×#135	C₂²×C₃₁	1	2	yes	complemented
440	C₂²×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
441	C₂²×Q₁₆	C₂²×C₃₁	1	2	yes	complemented
442	C₂×#131	C₂²×C₃₁	1	1	yes	characteristic, complemented
443	C₂²×M₁₆	C₂²×C₃₁	1	1	yes	characteristic
444	D₄×Q₈	C₂²×C₃₁	1	4	yes	complemented
445	#548	C₂²×C₃₁	1	4	yes	—
446	#547	—	2	4	no	—
447	#547	C₂²×C₃₁	1	4	yes	—
448	#546	—	2	4	no	—
449	#546	C₂²×C₃₁	1	4	yes	complemented
450	#537	—	2	2	no	—
451	#537	C₂²×C₃₁	1	2	yes	complemented
452	#536	—	2	2	no	—
453	#536	C₂²×C₃₁	1	2	yes	complemented
454	#525	—	2	2	no	—
455	#525	C₂²×C₃₁	1	1	yes	characteristic
456	C₂×C₂²⋊Q₈	—	2	2	no	—
457	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	—
458	#520	C₂²×C₃₁	1	2	yes	complemented
459	#497	C₂²×C₃₁	1	4	yes	complemented
460	#495	C₂²×C₃₁	1	2	yes	complemented
461	#494	C₂²×C₃₁	1	2	yes	complemented
462	#470	C₂²×C₃₁	1	4	yes	complemented
463	#470	C₂²×C₃₁	1	4	yes	complemented
464	#470	C₂²×C₃₁	1	2	yes	complemented
465	#469	C₂²×C₃₁	1	2	yes	complemented
466	#465	C₂²×C₃₁	1	4	yes	complemented
467	#464	C₂²×C₃₁	1	4	yes	complemented
468	#463	C₂²×C₃₁	1	4	yes	complemented
469	#462	C₂²×C₃₁	1	4	yes	complemented
470	#461	C₂²×C₃₁	1	4	yes	complemented
471	#452	C₂²×C₃₁	1	4	yes	—
472	#452	C₂²×C₃₁	1	4	yes	—
473	#452	C₂²×C₃₁	1	4	yes	complemented
474	#451	C₂²×C₃₁	1	4	yes	complemented
475	#451	C₂²×C₃₁	1	4	yes	complemented
476	#450	C₂²×C₃₁	1	4	yes	complemented
477	#449	C₂²×C₃₁	1	4	yes	complemented
478	#448	C₂²×C₃₁	1	4	yes	complemented
479	#442	C₂²×C₃₁	1	2	yes	complemented
480	#441	C₂²×C₃₁	1	2	yes	complemented
481	C₄×SD₁₆	C₂²×C₃₁	1	4	yes	complemented
482	#436	C₂²×C₃₁	1	4	yes	complemented
483	#435	C₂²×C₃₁	1	4	yes	complemented
484	C₂×#106	C₂²×C₃₁	1	1	yes	characteristic, complemented
485	#424	C₂²×C₃₁	1	1	yes	characteristic, complemented
486	#417	C₂²×C₃₁	1	2	yes	complemented
487	#417	C₂²×C₃₁	1	2	yes	complemented
488	C₂×#103	C₂²×C₃₁	1	2	yes	complemented
489	#408	C₂²×C₃₁	1	1	yes	characteristic, complemented
490	#407	C₂²×C₃₁	1	1	yes	characteristic
491	#405	C₂²×C₃₁	1	1	yes	characteristic, complemented
492	C₂×C₃₁	—	2	2	no	—
493	C₂×C₃₁	—	4	2	no	—
494	C₂×C₃₁	—	4	2	no	—
495	C₂×C₃₁	—	4	4	no	—
496	C₂×C₃₁	—	8	2	no	—
497	C₂×C₃₁	C₂×D₄²	1	1	yes	characteristic
498	C₂×C₃₁	#3586	1	2	yes	—
499	2₋¹⁺⁴	—	2	8	no	—
500	2₋¹⁺⁴	—	4	4	no	—
501	C₂×#41	—	2	2	no	—
502	C₂×#41	—	2	4	no	—
503	C₂×#41	—	2	2	no	—
504	C₂×#41	—	2	2	no	—
505	C₂×#41	—	2	8	no	—
506	C₂×#41	—	4	4	no	—
507	C₂×#41	C₂³×C₃₁	1	2	yes	—
508	C₂×#41	C₂³×C₃₁	1	4	yes	—
509	C₂×#41	C₂³×C₃₁	1	2	yes	—
510	C₂×#41	C₂³×C₃₁	1	2	yes	—
511	C₂×#41	C₂³×C₃₁	1	2	yes	—
512	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
513	C₂²×Q₈	—	2	2	no	—
514	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
515	C₂²×Q₈	C₂³×C₃₁	1	4	yes	—
516	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
517	C₂²×D₄	—	2	2	no	—
518	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
519	C₂³×C₄	—	2	2	no	—
520	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
521	#137	—	2	8	no	—
522	#137	—	2	8	no	—
523	#137	—	2	8	no	—
524	#137	—	2	16	no	—
525	#137	—	4	4	no	—
526	AGL(1,ℤ/8)	—	2	8	no	—
527	AGL(1,ℤ/8)	—	2	8	no	—
528	#135	—	2	8	no	—
529	#135	—	2	8	no	—
530	#135	—	2	4	no	—
531	#135	D₄×C₃₁	1	8	yes	complemented
532	C₂×Q₁₆	—	2	8	no	—
533	C₂×Q₁₆	—	2	4	no	—
534	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
535	C₂×Q₁₆	C₂³×C₃₁	1	4	yes	—
536	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
537	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
538	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
539	C₂×Q₁₆	C₂³×C₃₁	1	4	yes	—
540	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
541	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
542	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
543	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
544	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
545	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
546	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
547	C₂×D₈	C₂³×C₃₁	1	2	yes	—
548	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
549	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
550	#131	—	2	4	no	—
551	C₂×M₁₆	—	2	4	no	—
552	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
553	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
554	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
555	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
556	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
557	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
558	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
559	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
560	C₄⋊Q₈	—	2	4	no	—
561	C₄⋊Q₈	C₂³×C₃₁	1	4	yes	—
562	#124	—	2	4	no	—
563	#124	C₂³×C₃₁	1	4	yes	—
564	#123	—	2	4	no	—
565	#123	—	2	4	no	—
566	#123	—	2	4	no	—
567	#123	—	2	4	no	—
568	#123	D₄×C₃₁	1	2	yes	—
569	C₂²⋊Q₈	—	2	2	no	—
570	C₂²⋊Q₈	—	2	2	no	—
571	C₂²⋊Q₈	—	2	2	no	—
572	C₂²⋊Q₈	—	2	2	no	—
573	C₂²⋊Q₈	—	2	4	no	—
574	C₂²⋊Q₈	—	2	2	no	—
575	C₂²⋊Q₈	—	2	4	no	—
576	C₂²⋊Q₈	—	2	4	no	—
577	C₂²⋊Q₈	D₄×C₃₁	1	2	yes	—
578	C₂²⋊Q₈	C₂³×C₃₁	1	4	yes	—
579	C₂²⋊Q₈	C₂³×C₃₁	1	4	yes	—
580	C₂²⋊Q₈	C₂³×C₃₁	1	4	yes	—
581	#121	—	2	2	no	—
582	#121	—	2	4	no	—
583	#121	—	2	4	no	—
584	#121	—	2	4	no	—
585	#121	—	2	4	no	—
586	#121	D₄×C₃₁	1	2	yes	—
587	#121	C₂³×C₃₁	1	4	yes	—
588	#120	—	2	4	no	—
589	#120	D₄×C₃₁	1	2	yes	—
590	C₄×Q₈	C₂³×C₃₁	1	4	yes	—
591	C₄×D₄	—	2	4	no	—
592	C₄×D₄	—	2	4	no	—
593	C₄×D₄	—	2	4	no	—
594	C₄×D₄	C₂³×C₃₁	1	4	yes	—
595	C₄×D₄	C₂³×C₃₁	1	4	yes	—
596	#117	—	2	2	no	—
597	#117	C₂³×C₃₁	1	1	yes	characteristic
598	C₂×C₄⋊C₄	—	2	2	no	—
599	C₂×C₄⋊C₄	—	2	2	no	—
600	C₂×C₄⋊C₄	—	2	4	no	—
601	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
602	C₂×C₂²⋊C₄	—	2	2	no	—
603	C₂×C₂²⋊C₄	—	2	4	no	—
604	#106	C₂³×C₃₁	1	2	yes	—
605	#106	C₂³×C₃₁	1	2	yes	—
606	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
607	#103	C₂³×C₃₁	1	4	yes	—
608	#103	C₂³×C₃₁	1	4	yes	—
609	#103	C₂³×C₃₁	1	4	yes	—
610	#103	C₂³×C₃₁	1	4	yes	—
611	#102	C₂³×C₃₁	1	4	yes	—
612	#102	C₂³×C₃₁	1	4	yes	—
613	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
614	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
615	#97	C₂³×C₃₁	1	2	yes	—
616	C₄×C₈	C₂³×C₃₁	1	2	yes	—
617	C₃₁	#61064	1	1	yes	characteristic, direct product factor, Sylow
618	C₂⁴	—	2	2	no	—
619	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
620	#41	—	2	2	no	—
621	#41	—	2	4	no	—
622	#41	—	2	2	no	—
623	#41	—	2	4	no	—
624	#41	—	2	8	no	—
625	#41	—	2	4	no	—
626	#41	—	2	4	no	—
627	#41	—	2	4	no	—
628	#41	—	4	8	no	—
629	#41	—	4	2	no	—
630	#41	—	4	2	no	—
631	#41	—	4	4	no	—
632	#41	—	4	8	no	—
633	#41	—	4	8	no	—
634	#41	—	4	16	no	—
635	#41	C₂×D₄×C₃₁	1	8	yes	—
636	C₂×Q₈	—	2	2	no	—
637	C₂×Q₈	—	2	4	no	—
638	C₂×Q₈	—	2	2	no	—
639	C₂×Q₈	—	2	8	no	—
640	C₂×Q₈	—	2	4	no	—
641	C₂×Q₈	—	2	4	no	—
642	C₂×Q₈	—	2	4	no	—
643	C₂×Q₈	—	4	2	no	—
644	C₂×Q₈	—	4	4	no	—
645	C₂×Q₈	—	4	8	no	—
646	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
647	C₂×Q₈	C₂⁴×C₃₁	1	4	yes	—
648	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
649	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
650	C₂×D₄	—	2	2	no	—
651	C₂×D₄	—	2	4	no	—
652	C₂×D₄	—	2	4	no	—
653	C₂×D₄	—	2	2	no	—
654	C₂×D₄	—	2	2	no	—
655	C₂×D₄	—	2	2	no	—
656	C₂×D₄	—	2	4	no	—
657	C₂×D₄	—	2	2	no	—
658	C₂×D₄	—	4	2	no	—
659	C₂×D₄	—	4	8	no	—
660	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
661	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
662	C₂×D₄	C₂×D₄×C₃₁	1	4	yes	—
663	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
664	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
665	C₂²×C₄	—	2	2	no	—
666	C₂²×C₄	—	2	2	no	—
667	C₂²×C₄	—	2	2	no	—
668	C₂²×C₄	—	2	2	no	—
669	C₂²×C₄	—	2	4	no	—
670	C₂²×C₄	—	2	2	no	—
671	C₂²×C₄	—	2	2	no	—
672	C₂²×C₄	—	2	4	no	—
673	C₂²×C₄	—	2	2	no	—
674	C₂²×C₄	—	2	2	no	—
675	C₂²×C₄	—	2	2	no	—
676	C₂²×C₄	—	2	4	no	—
677	C₂²×C₄	—	4	8	no	—
678	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
679	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
680	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
681	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
682	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
683	Q₁₆	—	2	8	no	—
684	Q₁₆	—	2	4	no	—
685	Q₁₆	—	2	4	no	—
686	Q₁₆	—	2	4	no	—
687	Q₁₆	—	2	2	no	—
688	Q₁₆	—	4	4	no	—
689	Q₁₆	C₂×D₄×C₃₁	1	4	yes	—
690	SD₁₆	—	2	4	no	—
691	SD₁₆	—	2	4	no	—
692	SD₁₆	—	2	8	no	—
693	SD₁₆	—	2	4	no	—
694	SD₁₆	—	4	4	no	—
695	SD₁₆	C₂×D₄×C₃₁	1	8	yes	—
696	D₈	—	2	4	no	—
697	D₈	—	2	2	no	—
698	D₈	C₂×D₄×C₃₁	1	4	yes	—
699	M₁₆	—	2	2	no	—
700	M₁₆	—	2	2	no	—
701	M₁₆	—	2	4	no	—
702	M₁₆	—	2	4	no	—
703	M₁₆	—	2	4	no	—
704	C₂×C₈	—	2	2	no	—
705	C₂×C₈	—	2	4	no	—
706	C₂×C₈	C₂×D₄×C₃₁	1	4	yes	—
707	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
708	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
709	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
710	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
711	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
712	C₄⋊C₄	—	2	4	no	—
713	C₄⋊C₄	—	2	2	no	—
714	C₄⋊C₄	—	2	4	no	—
715	C₄⋊C₄	—	2	4	no	—
716	C₄⋊C₄	—	2	4	no	—
717	C₄⋊C₄	—	2	4	no	—
718	C₄⋊C₄	—	2	4	no	—
719	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
720	C₄⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
721	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
722	C₂²⋊C₄	—	2	4	no	—
723	C₂²⋊C₄	—	2	4	no	—
724	C₂²⋊C₄	—	2	4	no	—
725	C₂²⋊C₄	—	2	4	no	—
726	C₂²⋊C₄	—	2	4	no	—
727	C₂²⋊C₄	—	2	4	no	—
728	C₂²⋊C₄	—	2	4	no	—
729	C₂²⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
730	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
731	C₂²⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
732	C₄²	—	2	4	no	—
733	C₄²	C₂⁴×C₃₁	1	2	yes	—
734	C₂³	—	2	2	no	—
735	C₂³	—	2	2	no	—
736	C₂³	—	2	2	no	—
737	C₂³	—	4	2	no	—
738	C₂³	—	4	4	no	—
739	C₂³	—	4	4	no	—
740	C₂³	—	8	2	no	—
741	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
742	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
743	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
744	Q₈	—	2	2	no	—
745	Q₈	—	2	2	no	—
746	Q₈	—	2	2	no	—
747	Q₈	—	2	4	no	—
748	Q₈	—	2	4	no	—
749	Q₈	—	2	2	no	—
750	Q₈	—	4	8	no	—
751	Q₈	—	4	4	no	—
752	Q₈	—	4	4	no	—
753	Q₈	C₂²×D₄×C₃₁	1	4	yes	—
754	D₄	—	2	8	no	—
755	D₄	—	2	4	no	—
756	D₄	—	2	2	no	—
757	D₄	—	2	2	no	—
758	D₄	—	2	2	no	—
759	D₄	—	2	2	no	—
760	D₄	—	4	4	no	—
761	D₄	—	4	4	no	—
762	D₄	—	4	4	no	—
763	D₄	—	4	4	no	—
764	D₄	—	4	8	no	—
765	D₄	—	4	4	no	—
766	D₄	—	8	4	no	—
767	D₄	C₂²×D₄×C₃₁	1	4	yes	—
768	C₂×C₄	—	2	2	no	—
769	C₂×C₄	—	2	2	no	—
770	C₂×C₄	—	2	4	no	—
771	C₂×C₄	—	2	8	no	—
772	C₂×C₄	—	2	2	no	—
773	C₂×C₄	—	2	2	no	—
774	C₂×C₄	—	2	2	no	—
775	C₂×C₄	—	2	2	no	—
776	C₂×C₄	—	2	4	no	—
777	C₂×C₄	—	2	4	no	—
778	C₂×C₄	—	2	2	no	—
779	C₂×C₄	—	4	4	no	—
780	C₂×C₄	—	4	4	no	—
781	C₂×C₄	—	4	4	no	—
782	C₂×C₄	—	4	8	no	—
783	C₂×C₄	—	4	8	no	—
784	C₂×C₄	—	4	4	no	—
785	C₂×C₄	—	4	4	no	—
786	C₂×C₄	—	8	4	no	—
787	C₂×C₄	—	8	2	no	—
788	C₂×C₄	C₂²×D₄×C₃₁	1	4	yes	—
789	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
790	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
791	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
792	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
793	C₂×C₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
794	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
795	C₈	—	2	2	no	—
796	C₈	—	2	2	no	—
797	C₈	—	2	2	no	—
798	C₈	C₂²×D₄×C₃₁	1	2	yes	—
799	C₈	C₂²×D₄×C₃₁	1	2	yes	—
800	C₂²	—	2	2	no	—
801	C₂²	—	2	2	no	—
802	C₂²	—	2	2	no	—
803	C₂²	—	2	4	no	—
804	C₂²	—	2	2	no	—
805	C₂²	—	2	4	no	—
806	C₂²	—	2	2	no	—
807	C₂²	—	4	2	no	—
808	C₂²	—	4	2	no	—
809	C₂²	—	4	2	no	—
810	C₂²	—	4	2	no	—
811	C₂²	—	4	2	no	—
812	C₂²	—	8	2	no	—
813	C₂²	—	8	8	no	—
814	C₂²	D₄²×C₃₁	1	2	yes	—
815	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
816	C₄	—	2	2	no	—
817	C₄	—	2	4	no	—
818	C₄	—	2	2	no	—
819	C₄	—	2	4	no	—
820	C₄	—	4	2	no	—
821	C₄	—	4	4	no	—
822	C₄	—	4	4	no	—
823	C₄	D₄²×C₃₁	1	2	yes	—
824	C₄	C₂³×D₄×C₃₁	1	1	yes	characteristic
825	C₄	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
826	C₂	—	2	2	no	—
827	C₂	—	4	2	no	—
828	C₂	—	4	2	no	—
829	C₂	—	4	4	no	—
830	C₂	—	8	2	no	—
831	C₂	C₂×D₄²×C₃₁	1	1	yes	characteristic
832	C₂	C₃₁×#3586	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. C₂×C₃₁×#578	C₂	semidirect
2. C₂×C₃₁×#575	C₂	semidirect
3. C₃₁×#3489	C₂	semidirect
4. C₃₁×#3276	C₂	semidirect
5. C₃₁×#3275	C₂	semidirect
6. C₃₁×#3270	C₂	semidirect
7. C₃₁×#3267	C₂	semidirect
8. C₃₁×#3156	C₂	semidirect
9. C₃₁×#3060	C₂	semidirect
10. C₂×C₃₁×#470	C₂	semidirect
11. C₃₁×#3046	C₂	semidirect
12. C₃₁×#3013	C₂	semidirect
13. C₃₁×#3007	C₂	semidirect
14. C₃₁×#2952	C₂	semidirect
15. C₃₁×#2930	C₂	semidirect
16. C₂×C₃₁×2₋¹⁺⁴	C₂²	semidirect
22. C₂×C₃₁×#137	C₂²	semidirect
23. C₂×C₃₁×#137	C₂²	semidirect
24. C₂×C₃₁×#137	C₂²	semidirect
30. C₂×C₃₁×#135	C₂²	semidirect
31. C₂²×Q₁₆×C₃₁	C₂²	semidirect
32. C₂²×Q₁₆×C₃₁	C₂²	semidirect
33. C₂×C₃₁×#131	C₂²	semidirect
35. D₄×Q₈×C₃₁	C₂²	semidirect
40. C₃₁×#546	C₂²	semidirect
42. C₃₁×#537	C₂²	semidirect
44. C₃₁×#536	C₂²	semidirect
49. C₃₁×#520	C₂²	semidirect
50. C₃₁×#497	C₂²	semidirect
51. C₃₁×#495	C₂²	semidirect
52. C₃₁×#494	C₂²	semidirect
53. C₃₁×#470	C₂²	semidirect
54. C₃₁×#470	C₂²	semidirect
55. C₃₁×#470	C₂²	semidirect
56. C₃₁×#469	C₂²	semidirect
57. C₃₁×#465	C₂²	semidirect
58. C₃₁×#464	C₂²	semidirect
59. C₃₁×#463	C₂²	semidirect
60. C₃₁×#462	C₂²	semidirect
61. C₃₁×#461	C₂²	semidirect
64. C₃₁×#452	C₂²	semidirect
65. C₃₁×#451	C₂²	semidirect
66. C₃₁×#451	C₂²	semidirect
67. C₃₁×#450	C₂²	semidirect
68. C₃₁×#449	C₂²	semidirect
69. C₃₁×#448	C₂²	semidirect
70. C₃₁×#442	C₂²	semidirect
71. C₃₁×#441	C₂²	semidirect
72. C₄×SD₁₆×C₃₁	C₂²	semidirect
73. C₃₁×#436	C₂²	semidirect
74. C₃₁×#435	C₂²	semidirect
75. C₂×C₃₁×#106	C₂²	semidirect
76. C₃₁×#424	C₂²	semidirect
77. C₃₁×#417	C₂²	semidirect
78. C₃₁×#417	C₂²	semidirect
79. C₂×C₃₁×#103	C₂²	semidirect
80. C₃₁×#408	C₂²	semidirect
82. C₃₁×#405	C₂²	semidirect
115. C₃₁×#135	D₄	semidirect
317. #61064	C₃₁	direct (N × H)
384. C₂×#578	C₂×C₃₁	semidirect
385. C₂×#575	C₂×C₃₁	semidirect
386. #3489	C₂×C₃₁	semidirect
387. #3276	C₂×C₃₁	semidirect
388. #3275	C₂×C₃₁	semidirect
389. #3270	C₂×C₃₁	semidirect
390. #3267	C₂×C₃₁	semidirect
391. #3156	C₂×C₃₁	semidirect
392. #3060	C₂×C₃₁	semidirect
393. C₂×#470	C₂×C₃₁	semidirect
394. #3046	C₂×C₃₁	semidirect
395. #3013	C₂×C₃₁	semidirect
396. #3007	C₂×C₃₁	semidirect
397. #2952	C₂×C₃₁	semidirect
398. #2930	C₂×C₃₁	semidirect
425. C₂×2₋¹⁺⁴	C₂²×C₃₁	semidirect
431. C₂×#137	C₂²×C₃₁	semidirect
432. C₂×#137	C₂²×C₃₁	semidirect
433. C₂×#137	C₂²×C₃₁	semidirect
439. C₂×#135	C₂²×C₃₁	semidirect
440. C₂²×Q₁₆	C₂²×C₃₁	semidirect
441. C₂²×Q₁₆	C₂²×C₃₁	semidirect
442. C₂×#131	C₂²×C₃₁	semidirect
444. D₄×Q₈	C₂²×C₃₁	semidirect
449. #546	C₂²×C₃₁	semidirect
451. #537	C₂²×C₃₁	semidirect
453. #536	C₂²×C₃₁	semidirect
458. #520	C₂²×C₃₁	semidirect
459. #497	C₂²×C₃₁	semidirect
460. #495	C₂²×C₃₁	semidirect
461. #494	C₂²×C₃₁	semidirect
462. #470	C₂²×C₃₁	semidirect
463. #470	C₂²×C₃₁	semidirect
464. #470	C₂²×C₃₁	semidirect
465. #469	C₂²×C₃₁	semidirect
466. #465	C₂²×C₃₁	semidirect
467. #464	C₂²×C₃₁	semidirect
468. #463	C₂²×C₃₁	semidirect
469. #462	C₂²×C₃₁	semidirect
470. #461	C₂²×C₃₁	semidirect
473. #452	C₂²×C₃₁	semidirect
474. #451	C₂²×C₃₁	semidirect
475. #451	C₂²×C₃₁	semidirect
476. #450	C₂²×C₃₁	semidirect
477. #449	C₂²×C₃₁	semidirect
478. #448	C₂²×C₃₁	semidirect
479. #442	C₂²×C₃₁	semidirect
480. #441	C₂²×C₃₁	semidirect
481. C₄×SD₁₆	C₂²×C₃₁	semidirect
482. #436	C₂²×C₃₁	semidirect
483. #435	C₂²×C₃₁	semidirect
484. C₂×#106	C₂²×C₃₁	semidirect
485. #424	C₂²×C₃₁	semidirect
486. #417	C₂²×C₃₁	semidirect
487. #417	C₂²×C₃₁	semidirect
488. C₂×#103	C₂²×C₃₁	semidirect
489. #408	C₂²×C₃₁	semidirect
491. #405	C₂²×C₃₁	semidirect
531. #135	D₄×C₃₁	semidirect
617. C₃₁	#61064	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃₁×#578	2
C₂×C₃₁×#575	2
C₃₁×#3489	2
C₃₁×#3276	2
C₃₁×#3275	2
C₃₁×#3270	2
C₃₁×#3267	2
C₃₁×#3156	2
C₃₁×#3060	2
C₂×C₃₁×#470	2
C₃₁×#3046	2
C₃₁×#3013	2
C₃₁×#3007	2
C₃₁×#2952	2
C₃₁×#2930	2
#61064	31

Subgroups — C31×#61064 #21517823

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61064 #21517823