Subgroups — C₃₁×#61218 #21517977

Order 7936.

2166 conjugacy classes of subgroups.

The subgroup lattice has 830 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3506	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3496	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3319	C₂	1	4	yes	maximal, complemented
4	C₃₁×#3318	C₂	1	4	yes	maximal, complemented
5	C₃₁×#3307	C₂	1	4	yes	maximal, complemented
6	C₃₁×#3306	C₂	1	4	yes	maximal, complemented
7	C₃₁×#3135	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#3099	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3077	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#3062	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3036	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3008	C₂	1	2	yes	maximal, complemented
13	C₂×C₃₁×#442	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#2932	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#2897	C₂	1	2	yes	maximal, complemented
16	C₂×C₃₁×H(5,𝔽₂)	C₂²	1	2	yes	—
17	C₂×C₃₁×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
18	C₂²×D₈×C₃₁	C₂²	1	1	yes	characteristic
19	C₂×C₃₁×#131	C₂²	1	2	yes	complemented
20	C₃₁×#559	—	2	2	no	—
21	C₃₁×#556	—	2	1	no	—
22	C₃₁×#555	C₂²	1	2	yes	complemented
23	C₃₁×#553	C₂²	1	4	yes	complemented
24	C₃₁×#550	—	2	1	no	—
25	C₃₁×#547	—	2	1	no	—
26	C₃₁×#547	C₂²	1	2	yes	complemented
27	C₃₁×#547	C₂²	1	2	yes	complemented
28	C₃₁×#546	—	2	2	no	—
29	C₃₁×#546	C₂²	1	4	yes	complemented
30	D₄²×C₃₁	—	2	1	no	—
31	D₄²×C₃₁	C₂²	1	2	yes	complemented
32	C₃₁×#538	—	2	2	no	—
33	C₃₁×#537	C₂²	1	2	yes	—
34	C₃₁×#535	C₂²	1	2	yes	complemented
35	C₃₁×#534	—	2	2	no	—
36	C₃₁×#533	C₂²	1	1	yes	characteristic, complemented
37	C₃₁×#532	C₂²	1	1	yes	characteristic
38	C₃₁×#532	C₂²	1	1	yes	characteristic
39	C₃₁×#525	—	2	2	no	—
40	C₂×C₃₁×#121	—	2	2	no	—
41	C₃₁×#520	C₂²	1	2	yes	complemented
42	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
43	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
44	C₃₁×#491	C₂²	1	2	yes	complemented
45	C₃₁×#490	C₂²	1	2	yes	complemented
46	C₃₁×#489	C₂²	1	2	yes	complemented
47	C₃₁×#489	C₂²	1	2	yes	complemented
48	C₃₁×#485	C₂²	1	4	yes	complemented
49	C₃₁×#483	C₂²	1	4	yes	complemented
50	C₃₁×#482	C₂²	1	4	yes	complemented
51	C₃₁×#481	C₂²	1	4	yes	complemented
52	C₃₁×#478	C₂²	1	4	yes	complemented
53	C₃₁×#476	C₂²	1	2	yes	complemented
54	C₃₁×#474	C₂²	1	2	yes	complemented
55	C₃₁×#469	C₂²	1	4	yes	complemented
56	C₃₁×#468	C₂²	1	4	yes	complemented
57	C₃₁×#466	C₂²	1	4	yes	complemented
58	C₃₁×#465	C₂²	1	4	yes	complemented
59	C₃₁×#463	C₂²	1	4	yes	complemented
60	C₃₁×#461	C₂²	1	2	yes	complemented
61	C₃₁×#459	C₂²	1	2	yes	complemented
62	C₃₁×#449	C₂²	1	4	yes	complemented
63	C₃₁×#449	C₂²	1	4	yes	complemented
64	C₃₁×#447	C₂²	1	4	yes	complemented
65	C₃₁×#447	C₂²	1	4	yes	complemented
66	C₃₁×#442	C₂²	1	4	yes	complemented
67	C₃₁×#442	C₂²	1	4	yes	complemented
68	C₃₁×#435	C₂²	1	4	yes	complemented
69	C₃₁×#435	C₂²	1	4	yes	complemented
70	C₃₁×#428	C₂²	1	2	yes	complemented
71	C₂×C₃₁×#106	C₂²	1	1	yes	characteristic, complemented
72	C₃₁×#423	C₂²	1	1	yes	characteristic, complemented
73	C₃₁×#418	C₂²	1	2	yes	—
74	C₃₁×#418	C₂²	1	4	yes	complemented
75	C₃₁×#417	C₂²	1	2	yes	complemented
76	C₃₁×#417	C₂²	1	4	yes	complemented
77	C₃₁×#416	C₂²	1	2	yes	complemented
78	C₃₁×#416	C₂²	1	2	yes	complemented
79	C₃₁×#416	C₂²	1	4	yes	complemented
80	C₂×C₃₁×#102	C₂²	1	1	yes	characteristic
81	C₂×C₃₁×#102	C₂²	1	4	yes	complemented
82	C₂×C₃₁×#102	C₂²	1	1	yes	characteristic, complemented
83	C₃₁×#408	C₂²	1	2	yes	complemented
84	C₂×C₃₁×#97	C₂²	1	1	yes	characteristic, complemented
85	C₃₁×H(5,𝔽₂)	—	2	8	no	—
86	C₃₁×H(5,𝔽₂)	—	4	4	no	—
87	C₂×#41×C₃₁	—	2	2	no	—
88	C₂×#41×C₃₁	—	2	2	no	—
89	C₂×#41×C₃₁	C₂³	1	2	yes	—
90	C₂×#41×C₃₁	C₂³	1	4	yes	—
91	C₂×#41×C₃₁	C₂³	1	2	yes	—
92	C₂²×D₄×C₃₁	—	2	4	no	—
93	C₂²×D₄×C₃₁	—	2	2	no	—
94	C₂²×D₄×C₃₁	—	2	2	no	—
95	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
96	C₂²×D₄×C₃₁	C₂³	1	4	yes	—
97	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
98	C₂³×C₄×C₃₁	—	2	1	no	—
99	C₂³×C₄×C₃₁	—	2	1	no	—
100	C₃₁×AGL(1,ℤ/8)	—	4	4	no	—
101	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
102	C₂×D₈×C₃₁	—	2	4	no	—
103	C₂×D₈×C₃₁	C₂³	1	4	yes	—
104	C₂×D₈×C₃₁	C₂³	1	4	yes	—
105	C₃₁×#131	—	4	4	no	—
106	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
107	C₂×M₁₆×C₃₁	C₂³	1	4	yes	—
108	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
109	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
110	C₂²×C₈×C₃₁	C₂³	1	4	yes	—
111	C₃₁×C₄⋊Q₈	D₄	1	1	yes	characteristic
112	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
113	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
114	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
115	C₃₁×#127	—	2	2	no	—
116	C₃₁×#127	D₄	1	1	yes	characteristic
117	C₃₁×#127	C₂³	1	1	yes	characteristic
118	C₃₁×#126	—	2	4	no	—
119	C₃₁×#125	C₂³	1	2	yes	—
120	C₃₁×#124	—	2	2	no	—
121	C₃₁×#124	—	2	4	no	—
122	C₃₁×#124	D₄	1	2	yes	—
123	C₃₁×#124	C₂³	1	2	yes	—
124	C₃₁×#123	—	2	4	no	—
125	C₃₁×#123	—	2	4	no	—
126	C₃₁×#123	—	2	4	no	—
127	C₃₁×#123	—	2	4	no	—
128	C₃₁×C₂²⋊Q₈	—	2	2	no	—
129	C₃₁×C₂²⋊Q₈	—	2	1	no	—
130	C₃₁×C₂²⋊Q₈	—	2	1	no	—
131	C₃₁×C₂²⋊Q₈	—	2	2	no	—
132	C₃₁×C₂²⋊Q₈	C₂³	1	4	yes	—
133	C₃₁×#121	—	2	4	no	—
134	C₃₁×#121	—	2	2	no	—
135	C₃₁×#121	—	2	2	no	—
136	C₃₁×#121	—	2	2	no	—
137	C₃₁×#121	—	2	4	no	—
138	C₃₁×#121	—	2	1	no	—
139	C₃₁×#121	—	2	1	no	—
140	C₃₁×#121	—	2	2	no	—
141	C₃₁×#121	—	2	4	no	—
142	C₃₁×#121	D₄	1	2	yes	—
143	C₃₁×#121	D₄	1	2	yes	—
144	C₃₁×#121	C₂³	1	4	yes	—
145	C₃₁×#121	C₂³	1	4	yes	—
146	C₃₁×#121	C₂³	1	4	yes	—
147	C₃₁×#120	—	2	4	no	—
148	C₃₁×#120	—	2	4	no	—
149	C₃₁×#120	—	2	4	no	—
150	C₄×Q₈×C₃₁	—	2	2	no	—
151	C₄×Q₈×C₃₁	—	2	1	no	—
152	C₄×Q₈×C₃₁	—	2	1	no	—
153	C₄×D₄×C₃₁	—	2	4	no	—
154	C₄×D₄×C₃₁	—	2	2	no	—
155	C₄×D₄×C₃₁	—	2	4	no	—
156	C₄×D₄×C₃₁	—	2	1	no	—
157	C₄×D₄×C₃₁	—	2	1	no	—
158	C₄×D₄×C₃₁	—	2	1	no	—
159	C₄×D₄×C₃₁	—	2	1	no	—
160	C₄×D₄×C₃₁	—	2	1	no	—
161	C₄×D₄×C₃₁	—	2	1	no	—
162	C₄×D₄×C₃₁	C₂³	1	2	yes	—
163	C₄×D₄×C₃₁	C₂³	1	2	yes	—
164	C₄×D₄×C₃₁	C₂³	1	2	yes	—
165	C₄×D₄×C₃₁	C₂³	1	2	yes	—
166	C₄×D₄×C₃₁	C₂³	1	2	yes	—
167	C₄×D₄×C₃₁	C₂³	1	2	yes	—
168	C₃₁×#117	—	2	2	no	—
169	C₃₁×#117	C₂³	1	2	yes	—
170	C₃₁×#117	C₂³	1	4	yes	—
171	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
172	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
173	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
174	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
175	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
176	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
177	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
178	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
179	C₃₁×#107	C₂³	1	4	yes	—
180	C₃₁×#106	C₂³	1	4	yes	—
181	C₃₁×#106	C₂³	1	4	yes	—
182	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
183	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
184	C₃₁×#103	C₂³	1	2	yes	—
185	C₃₁×#103	C₂³	1	4	yes	—
186	C₃₁×#103	C₂³	1	2	yes	—
187	C₃₁×#103	C₂³	1	2	yes	—
188	C₃₁×#103	C₂³	1	2	yes	—
189	C₃₁×#102	C₂³	1	4	yes	—
190	C₃₁×#102	C₂³	1	2	yes	—
191	C₃₁×#102	C₂³	1	4	yes	—
192	C₃₁×#102	C₂³	1	4	yes	—
193	C₃₁×#102	C₂³	1	4	yes	—
194	C₃₁×#102	C₂³	1	4	yes	—
195	C₃₁×#102	C₂³	1	2	yes	—
196	C₃₁×#102	C₂³	1	2	yes	—
197	C₃₁×#102	C₂³	1	2	yes	—
198	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
199	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
200	C₃₁×#97	C₂³	1	2	yes	—
201	C₃₁×#97	C₂³	1	2	yes	—
202	C₂⁴×C₃₁	—	2	1	no	—
203	C₂⁴×C₃₁	—	2	1	no	—
204	C₂⁴×C₃₁	—	2	4	no	—
205	#41×C₃₁	—	2	4	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	—	4	4	no	—
211	#41×C₃₁	—	4	8	no	—
212	#41×C₃₁	—	8	4	no	—
213	C₂×Q₈×C₃₁	—	2	1	no	—
214	C₂×Q₈×C₃₁	—	2	1	no	—
215	C₂×Q₈×C₃₁	C₂×D₄	1	2	yes	—
216	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
217	C₂×D₄×C₃₁	—	2	8	no	—
218	C₂×D₄×C₃₁	—	2	4	no	—
219	C₂×D₄×C₃₁	—	2	2	no	—
220	C₂×D₄×C₃₁	—	2	4	no	—
221	C₂×D₄×C₃₁	—	2	4	no	—
222	C₂×D₄×C₃₁	—	2	4	no	—
223	C₂×D₄×C₃₁	—	2	1	no	—
224	C₂×D₄×C₃₁	—	2	1	no	—
225	C₂×D₄×C₃₁	—	2	1	no	—
226	C₂×D₄×C₃₁	—	2	4	no	—
227	C₂×D₄×C₃₁	—	2	1	no	—
228	C₂×D₄×C₃₁	—	2	2	no	—
229	C₂×D₄×C₃₁	—	2	2	no	—
230	C₂×D₄×C₃₁	—	2	2	no	—
231	C₂×D₄×C₃₁	—	4	4	no	—
232	C₂×D₄×C₃₁	—	4	8	no	—
233	C₂×D₄×C₃₁	—	4	16	no	—
234	C₂×D₄×C₃₁	—	8	4	no	—
235	C₂×D₄×C₃₁	C₂×D₄	1	4	yes	—
236	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
237	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
238	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
239	C₂×D₄×C₃₁	#41	1	4	yes	complemented
240	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
241	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
242	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
243	C₂²×C₄×C₃₁	—	2	1	no	—
244	C₂²×C₄×C₃₁	—	2	1	no	—
245	C₂²×C₄×C₃₁	—	2	4	no	—
246	C₂²×C₄×C₃₁	—	2	4	no	—
247	C₂²×C₄×C₃₁	—	2	2	no	—
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	—	8	2	no	—
253	C₂²×C₄×C₃₁	—	8	2	no	—
254	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
255	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
256	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
257	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
258	SD₁₆×C₃₁	—	4	4	no	—
259	D₈×C₃₁	—	2	8	no	—
260	D₈×C₃₁	—	4	4	no	—
261	M₁₆×C₃₁	—	2	4	no	—
262	M₁₆×C₃₁	—	4	4	no	—
263	C₂×C₈×C₃₁	—	2	2	no	—
264	C₂×C₈×C₃₁	—	2	2	no	—
265	C₂×C₈×C₃₁	—	4	4	no	—
266	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
267	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
268	C₂×C₈×C₃₁	C₂⁴	1	4	yes	—
269	C₄⋊C₄×C₃₁	—	2	1	no	—
270	C₄⋊C₄×C₃₁	—	2	4	no	—
271	C₄⋊C₄×C₃₁	—	2	1	no	—
272	C₄⋊C₄×C₃₁	—	2	1	no	—
273	C₄⋊C₄×C₃₁	—	2	4	no	—
274	C₄⋊C₄×C₃₁	—	2	1	no	—
275	C₄⋊C₄×C₃₁	—	2	2	no	—
276	C₄⋊C₄×C₃₁	—	2	1	no	—
277	C₄⋊C₄×C₃₁	—	2	2	no	—
278	C₄⋊C₄×C₃₁	—	2	1	no	—
279	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
280	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
281	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
282	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
283	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
284	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
285	C₂²⋊C₄×C₃₁	—	2	4	no	—
286	C₂²⋊C₄×C₃₁	—	2	2	no	—
287	C₂²⋊C₄×C₃₁	—	2	4	no	—
288	C₂²⋊C₄×C₃₁	—	2	2	no	—
289	C₂²⋊C₄×C₃₁	—	2	2	no	—
290	C₂²⋊C₄×C₃₁	—	2	2	no	—
291	C₂²⋊C₄×C₃₁	—	2	2	no	—
292	C₂²⋊C₄×C₃₁	—	2	2	no	—
293	C₂²⋊C₄×C₃₁	—	2	4	no	—
294	C₂²⋊C₄×C₃₁	—	2	4	no	—
295	C₂²⋊C₄×C₃₁	—	2	2	no	—
296	C₂²⋊C₄×C₃₁	—	2	4	no	—
297	C₂²⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
298	C₂²⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
299	C₄²×C₃₁	—	2	4	no	—
300	C₄²×C₃₁	—	2	2	no	—
301	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
302	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
303	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
304	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
305	#61218	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
306	C₂³×C₃₁	—	2	2	no	—
307	C₂³×C₃₁	—	2	4	no	—
308	C₂³×C₃₁	—	2	2	no	—
309	C₂³×C₃₁	—	2	2	no	—
310	C₂³×C₃₁	—	4	8	no	—
311	C₂³×C₃₁	—	4	2	no	—
312	C₂³×C₃₁	—	8	1	no	—
313	C₂³×C₃₁	—	8	1	no	—
314	C₂³×C₃₁	—	8	1	no	—
315	C₂³×C₃₁	—	8	1	no	—
316	C₂³×C₃₁	—	8	4	no	—
317	C₂³×C₃₁	—	8	4	no	—
318	C₂³×C₃₁	C₂²×D₄	1	4	yes	—
319	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
320	Q₈×C₃₁	—	2	4	no	—
321	Q₈×C₃₁	—	2	2	no	—
322	Q₈×C₃₁	—	2	2	no	—
323	Q₈×C₃₁	—	4	2	no	—
324	Q₈×C₃₁	—	8	1	no	—
325	D₄×C₃₁	—	2	8	no	—
326	D₄×C₃₁	—	2	4	no	—
327	D₄×C₃₁	—	2	4	no	—
328	D₄×C₃₁	—	2	2	no	—
329	D₄×C₃₁	—	2	2	no	—
330	D₄×C₃₁	—	2	2	no	—
331	D₄×C₃₁	—	2	2	no	—
332	D₄×C₃₁	—	2	2	no	—
333	D₄×C₃₁	—	4	2	no	—
334	D₄×C₃₁	—	4	2	no	—
335	D₄×C₃₁	—	4	8	no	—
336	D₄×C₃₁	—	4	2	no	—
337	D₄×C₃₁	—	4	8	no	—
338	D₄×C₃₁	—	4	4	no	—
339	D₄×C₃₁	—	4	2	no	—
340	D₄×C₃₁	—	8	1	no	—
341	D₄×C₃₁	—	8	4	no	—
342	D₄×C₃₁	—	8	4	no	—
343	D₄×C₃₁	—	8	4	no	—
344	D₄×C₃₁	C₂×#41	1	4	yes	—
345	C₂×C₄×C₃₁	—	2	4	no	—
346	C₂×C₄×C₃₁	—	2	4	no	—
347	C₂×C₄×C₃₁	—	2	2	no	—
348	C₂×C₄×C₃₁	—	2	2	no	—
349	C₂×C₄×C₃₁	—	2	2	no	—
350	C₂×C₄×C₃₁	—	2	2	no	—
351	C₂×C₄×C₃₁	—	2	2	no	—
352	C₂×C₄×C₃₁	—	4	1	no	—
353	C₂×C₄×C₃₁	—	4	1	no	—
354	C₂×C₄×C₃₁	—	4	8	no	—
355	C₂×C₄×C₃₁	—	4	4	no	—
356	C₂×C₄×C₃₁	—	4	4	no	—
357	C₂×C₄×C₃₁	—	4	4	no	—
358	C₂×C₄×C₃₁	—	8	2	no	—
359	C₂×C₄×C₃₁	—	8	2	no	—
360	C₂×C₄×C₃₁	—	8	1	no	—
361	C₂×C₄×C₃₁	—	8	1	no	—
362	C₂×C₄×C₃₁	—	8	4	no	—
363	C₂×C₄×C₃₁	C₂²×D₄	1	4	yes	—
364	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
365	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
366	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
367	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
368	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
369	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
370	C₂×C₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
371	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
372	C₈×C₃₁	—	2	2	no	—
373	C₈×C₃₁	—	2	2	no	—
374	C₈×C₃₁	—	2	4	no	—
375	#3506	C₂×C₃₁	1	1	yes	characteristic, complemented
376	#3496	C₂×C₃₁	1	1	yes	characteristic, complemented
377	#3319	C₂×C₃₁	1	4	yes	complemented
378	#3318	C₂×C₃₁	1	4	yes	complemented
379	#3307	C₂×C₃₁	1	4	yes	complemented
380	#3306	C₂×C₃₁	1	4	yes	complemented
381	#3135	C₂×C₃₁	1	1	yes	characteristic, complemented
382	#3099	C₂×C₃₁	1	2	yes	complemented
383	#3077	C₂×C₃₁	1	1	yes	characteristic, complemented
384	#3062	C₂×C₃₁	1	2	yes	complemented
385	#3036	C₂×C₃₁	1	1	yes	characteristic, complemented
386	#3008	C₂×C₃₁	1	2	yes	complemented
387	C₂×#442	C₂×C₃₁	1	1	yes	characteristic, complemented
388	#2932	C₂×C₃₁	1	1	yes	characteristic, complemented
389	#2897	C₂×C₃₁	1	2	yes	complemented
390	C₂²×C₃₁	—	2	1	no	—
391	C₂²×C₃₁	—	2	1	no	—
392	C₂²×C₃₁	—	2	4	no	—
393	C₂²×C₃₁	—	2	4	no	—
394	C₂²×C₃₁	—	2	4	no	—
395	C₂²×C₃₁	—	2	4	no	—
396	C₂²×C₃₁	—	4	2	no	—
397	C₂²×C₃₁	—	4	2	no	—
398	C₂²×C₃₁	—	4	2	no	—
399	C₂²×C₃₁	—	4	2	no	—
400	C₂²×C₃₁	—	4	2	no	—
401	C₂²×C₃₁	—	4	2	no	—
402	C₂²×C₃₁	—	4	2	no	—
403	C₂²×C₃₁	—	4	2	no	—
404	C₂²×C₃₁	—	8	4	no	—
405	C₂²×C₃₁	—	8	4	no	—
406	C₂²×C₃₁	—	16	8	no	—
407	C₂²×C₃₁	#546	1	2	yes	—
408	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
409	C₄×C₃₁	—	2	1	no	—
410	C₄×C₃₁	—	2	1	no	—
411	C₄×C₃₁	—	2	1	no	—
412	C₄×C₃₁	—	2	1	no	—
413	C₄×C₃₁	—	2	4	no	—
414	C₄×C₃₁	—	4	2	no	—
415	C₄×C₃₁	—	4	2	no	—
416	C₄×C₃₁	—	4	2	no	—
417	C₄×C₃₁	—	4	2	no	—
418	C₄×C₃₁	—	4	2	no	—
419	C₄×C₃₁	#546	1	2	yes	—
420	C₄×C₃₁	C₂²×#41	1	1	yes	characteristic
421	C₄×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
422	C₂×H(5,𝔽₂)	C₂²×C₃₁	1	2	yes	—
423	C₂×AGL(1,ℤ/8)	C₂²×C₃₁	1	2	yes	complemented
424	C₂²×D₈	C₂²×C₃₁	1	1	yes	characteristic
425	C₂×#131	C₂²×C₃₁	1	2	yes	complemented
426	#559	—	2	2	no	—
427	#556	—	2	1	no	—
428	#555	C₂²×C₃₁	1	2	yes	complemented
429	#553	C₂²×C₃₁	1	4	yes	complemented
430	#550	—	2	1	no	—
431	#547	—	2	1	no	—
432	#547	C₂²×C₃₁	1	2	yes	complemented
433	#547	C₂²×C₃₁	1	2	yes	complemented
434	#546	—	2	2	no	—
435	#546	C₂²×C₃₁	1	4	yes	complemented
436	D₄²	—	2	1	no	—
437	D₄²	C₂²×C₃₁	1	2	yes	complemented
438	#538	—	2	2	no	—
439	#537	C₂²×C₃₁	1	2	yes	—
440	#535	C₂²×C₃₁	1	2	yes	complemented
441	#534	—	2	2	no	—
442	#533	C₂²×C₃₁	1	1	yes	characteristic, complemented
443	#532	C₂²×C₃₁	1	1	yes	characteristic
444	#532	C₂²×C₃₁	1	1	yes	characteristic
445	#525	—	2	2	no	—
446	C₂×#121	—	2	2	no	—
447	#520	C₂²×C₃₁	1	2	yes	complemented
448	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
449	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
450	#491	C₂²×C₃₁	1	2	yes	complemented
451	#490	C₂²×C₃₁	1	2	yes	complemented
452	#489	C₂²×C₃₁	1	2	yes	complemented
453	#489	C₂²×C₃₁	1	2	yes	complemented
454	#485	C₂²×C₃₁	1	4	yes	complemented
455	#483	C₂²×C₃₁	1	4	yes	complemented
456	#482	C₂²×C₃₁	1	4	yes	complemented
457	#481	C₂²×C₃₁	1	4	yes	complemented
458	#478	C₂²×C₃₁	1	4	yes	complemented
459	#476	C₂²×C₃₁	1	2	yes	complemented
460	#474	C₂²×C₃₁	1	2	yes	complemented
461	#469	C₂²×C₃₁	1	4	yes	complemented
462	#468	C₂²×C₃₁	1	4	yes	complemented
463	#466	C₂²×C₃₁	1	4	yes	complemented
464	#465	C₂²×C₃₁	1	4	yes	complemented
465	#463	C₂²×C₃₁	1	4	yes	complemented
466	#461	C₂²×C₃₁	1	2	yes	complemented
467	#459	C₂²×C₃₁	1	2	yes	complemented
468	#449	C₂²×C₃₁	1	4	yes	complemented
469	#449	C₂²×C₃₁	1	4	yes	complemented
470	#447	C₂²×C₃₁	1	4	yes	complemented
471	#447	C₂²×C₃₁	1	4	yes	complemented
472	#442	C₂²×C₃₁	1	4	yes	complemented
473	#442	C₂²×C₃₁	1	4	yes	complemented
474	#435	C₂²×C₃₁	1	4	yes	complemented
475	#435	C₂²×C₃₁	1	4	yes	complemented
476	#428	C₂²×C₃₁	1	2	yes	complemented
477	C₂×#106	C₂²×C₃₁	1	1	yes	characteristic, complemented
478	#423	C₂²×C₃₁	1	1	yes	characteristic, complemented
479	#418	C₂²×C₃₁	1	2	yes	—
480	#418	C₂²×C₃₁	1	4	yes	complemented
481	#417	C₂²×C₃₁	1	2	yes	complemented
482	#417	C₂²×C₃₁	1	4	yes	complemented
483	#416	C₂²×C₃₁	1	2	yes	complemented
484	#416	C₂²×C₃₁	1	2	yes	complemented
485	#416	C₂²×C₃₁	1	4	yes	complemented
486	C₂×#102	C₂²×C₃₁	1	1	yes	characteristic
487	C₂×#102	C₂²×C₃₁	1	4	yes	complemented
488	C₂×#102	C₂²×C₃₁	1	1	yes	characteristic, complemented
489	#408	C₂²×C₃₁	1	2	yes	complemented
490	C₂×#97	C₂²×C₃₁	1	1	yes	characteristic, complemented
491	C₂×C₃₁	—	2	2	no	—
492	C₂×C₃₁	—	4	4	no	—
493	C₂×C₃₁	—	4	4	no	—
494	C₂×C₃₁	—	8	2	no	—
495	C₂×C₃₁	—	8	2	no	—
496	C₂×C₃₁	C₂×#546	1	1	yes	characteristic
497	C₂×C₃₁	#3585	1	1	yes	characteristic
498	C₂×C₃₁	#3585	1	1	yes	characteristic
499	H(5,𝔽₂)	—	2	8	no	—
500	H(5,𝔽₂)	—	4	4	no	—
501	C₂×#41	—	2	2	no	—
502	C₂×#41	—	2	2	no	—
503	C₂×#41	C₂³×C₃₁	1	2	yes	—
504	C₂×#41	C₂³×C₃₁	1	4	yes	—
505	C₂×#41	C₂³×C₃₁	1	2	yes	—
506	C₂²×D₄	—	2	4	no	—
507	C₂²×D₄	—	2	2	no	—
508	C₂²×D₄	—	2	2	no	—
509	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
510	C₂²×D₄	C₂³×C₃₁	1	4	yes	—
511	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
512	C₂³×C₄	—	2	1	no	—
513	C₂³×C₄	—	2	1	no	—
514	AGL(1,ℤ/8)	—	4	4	no	—
515	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
516	C₂×D₈	—	2	4	no	—
517	C₂×D₈	C₂³×C₃₁	1	4	yes	—
518	C₂×D₈	C₂³×C₃₁	1	4	yes	—
519	#131	—	4	4	no	—
520	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
521	C₂×M₁₆	C₂³×C₃₁	1	4	yes	—
522	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
523	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
524	C₂²×C₈	C₂³×C₃₁	1	4	yes	—
525	C₄⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
526	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
527	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
528	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
529	#127	—	2	2	no	—
530	#127	D₄×C₃₁	1	1	yes	characteristic
531	#127	C₂³×C₃₁	1	1	yes	characteristic
532	#126	—	2	4	no	—
533	#125	C₂³×C₃₁	1	2	yes	—
534	#124	—	2	2	no	—
535	#124	—	2	4	no	—
536	#124	D₄×C₃₁	1	2	yes	—
537	#124	C₂³×C₃₁	1	2	yes	—
538	#123	—	2	4	no	—
539	#123	—	2	4	no	—
540	#123	—	2	4	no	—
541	#123	—	2	4	no	—
542	C₂²⋊Q₈	—	2	2	no	—
543	C₂²⋊Q₈	—	2	1	no	—
544	C₂²⋊Q₈	—	2	1	no	—
545	C₂²⋊Q₈	—	2	2	no	—
546	C₂²⋊Q₈	C₂³×C₃₁	1	4	yes	—
547	#121	—	2	4	no	—
548	#121	—	2	2	no	—
549	#121	—	2	2	no	—
550	#121	—	2	2	no	—
551	#121	—	2	4	no	—
552	#121	—	2	1	no	—
553	#121	—	2	1	no	—
554	#121	—	2	2	no	—
555	#121	—	2	4	no	—
556	#121	D₄×C₃₁	1	2	yes	—
557	#121	D₄×C₃₁	1	2	yes	—
558	#121	C₂³×C₃₁	1	4	yes	—
559	#121	C₂³×C₃₁	1	4	yes	—
560	#121	C₂³×C₃₁	1	4	yes	—
561	#120	—	2	4	no	—
562	#120	—	2	4	no	—
563	#120	—	2	4	no	—
564	C₄×Q₈	—	2	2	no	—
565	C₄×Q₈	—	2	1	no	—
566	C₄×Q₈	—	2	1	no	—
567	C₄×D₄	—	2	4	no	—
568	C₄×D₄	—	2	2	no	—
569	C₄×D₄	—	2	4	no	—
570	C₄×D₄	—	2	1	no	—
571	C₄×D₄	—	2	1	no	—
572	C₄×D₄	—	2	1	no	—
573	C₄×D₄	—	2	1	no	—
574	C₄×D₄	—	2	1	no	—
575	C₄×D₄	—	2	1	no	—
576	C₄×D₄	C₂³×C₃₁	1	2	yes	—
577	C₄×D₄	C₂³×C₃₁	1	2	yes	—
578	C₄×D₄	C₂³×C₃₁	1	2	yes	—
579	C₄×D₄	C₂³×C₃₁	1	2	yes	—
580	C₄×D₄	C₂³×C₃₁	1	2	yes	—
581	C₄×D₄	C₂³×C₃₁	1	2	yes	—
582	#117	—	2	2	no	—
583	#117	C₂³×C₃₁	1	2	yes	—
584	#117	C₂³×C₃₁	1	4	yes	—
585	C₂×C₄⋊C₄	—	2	2	no	—
586	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
587	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
588	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
589	C₂×C₂²⋊C₄	—	2	1	no	—
590	C₂×C₂²⋊C₄	—	2	1	no	—
591	C₂×C₂²⋊C₄	—	2	4	no	—
592	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
593	#107	C₂³×C₃₁	1	4	yes	—
594	#106	C₂³×C₃₁	1	4	yes	—
595	#106	C₂³×C₃₁	1	4	yes	—
596	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
597	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
598	#103	C₂³×C₃₁	1	2	yes	—
599	#103	C₂³×C₃₁	1	4	yes	—
600	#103	C₂³×C₃₁	1	2	yes	—
601	#103	C₂³×C₃₁	1	2	yes	—
602	#103	C₂³×C₃₁	1	2	yes	—
603	#102	C₂³×C₃₁	1	4	yes	—
604	#102	C₂³×C₃₁	1	2	yes	—
605	#102	C₂³×C₃₁	1	4	yes	—
606	#102	C₂³×C₃₁	1	4	yes	—
607	#102	C₂³×C₃₁	1	4	yes	—
608	#102	C₂³×C₃₁	1	4	yes	—
609	#102	C₂³×C₃₁	1	2	yes	—
610	#102	C₂³×C₃₁	1	2	yes	—
611	#102	C₂³×C₃₁	1	2	yes	—
612	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
613	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
614	#97	C₂³×C₃₁	1	2	yes	—
615	#97	C₂³×C₃₁	1	2	yes	—
616	C₃₁	#61218	1	1	yes	characteristic, direct product factor, Sylow
617	C₂⁴	—	2	1	no	—
618	C₂⁴	—	2	1	no	—
619	C₂⁴	—	2	4	no	—
620	#41	—	2	4	no	—
621	#41	—	2	4	no	—
622	#41	—	2	8	no	—
623	#41	—	2	4	no	—
624	#41	—	2	4	no	—
625	#41	—	4	4	no	—
626	#41	—	4	8	no	—
627	#41	—	8	4	no	—
628	C₂×Q₈	—	2	1	no	—
629	C₂×Q₈	—	2	1	no	—
630	C₂×Q₈	C₂×D₄×C₃₁	1	2	yes	—
631	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
632	C₂×D₄	—	2	8	no	—
633	C₂×D₄	—	2	4	no	—
634	C₂×D₄	—	2	2	no	—
635	C₂×D₄	—	2	4	no	—
636	C₂×D₄	—	2	4	no	—
637	C₂×D₄	—	2	4	no	—
638	C₂×D₄	—	2	1	no	—
639	C₂×D₄	—	2	1	no	—
640	C₂×D₄	—	2	1	no	—
641	C₂×D₄	—	2	4	no	—
642	C₂×D₄	—	2	1	no	—
643	C₂×D₄	—	2	2	no	—
644	C₂×D₄	—	2	2	no	—
645	C₂×D₄	—	2	2	no	—
646	C₂×D₄	—	4	4	no	—
647	C₂×D₄	—	4	8	no	—
648	C₂×D₄	—	4	16	no	—
649	C₂×D₄	—	8	4	no	—
650	C₂×D₄	C₂×D₄×C₃₁	1	4	yes	—
651	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
652	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
653	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
654	C₂×D₄	#41×C₃₁	1	4	yes	complemented
655	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
656	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
657	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
658	C₂²×C₄	—	2	1	no	—
659	C₂²×C₄	—	2	1	no	—
660	C₂²×C₄	—	2	4	no	—
661	C₂²×C₄	—	2	4	no	—
662	C₂²×C₄	—	2	2	no	—
663	C₂²×C₄	—	2	2	no	—
664	C₂²×C₄	—	2	2	no	—
665	C₂²×C₄	—	2	2	no	—
666	C₂²×C₄	—	2	2	no	—
667	C₂²×C₄	—	8	2	no	—
668	C₂²×C₄	—	8	2	no	—
669	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
670	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
671	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
672	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
673	SD₁₆	—	4	4	no	—
674	D₈	—	2	8	no	—
675	D₈	—	4	4	no	—
676	M₁₆	—	2	4	no	—
677	M₁₆	—	4	4	no	—
678	C₂×C₈	—	2	2	no	—
679	C₂×C₈	—	2	2	no	—
680	C₂×C₈	—	4	4	no	—
681	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
682	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
683	C₂×C₈	C₂⁴×C₃₁	1	4	yes	—
684	C₄⋊C₄	—	2	1	no	—
685	C₄⋊C₄	—	2	4	no	—
686	C₄⋊C₄	—	2	1	no	—
687	C₄⋊C₄	—	2	1	no	—
688	C₄⋊C₄	—	2	4	no	—
689	C₄⋊C₄	—	2	1	no	—
690	C₄⋊C₄	—	2	2	no	—
691	C₄⋊C₄	—	2	1	no	—
692	C₄⋊C₄	—	2	2	no	—
693	C₄⋊C₄	—	2	1	no	—
694	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
695	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
696	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
697	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
698	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
699	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
700	C₂²⋊C₄	—	2	4	no	—
701	C₂²⋊C₄	—	2	2	no	—
702	C₂²⋊C₄	—	2	4	no	—
703	C₂²⋊C₄	—	2	2	no	—
704	C₂²⋊C₄	—	2	2	no	—
705	C₂²⋊C₄	—	2	2	no	—
706	C₂²⋊C₄	—	2	2	no	—
707	C₂²⋊C₄	—	2	2	no	—
708	C₂²⋊C₄	—	2	4	no	—
709	C₂²⋊C₄	—	2	4	no	—
710	C₂²⋊C₄	—	2	2	no	—
711	C₂²⋊C₄	—	2	4	no	—
712	C₂²⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
713	C₂²⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
714	C₄²	—	2	4	no	—
715	C₄²	—	2	2	no	—
716	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
717	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
718	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
719	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
720	C₂³	—	2	2	no	—
721	C₂³	—	2	4	no	—
722	C₂³	—	2	2	no	—
723	C₂³	—	2	2	no	—
724	C₂³	—	4	8	no	—
725	C₂³	—	4	2	no	—
726	C₂³	—	8	1	no	—
727	C₂³	—	8	1	no	—
728	C₂³	—	8	1	no	—
729	C₂³	—	8	1	no	—
730	C₂³	—	8	4	no	—
731	C₂³	—	8	4	no	—
732	C₂³	C₂²×D₄×C₃₁	1	4	yes	—
733	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
734	Q₈	—	2	4	no	—
735	Q₈	—	2	2	no	—
736	Q₈	—	2	2	no	—
737	Q₈	—	4	2	no	—
738	Q₈	—	8	1	no	—
739	D₄	—	2	8	no	—
740	D₄	—	2	4	no	—
741	D₄	—	2	4	no	—
742	D₄	—	2	2	no	—
743	D₄	—	2	2	no	—
744	D₄	—	2	2	no	—
745	D₄	—	2	2	no	—
746	D₄	—	2	2	no	—
747	D₄	—	4	2	no	—
748	D₄	—	4	2	no	—
749	D₄	—	4	8	no	—
750	D₄	—	4	2	no	—
751	D₄	—	4	8	no	—
752	D₄	—	4	4	no	—
753	D₄	—	4	2	no	—
754	D₄	—	8	1	no	—
755	D₄	—	8	4	no	—
756	D₄	—	8	4	no	—
757	D₄	—	8	4	no	—
758	D₄	C₂×#41×C₃₁	1	4	yes	—
759	C₂×C₄	—	2	4	no	—
760	C₂×C₄	—	2	4	no	—
761	C₂×C₄	—	2	2	no	—
762	C₂×C₄	—	2	2	no	—
763	C₂×C₄	—	2	2	no	—
764	C₂×C₄	—	2	2	no	—
765	C₂×C₄	—	2	2	no	—
766	C₂×C₄	—	4	1	no	—
767	C₂×C₄	—	4	1	no	—
768	C₂×C₄	—	4	8	no	—
769	C₂×C₄	—	4	4	no	—
770	C₂×C₄	—	4	4	no	—
771	C₂×C₄	—	4	4	no	—
772	C₂×C₄	—	8	2	no	—
773	C₂×C₄	—	8	2	no	—
774	C₂×C₄	—	8	1	no	—
775	C₂×C₄	—	8	1	no	—
776	C₂×C₄	—	8	4	no	—
777	C₂×C₄	C₂²×D₄×C₃₁	1	4	yes	—
778	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
779	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
780	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
781	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
782	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
783	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
784	C₂×C₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
785	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
786	C₈	—	2	2	no	—
787	C₈	—	2	2	no	—
788	C₈	—	2	4	no	—
789	C₂²	—	2	1	no	—
790	C₂²	—	2	1	no	—
791	C₂²	—	2	4	no	—
792	C₂²	—	2	4	no	—
793	C₂²	—	2	4	no	—
794	C₂²	—	2	4	no	—
795	C₂²	—	4	2	no	—
796	C₂²	—	4	2	no	—
797	C₂²	—	4	2	no	—
798	C₂²	—	4	2	no	—
799	C₂²	—	4	2	no	—
800	C₂²	—	4	2	no	—
801	C₂²	—	4	2	no	—
802	C₂²	—	4	2	no	—
803	C₂²	—	8	4	no	—
804	C₂²	—	8	4	no	—
805	C₂²	—	16	8	no	—
806	C₂²	C₃₁×#546	1	2	yes	—
807	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
808	C₄	—	2	4	no	—
809	C₄	—	2	1	no	—
810	C₄	—	2	1	no	—
811	C₄	—	2	1	no	—
812	C₄	—	2	1	no	—
813	C₄	—	4	2	no	—
814	C₄	—	4	2	no	—
815	C₄	—	4	2	no	—
816	C₄	—	4	2	no	—
817	C₄	—	4	2	no	—
818	C₄	C₃₁×#546	1	2	yes	—
819	C₄	C₂²×#41×C₃₁	1	1	yes	characteristic
820	C₄	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
821	C₂	—	2	2	no	—
822	C₂	—	4	4	no	—
823	C₂	—	4	4	no	—
824	C₂	—	8	2	no	—
825	C₂	—	8	2	no	—
826	C₂	C₂×C₃₁×#546	1	1	yes	characteristic
827	C₂	C₃₁×#3585	1	1	yes	characteristic
828	C₂	C₃₁×#3585	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 ◁ C₃₁×#532 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3506	C₂	semidirect
2. C₃₁×#3496	C₂	semidirect
3. C₃₁×#3319	C₂	semidirect
4. C₃₁×#3318	C₂	semidirect
5. C₃₁×#3307	C₂	semidirect
6. C₃₁×#3306	C₂	semidirect
7. C₃₁×#3135	C₂	semidirect
8. C₃₁×#3099	C₂	semidirect
9. C₃₁×#3077	C₂	semidirect
10. C₃₁×#3062	C₂	semidirect
11. C₃₁×#3036	C₂	semidirect
12. C₃₁×#3008	C₂	semidirect
13. C₂×C₃₁×#442	C₂	semidirect
14. C₃₁×#2932	C₂	semidirect
15. C₃₁×#2897	C₂	semidirect
17. C₂×C₃₁×AGL(1,ℤ/8)	C₂²	semidirect
19. C₂×C₃₁×#131	C₂²	semidirect
22. C₃₁×#555	C₂²	semidirect
23. C₃₁×#553	C₂²	semidirect
26. C₃₁×#547	C₂²	semidirect
27. C₃₁×#547	C₂²	semidirect
29. C₃₁×#546	C₂²	semidirect
31. D₄²×C₃₁	C₂²	semidirect
34. C₃₁×#535	C₂²	semidirect
36. C₃₁×#533	C₂²	semidirect
41. C₃₁×#520	C₂²	semidirect
43. C₂×C₄×D₄×C₃₁	C₂²	semidirect
44. C₃₁×#491	C₂²	semidirect
45. C₃₁×#490	C₂²	semidirect
46. C₃₁×#489	C₂²	semidirect
47. C₃₁×#489	C₂²	semidirect
48. C₃₁×#485	C₂²	semidirect
49. C₃₁×#483	C₂²	semidirect
50. C₃₁×#482	C₂²	semidirect
51. C₃₁×#481	C₂²	semidirect
52. C₃₁×#478	C₂²	semidirect
53. C₃₁×#476	C₂²	semidirect
54. C₃₁×#474	C₂²	semidirect
55. C₃₁×#469	C₂²	semidirect
56. C₃₁×#468	C₂²	semidirect
57. C₃₁×#466	C₂²	semidirect
58. C₃₁×#465	C₂²	semidirect
59. C₃₁×#463	C₂²	semidirect
60. C₃₁×#461	C₂²	semidirect
61. C₃₁×#459	C₂²	semidirect
62. C₃₁×#449	C₂²	semidirect
63. C₃₁×#449	C₂²	semidirect
64. C₃₁×#447	C₂²	semidirect
65. C₃₁×#447	C₂²	semidirect
66. C₃₁×#442	C₂²	semidirect
67. C₃₁×#442	C₂²	semidirect
68. C₃₁×#435	C₂²	semidirect
69. C₃₁×#435	C₂²	semidirect
70. C₃₁×#428	C₂²	semidirect
71. C₂×C₃₁×#106	C₂²	semidirect
72. C₃₁×#423	C₂²	semidirect
74. C₃₁×#418	C₂²	semidirect
75. C₃₁×#417	C₂²	semidirect
76. C₃₁×#417	C₂²	semidirect
77. C₃₁×#416	C₂²	semidirect
78. C₃₁×#416	C₂²	semidirect
79. C₃₁×#416	C₂²	semidirect
81. C₂×C₃₁×#102	C₂²	semidirect
82. C₂×C₃₁×#102	C₂²	semidirect
83. C₃₁×#408	C₂²	semidirect
84. C₂×C₃₁×#97	C₂²	semidirect
239. C₂×D₄×C₃₁	#41	semidirect
305. #61218	C₃₁	direct (N × H)
375. #3506	C₂×C₃₁	semidirect
376. #3496	C₂×C₃₁	semidirect
377. #3319	C₂×C₃₁	semidirect
378. #3318	C₂×C₃₁	semidirect
379. #3307	C₂×C₃₁	semidirect
380. #3306	C₂×C₃₁	semidirect
381. #3135	C₂×C₃₁	semidirect
382. #3099	C₂×C₃₁	semidirect
383. #3077	C₂×C₃₁	semidirect
384. #3062	C₂×C₃₁	semidirect
385. #3036	C₂×C₃₁	semidirect
386. #3008	C₂×C₃₁	semidirect
387. C₂×#442	C₂×C₃₁	semidirect
388. #2932	C₂×C₃₁	semidirect
389. #2897	C₂×C₃₁	semidirect
423. C₂×AGL(1,ℤ/8)	C₂²×C₃₁	semidirect
425. C₂×#131	C₂²×C₃₁	semidirect
428. #555	C₂²×C₃₁	semidirect
429. #553	C₂²×C₃₁	semidirect
432. #547	C₂²×C₃₁	semidirect
433. #547	C₂²×C₃₁	semidirect
435. #546	C₂²×C₃₁	semidirect
437. D₄²	C₂²×C₃₁	semidirect
440. #535	C₂²×C₃₁	semidirect
442. #533	C₂²×C₃₁	semidirect
447. #520	C₂²×C₃₁	semidirect
449. C₂×C₄×D₄	C₂²×C₃₁	semidirect
450. #491	C₂²×C₃₁	semidirect
451. #490	C₂²×C₃₁	semidirect
452. #489	C₂²×C₃₁	semidirect
453. #489	C₂²×C₃₁	semidirect
454. #485	C₂²×C₃₁	semidirect
455. #483	C₂²×C₃₁	semidirect
456. #482	C₂²×C₃₁	semidirect
457. #481	C₂²×C₃₁	semidirect
458. #478	C₂²×C₃₁	semidirect
459. #476	C₂²×C₃₁	semidirect
460. #474	C₂²×C₃₁	semidirect
461. #469	C₂²×C₃₁	semidirect
462. #468	C₂²×C₃₁	semidirect
463. #466	C₂²×C₃₁	semidirect
464. #465	C₂²×C₃₁	semidirect
465. #463	C₂²×C₃₁	semidirect
466. #461	C₂²×C₃₁	semidirect
467. #459	C₂²×C₃₁	semidirect
468. #449	C₂²×C₃₁	semidirect
469. #449	C₂²×C₃₁	semidirect
470. #447	C₂²×C₃₁	semidirect
471. #447	C₂²×C₃₁	semidirect
472. #442	C₂²×C₃₁	semidirect
473. #442	C₂²×C₃₁	semidirect
474. #435	C₂²×C₃₁	semidirect
475. #435	C₂²×C₃₁	semidirect
476. #428	C₂²×C₃₁	semidirect
477. C₂×#106	C₂²×C₃₁	semidirect
478. #423	C₂²×C₃₁	semidirect
480. #418	C₂²×C₃₁	semidirect
481. #417	C₂²×C₃₁	semidirect
482. #417	C₂²×C₃₁	semidirect
483. #416	C₂²×C₃₁	semidirect
484. #416	C₂²×C₃₁	semidirect
485. #416	C₂²×C₃₁	semidirect
487. C₂×#102	C₂²×C₃₁	semidirect
488. C₂×#102	C₂²×C₃₁	semidirect
489. #408	C₂²×C₃₁	semidirect
490. C₂×#97	C₂²×C₃₁	semidirect
616. C₃₁	#61218	direct (N × H)
654. C₂×D₄	#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×#3506	2
C₃₁×#3496	2
C₃₁×#3319	2
C₃₁×#3318	2
C₃₁×#3307	2
C₃₁×#3306	2
C₃₁×#3135	2
C₃₁×#3099	2
C₃₁×#3077	2
C₃₁×#3062	2
C₃₁×#3036	2
C₃₁×#3008	2
C₂×C₃₁×#442	2
C₃₁×#2932	2
C₃₁×#2897	2
#61218	31

Subgroups — C31×#61218 #21517977

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61218 #21517977