Subgroups — C₃₁×#60803 #21517562

Order 7936.

2444 conjugacy classes of subgroups.

The subgroup lattice has 802 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#532	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃₁×#532	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3214	C₂	1	4	yes	maximal, complemented
4	C₃₁×#3213	C₂	1	4	yes	maximal, complemented
5	C₃₁×#3207	C₂	1	4	yes	maximal, complemented
6	C₃₁×#3206	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3205	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3151	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3141	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3036	C₂	1	4	yes	maximal, complemented
11	C₃₁×#3006	C₂	1	4	yes	maximal, complemented
12	C₃₁×#2920	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×#41×C₃₁	—	2	1	no	—
14	C₂²×#41×C₃₁	C₂²	1	2	yes	—
15	C₂×C₃₁×AGL(1,ℤ/8)	C₂²	1	8	yes	complemented
16	C₃₁×#532	—	2	1	no	—
17	C₃₁×#532	—	2	1	no	—
18	C₃₁×#532	—	2	1	no	—
19	C₃₁×#532	—	2	1	no	—
20	C₃₁×#532	—	2	1	no	—
21	C₃₁×#532	—	2	1	no	—
22	C₃₁×#532	—	2	1	no	—
23	C₃₁×#532	—	2	1	no	—
24	C₃₁×#532	C₂²	1	2	yes	—
25	C₃₁×#532	C₂²	1	2	yes	—
26	C₃₁×#532	C₂²	1	2	yes	—
27	C₃₁×#532	C₂²	1	2	yes	—
28	C₃₁×#532	C₂²	1	2	yes	complemented
29	C₃₁×#532	C₂²	1	2	yes	complemented
30	C₃₁×#532	C₂²	1	2	yes	complemented
31	C₃₁×#532	C₂²	1	2	yes	complemented
32	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
33	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
34	C₂×C₃₁×#127	C₂²	1	1	yes	characteristic, complemented
35	C₂×C₃₁×#127	C₂²	1	1	yes	characteristic, complemented
36	C₂×C₃₁×#124	—	2	1	no	—
37	C₂×C₃₁×#124	C₂²	1	2	yes	complemented
38	C₂×C₃₁×#121	—	2	1	no	—
39	C₂×C₃₁×#121	—	2	1	no	—
40	C₂×C₃₁×#121	—	2	1	no	—
41	C₂×C₃₁×#121	C₂²	1	2	yes	—
42	C₂×C₄×D₄×C₃₁	—	2	1	no	—
43	C₂×C₄×D₄×C₃₁	—	2	1	no	—
44	C₂×C₄×D₄×C₃₁	—	2	1	no	—
45	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	complemented
46	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
47	C₃₁×#496	C₂²	1	8	yes	complemented
48	C₃₁×#493	C₂²	1	4	yes	complemented
49	C₃₁×#492	C₂²	1	4	yes	complemented
50	C₃₁×#489	C₂²	1	8	yes	complemented
51	C₃₁×#487	C₂²	1	4	yes	complemented
52	C₃₁×#486	C₂²	1	4	yes	complemented
53	C₃₁×#463	C₂²	1	16	yes	complemented
54	C₃₁×#461	C₂²	1	8	yes	complemented
55	C₃₁×#459	C₂²	1	8	yes	complemented
56	C₃₁×#449	C₂²	1	16	yes	complemented
57	C₃₁×#448	C₂²	1	8	yes	complemented
58	C₃₁×#447	C₂²	1	8	yes	complemented
59	C₃₁×#432	C₂²	1	2	yes	complemented
60	C₃₁×#432	C₂²	1	2	yes	complemented
61	C₃₁×#431	C₂²	1	2	yes	complemented
62	C₃₁×#431	C₂²	1	2	yes	complemented
63	C₃₁×#423	C₂²	1	2	yes	complemented
64	C₃₁×#417	C₂²	1	8	yes	complemented
65	C₃₁×#407	C₂²	1	2	yes	—
66	C₄×M₁₆×C₃₁	C₂²	1	2	yes	complemented
67	C₂×#41×C₃₁	—	2	2	no	—
68	C₂×#41×C₃₁	—	2	2	no	—
69	C₂×#41×C₃₁	—	2	2	no	—
70	C₂×#41×C₃₁	—	2	2	no	—
71	C₂×#41×C₃₁	—	2	2	no	—
72	C₂×#41×C₃₁	—	2	2	no	—
73	C₂×#41×C₃₁	—	4	8	no	—
74	C₂×#41×C₃₁	—	4	8	no	—
75	C₂×#41×C₃₁	C₂³	1	4	yes	—
76	C₂×#41×C₃₁	C₂³	1	4	yes	—
77	C₂²×Q₈×C₃₁	—	2	1	no	—
78	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
79	C₂²×D₄×C₃₁	—	2	2	no	—
80	C₂²×D₄×C₃₁	—	2	2	no	—
81	C₂²×D₄×C₃₁	—	2	1	no	—
82	C₂²×D₄×C₃₁	—	2	1	no	—
83	C₂²×D₄×C₃₁	—	2	1	no	—
84	C₂²×D₄×C₃₁	—	2	1	no	—
85	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
86	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
87	C₂³×C₄×C₃₁	—	2	2	no	—
88	C₂³×C₄×C₃₁	—	2	2	no	—
89	C₂³×C₄×C₃₁	D₄	1	1	yes	characteristic
90	C₂³×C₄×C₃₁	D₄	1	1	yes	characteristic
91	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
92	C₃₁×AGL(1,ℤ/8)	—	4	16	no	—
93	C₂×SD₁₆×C₃₁	C₂³	1	16	yes	—
94	C₂×D₈×C₃₁	C₂³	1	16	yes	—
95	C₂×M₁₆×C₃₁	C₂³	1	4	yes	—
96	C₃₁×C₄⋊Q₈	—	2	1	no	—
97	C₃₁×C₄⋊Q₈	—	2	1	no	—
98	C₃₁×C₄⋊Q₈	—	2	1	no	—
99	C₃₁×C₄⋊Q₈	—	2	1	no	—
100	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
101	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
102	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
103	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
104	C₃₁×#127	—	2	1	no	—
105	C₃₁×#127	—	2	1	no	—
106	C₃₁×#127	—	2	1	no	—
107	C₃₁×#127	—	2	1	no	—
108	C₃₁×#127	C₂³	1	2	yes	—
109	C₃₁×#127	C₂³	1	2	yes	—
110	C₃₁×#127	C₂³	1	2	yes	—
111	C₃₁×#127	C₂³	1	2	yes	—
112	C₃₁×#124	—	2	2	no	—
113	C₃₁×#124	—	2	2	no	—
114	C₃₁×#124	—	2	2	no	—
115	C₃₁×#124	—	2	2	no	—
116	C₃₁×#124	—	2	2	no	—
117	C₃₁×#124	—	2	2	no	—
118	C₃₁×#124	C₂³	1	4	yes	—
119	C₃₁×#124	C₂³	1	4	yes	—
120	C₃₁×#121	—	2	2	no	—
121	C₃₁×#121	—	2	2	no	—
122	C₃₁×#121	—	2	2	no	—
123	C₃₁×#121	—	2	2	no	—
124	C₃₁×#121	—	2	2	no	—
125	C₃₁×#121	—	2	2	no	—
126	C₃₁×#121	—	2	2	no	—
127	C₃₁×#121	—	2	2	no	—
128	C₃₁×#121	—	2	2	no	—
129	C₃₁×#121	—	2	2	no	—
130	C₃₁×#121	—	2	2	no	—
131	C₃₁×#121	—	2	2	no	—
132	C₃₁×#121	—	2	2	no	—
133	C₃₁×#121	—	2	2	no	—
134	C₃₁×#121	C₂³	1	4	yes	—
135	C₃₁×#121	C₂³	1	4	yes	—
136	C₄×D₄×C₃₁	—	2	2	no	—
137	C₄×D₄×C₃₁	—	2	2	no	—
138	C₄×D₄×C₃₁	—	2	2	no	—
139	C₄×D₄×C₃₁	—	2	2	no	—
140	C₄×D₄×C₃₁	—	2	2	no	—
141	C₄×D₄×C₃₁	—	2	2	no	—
142	C₄×D₄×C₃₁	—	2	2	no	—
143	C₄×D₄×C₃₁	—	2	2	no	—
144	C₄×D₄×C₃₁	—	2	2	no	—
145	C₄×D₄×C₃₁	—	2	2	no	—
146	C₄×D₄×C₃₁	—	2	2	no	—
147	C₄×D₄×C₃₁	—	2	2	no	—
148	C₄×D₄×C₃₁	—	2	2	no	—
149	C₄×D₄×C₃₁	—	2	2	no	—
150	C₄×D₄×C₃₁	C₂³	1	4	yes	—
151	C₄×D₄×C₃₁	C₂³	1	4	yes	—
152	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
153	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
154	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
155	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
156	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
157	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
158	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
159	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
160	C₂×C₄²×C₃₁	D₄	1	1	yes	characteristic
161	C₂×C₄²×C₃₁	D₄	1	1	yes	characteristic
162	C₂×C₄²×C₃₁	D₄	1	1	yes	characteristic
163	C₂×C₄²×C₃₁	D₄	1	1	yes	characteristic
164	C₂×C₄²×C₃₁	D₄	1	1	yes	characteristic
165	C₂×C₄²×C₃₁	D₄	1	1	yes	characteristic
166	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
167	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
168	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
169	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
170	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
171	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
172	C₃₁×C₄⋊C₈	C₂³	1	4	yes	—
173	C₃₁×C₄⋊C₈	C₂³	1	4	yes	—
174	C₃₁×#103	C₂³	1	16	yes	—
175	C₃₁×#102	C₂³	1	16	yes	—
176	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
177	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
178	C₃₁×#97	C₂³	1	4	yes	—
179	C₄×C₈×C₃₁	C₂³	1	4	yes	—
180	C₂⁴×C₃₁	—	2	2	no	—
181	C₂⁴×C₃₁	—	2	2	no	—
182	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
183	#41×C₃₁	—	2	16	no	—
184	#41×C₃₁	—	4	8	no	—
185	#41×C₃₁	—	4	8	no	—
186	#41×C₃₁	—	4	8	no	—
187	#41×C₃₁	—	4	8	no	—
188	#41×C₃₁	—	4	8	no	—
189	#41×C₃₁	—	4	8	no	—
190	#41×C₃₁	—	4	8	no	—
191	C₂×Q₈×C₃₁	—	2	2	no	—
192	C₂×Q₈×C₃₁	—	2	2	no	—
193	C₂×Q₈×C₃₁	—	2	2	no	—
194	C₂×Q₈×C₃₁	—	4	4	no	—
195	C₂×Q₈×C₃₁	—	4	4	no	—
196	C₂×Q₈×C₃₁	C₂⁴	1	4	yes	—
197	C₂×D₄×C₃₁	—	2	4	no	—
198	C₂×D₄×C₃₁	—	2	4	no	—
199	C₂×D₄×C₃₁	—	2	4	no	—
200	C₂×D₄×C₃₁	—	2	4	no	—
201	C₂×D₄×C₃₁	—	2	2	no	—
202	C₂×D₄×C₃₁	—	2	2	no	—
203	C₂×D₄×C₃₁	—	2	2	no	—
204	C₂×D₄×C₃₁	—	2	2	no	—
205	C₂×D₄×C₃₁	—	2	2	no	—
206	C₂×D₄×C₃₁	—	2	2	no	—
207	C₂×D₄×C₃₁	—	2	2	no	—
208	C₂×D₄×C₃₁	—	2	2	no	—
209	C₂×D₄×C₃₁	—	2	2	no	—
210	C₂×D₄×C₃₁	—	2	2	no	—
211	C₂×D₄×C₃₁	—	2	8	no	—
212	C₂×D₄×C₃₁	—	4	4	no	—
213	C₂×D₄×C₃₁	—	4	4	no	—
214	C₂×D₄×C₃₁	—	4	4	no	—
215	C₂×D₄×C₃₁	—	4	4	no	—
216	C₂×D₄×C₃₁	—	4	8	no	—
217	C₂×D₄×C₃₁	—	4	8	no	—
218	C₂×D₄×C₃₁	—	4	4	no	—
219	C₂×D₄×C₃₁	C₂⁴	1	4	yes	—
220	C₂×D₄×C₃₁	C₂⁴	1	4	yes	—
221	C₂²×C₄×C₃₁	—	2	4	no	—
222	C₂²×C₄×C₃₁	—	2	4	no	—
223	C₂²×C₄×C₃₁	—	2	2	no	—
224	C₂²×C₄×C₃₁	—	2	2	no	—
225	C₂²×C₄×C₃₁	—	2	4	no	—
226	C₂²×C₄×C₃₁	—	2	4	no	—
227	C₂²×C₄×C₃₁	—	2	4	no	—
228	C₂²×C₄×C₃₁	—	2	4	no	—
229	C₂²×C₄×C₃₁	—	4	2	no	—
230	C₂²×C₄×C₃₁	—	4	8	no	—
231	C₂²×C₄×C₃₁	—	4	8	no	—
232	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
233	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
234	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
235	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
236	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
237	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
238	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
239	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
240	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
241	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
242	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
243	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
244	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
245	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
246	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
247	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
248	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
249	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
250	SD₁₆×C₃₁	—	4	16	no	—
251	D₈×C₃₁	—	4	16	no	—
252	M₁₆×C₃₁	—	2	8	no	—
253	C₂×C₈×C₃₁	C₂⁴	1	8	yes	—
254	C₄⋊C₄×C₃₁	—	2	2	no	—
255	C₄⋊C₄×C₃₁	—	2	2	no	—
256	C₄⋊C₄×C₃₁	—	2	2	no	—
257	C₄⋊C₄×C₃₁	—	2	2	no	—
258	C₄⋊C₄×C₃₁	—	2	2	no	—
259	C₄⋊C₄×C₃₁	—	2	2	no	—
260	C₄⋊C₄×C₃₁	—	2	2	no	—
261	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
262	C₂²⋊C₄×C₃₁	—	2	4	no	—
263	C₂²⋊C₄×C₃₁	—	2	4	no	—
264	C₂²⋊C₄×C₃₁	—	2	4	no	—
265	C₂²⋊C₄×C₃₁	—	2	4	no	—
266	C₂²⋊C₄×C₃₁	—	2	4	no	—
267	C₂²⋊C₄×C₃₁	—	2	4	no	—
268	C₂²⋊C₄×C₃₁	—	2	4	no	—
269	C₂²⋊C₄×C₃₁	—	2	4	no	—
270	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
271	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
272	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
273	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
274	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
275	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
276	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
277	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
278	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
279	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
280	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
281	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
282	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
283	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
284	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
285	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
286	#60803	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
287	C₂³×C₃₁	—	2	2	no	—
288	C₂³×C₃₁	—	2	2	no	—
289	C₂³×C₃₁	—	2	4	no	—
290	C₂³×C₃₁	—	2	4	no	—
291	C₂³×C₃₁	—	4	1	no	—
292	C₂³×C₃₁	—	4	4	no	—
293	C₂³×C₃₁	—	4	4	no	—
294	C₂³×C₃₁	—	4	4	no	—
295	C₂³×C₃₁	—	4	4	no	—
296	C₂³×C₃₁	—	4	4	no	—
297	C₂³×C₃₁	—	4	4	no	—
298	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
299	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
300	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
301	Q₈×C₃₁	—	2	8	no	—
302	Q₈×C₃₁	—	4	4	no	—
303	Q₈×C₃₁	—	4	4	no	—
304	Q₈×C₃₁	—	4	4	no	—
305	D₄×C₃₁	—	2	8	no	—
306	D₄×C₃₁	—	2	8	no	—
307	D₄×C₃₁	—	4	4	no	—
308	D₄×C₃₁	—	4	4	no	—
309	D₄×C₃₁	—	4	4	no	—
310	D₄×C₃₁	—	4	4	no	—
311	D₄×C₃₁	—	4	8	no	—
312	D₄×C₃₁	—	4	8	no	—
313	D₄×C₃₁	—	4	8	no	—
314	D₄×C₃₁	—	4	8	no	—
315	D₄×C₃₁	—	4	4	no	—
316	D₄×C₃₁	—	4	4	no	—
317	D₄×C₃₁	—	4	4	no	—
318	D₄×C₃₁	—	4	4	no	—
319	D₄×C₃₁	—	4	4	no	—
320	D₄×C₃₁	—	4	4	no	—
321	C₂×C₄×C₃₁	—	2	2	no	—
322	C₂×C₄×C₃₁	—	2	2	no	—
323	C₂×C₄×C₃₁	—	2	2	no	—
324	C₂×C₄×C₃₁	—	2	2	no	—
325	C₂×C₄×C₃₁	—	2	2	no	—
326	C₂×C₄×C₃₁	—	2	2	no	—
327	C₂×C₄×C₃₁	—	2	2	no	—
328	C₂×C₄×C₃₁	—	2	2	no	—
329	C₂×C₄×C₃₁	—	2	2	no	—
330	C₂×C₄×C₃₁	—	2	2	no	—
331	C₂×C₄×C₃₁	—	2	2	no	—
332	C₂×C₄×C₃₁	—	2	2	no	—
333	C₂×C₄×C₃₁	—	2	2	no	—
334	C₂×C₄×C₃₁	—	2	4	no	—
335	C₂×C₄×C₃₁	—	2	4	no	—
336	C₂×C₄×C₃₁	—	4	1	no	—
337	C₂×C₄×C₃₁	—	4	1	no	—
338	C₂×C₄×C₃₁	—	4	1	no	—
339	C₂×C₄×C₃₁	—	4	8	no	—
340	C₂×C₄×C₃₁	—	4	8	no	—
341	C₂×C₄×C₃₁	—	4	4	no	—
342	C₂×C₄×C₃₁	—	4	4	no	—
343	C₂×C₄×C₃₁	—	4	8	no	—
344	C₂×C₄×C₃₁	—	4	8	no	—
345	C₂×C₄×C₃₁	AGL(1,ℤ/8)	1	4	yes	complemented
346	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
347	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
348	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
349	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
350	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
351	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
352	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
353	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
354	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
355	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
356	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
357	C₂×C₄×C₃₁	H(5,𝔽₂)	1	4	yes	—
358	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
359	C₈×C₃₁	—	2	8	no	—
360	C₂×#532	C₂×C₃₁	1	1	yes	characteristic, complemented
361	C₂×#532	C₂×C₃₁	1	1	yes	characteristic, complemented
362	#3214	C₂×C₃₁	1	4	yes	complemented
363	#3213	C₂×C₃₁	1	4	yes	complemented
364	#3207	C₂×C₃₁	1	4	yes	complemented
365	#3206	C₂×C₃₁	1	2	yes	complemented
366	#3205	C₂×C₃₁	1	2	yes	complemented
367	#3151	C₂×C₃₁	1	2	yes	complemented
368	#3141	C₂×C₃₁	1	2	yes	complemented
369	#3036	C₂×C₃₁	1	4	yes	complemented
370	#3006	C₂×C₃₁	1	4	yes	complemented
371	#2920	C₂×C₃₁	1	1	yes	characteristic, complemented
372	C₂²×C₃₁	—	2	1	no	—
373	C₂²×C₃₁	—	2	1	no	—
374	C₂²×C₃₁	—	2	1	no	—
375	C₂²×C₃₁	—	2	1	no	—
376	C₂²×C₃₁	—	2	1	no	—
377	C₂²×C₃₁	—	2	1	no	—
378	C₂²×C₃₁	—	2	1	no	—
379	C₂²×C₃₁	—	4	4	no	—
380	C₂²×C₃₁	—	4	4	no	—
381	C₂²×C₃₁	—	4	4	no	—
382	C₂²×C₃₁	—	4	4	no	—
383	C₂²×C₃₁	—	4	4	no	—
384	C₂²×C₃₁	—	4	4	no	—
385	C₂²×C₃₁	—	4	4	no	—
386	C₂²×C₃₁	—	8	8	no	—
387	C₂²×C₃₁	—	8	8	no	—
388	C₂²×C₃₁	#535	1	2	yes	—
389	C₂²×C₃₁	C₂×AGL(1,ℤ/8)	1	2	yes	—
390	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
391	C₄×C₃₁	—	2	1	no	—
392	C₄×C₃₁	—	2	1	no	—
393	C₄×C₃₁	—	2	1	no	—
394	C₄×C₃₁	—	2	1	no	—
395	C₄×C₃₁	—	2	1	no	—
396	C₄×C₃₁	—	2	1	no	—
397	C₄×C₃₁	—	2	1	no	—
398	C₄×C₃₁	—	4	4	no	—
399	C₄×C₃₁	—	4	4	no	—
400	C₄×C₃₁	#535	1	2	yes	—
401	C₄×C₃₁	C₂×AGL(1,ℤ/8)	1	2	yes	—
402	C₄×C₃₁	C₂×AGL(1,ℤ/8)	1	2	yes	—
403	C₄×C₃₁	#575	1	2	yes	—
404	C₄×C₃₁	C₂×H(5,𝔽₂)	1	2	yes	—
405	C₂²×#41	—	2	1	no	—
406	C₂²×#41	C₂²×C₃₁	1	2	yes	—
407	C₂×AGL(1,ℤ/8)	C₂²×C₃₁	1	8	yes	complemented
408	#532	—	2	1	no	—
409	#532	—	2	1	no	—
410	#532	—	2	1	no	—
411	#532	—	2	1	no	—
412	#532	—	2	1	no	—
413	#532	—	2	1	no	—
414	#532	—	2	1	no	—
415	#532	—	2	1	no	—
416	#532	C₂²×C₃₁	1	2	yes	—
417	#532	C₂²×C₃₁	1	2	yes	—
418	#532	C₂²×C₃₁	1	2	yes	—
419	#532	C₂²×C₃₁	1	2	yes	—
420	#532	C₂²×C₃₁	1	2	yes	complemented
421	#532	C₂²×C₃₁	1	2	yes	complemented
422	#532	C₂²×C₃₁	1	2	yes	complemented
423	#532	C₂²×C₃₁	1	2	yes	complemented
424	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
425	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
426	C₂×#127	C₂²×C₃₁	1	1	yes	characteristic, complemented
427	C₂×#127	C₂²×C₃₁	1	1	yes	characteristic, complemented
428	C₂×#124	—	2	1	no	—
429	C₂×#124	C₂²×C₃₁	1	2	yes	complemented
430	C₂×#121	—	2	1	no	—
431	C₂×#121	—	2	1	no	—
432	C₂×#121	—	2	1	no	—
433	C₂×#121	C₂²×C₃₁	1	2	yes	—
434	C₂×C₄×D₄	—	2	1	no	—
435	C₂×C₄×D₄	—	2	1	no	—
436	C₂×C₄×D₄	—	2	1	no	—
437	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	complemented
438	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
439	#496	C₂²×C₃₁	1	8	yes	complemented
440	#493	C₂²×C₃₁	1	4	yes	complemented
441	#492	C₂²×C₃₁	1	4	yes	complemented
442	#489	C₂²×C₃₁	1	8	yes	complemented
443	#487	C₂²×C₃₁	1	4	yes	complemented
444	#486	C₂²×C₃₁	1	4	yes	complemented
445	#463	C₂²×C₃₁	1	16	yes	complemented
446	#461	C₂²×C₃₁	1	8	yes	complemented
447	#459	C₂²×C₃₁	1	8	yes	complemented
448	#449	C₂²×C₃₁	1	16	yes	complemented
449	#448	C₂²×C₃₁	1	8	yes	complemented
450	#447	C₂²×C₃₁	1	8	yes	complemented
451	#432	C₂²×C₃₁	1	2	yes	complemented
452	#432	C₂²×C₃₁	1	2	yes	complemented
453	#431	C₂²×C₃₁	1	2	yes	complemented
454	#431	C₂²×C₃₁	1	2	yes	complemented
455	#423	C₂²×C₃₁	1	2	yes	complemented
456	#417	C₂²×C₃₁	1	8	yes	complemented
457	#407	C₂²×C₃₁	1	2	yes	—
458	C₄×M₁₆	C₂²×C₃₁	1	2	yes	complemented
459	C₂×C₃₁	—	2	2	no	—
460	C₂×C₃₁	—	2	2	no	—
461	C₂×C₃₁	—	4	1	no	—
462	C₂×C₃₁	—	8	4	no	—
463	C₂×C₃₁	—	8	4	no	—
464	C₂×C₃₁	C₂×#535	1	1	yes	characteristic
465	C₂×C₃₁	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
466	C₂×C₃₁	C₂×#575	1	1	yes	characteristic
467	C₂×#41	—	2	2	no	—
468	C₂×#41	—	2	2	no	—
469	C₂×#41	—	2	2	no	—
470	C₂×#41	—	2	2	no	—
471	C₂×#41	—	2	2	no	—
472	C₂×#41	—	2	2	no	—
473	C₂×#41	—	4	8	no	—
474	C₂×#41	—	4	8	no	—
475	C₂×#41	C₂³×C₃₁	1	4	yes	—
476	C₂×#41	C₂³×C₃₁	1	4	yes	—
477	C₂²×Q₈	—	2	1	no	—
478	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
479	C₂²×D₄	—	2	2	no	—
480	C₂²×D₄	—	2	2	no	—
481	C₂²×D₄	—	2	1	no	—
482	C₂²×D₄	—	2	1	no	—
483	C₂²×D₄	—	2	1	no	—
484	C₂²×D₄	—	2	1	no	—
485	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
486	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
487	C₂³×C₄	—	2	2	no	—
488	C₂³×C₄	—	2	2	no	—
489	C₂³×C₄	D₄×C₃₁	1	1	yes	characteristic
490	C₂³×C₄	D₄×C₃₁	1	1	yes	characteristic
491	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
492	AGL(1,ℤ/8)	—	4	16	no	—
493	C₂×SD₁₆	C₂³×C₃₁	1	16	yes	—
494	C₂×D₈	C₂³×C₃₁	1	16	yes	—
495	C₂×M₁₆	C₂³×C₃₁	1	4	yes	—
496	C₄⋊Q₈	—	2	1	no	—
497	C₄⋊Q₈	—	2	1	no	—
498	C₄⋊Q₈	—	2	1	no	—
499	C₄⋊Q₈	—	2	1	no	—
500	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
501	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
502	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
503	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
504	#127	—	2	1	no	—
505	#127	—	2	1	no	—
506	#127	—	2	1	no	—
507	#127	—	2	1	no	—
508	#127	C₂³×C₃₁	1	2	yes	—
509	#127	C₂³×C₃₁	1	2	yes	—
510	#127	C₂³×C₃₁	1	2	yes	—
511	#127	C₂³×C₃₁	1	2	yes	—
512	#124	—	2	2	no	—
513	#124	—	2	2	no	—
514	#124	—	2	2	no	—
515	#124	—	2	2	no	—
516	#124	—	2	2	no	—
517	#124	—	2	2	no	—
518	#124	C₂³×C₃₁	1	4	yes	—
519	#124	C₂³×C₃₁	1	4	yes	—
520	#121	—	2	2	no	—
521	#121	—	2	2	no	—
522	#121	—	2	2	no	—
523	#121	—	2	2	no	—
524	#121	—	2	2	no	—
525	#121	—	2	2	no	—
526	#121	—	2	2	no	—
527	#121	—	2	2	no	—
528	#121	—	2	2	no	—
529	#121	—	2	2	no	—
530	#121	—	2	2	no	—
531	#121	—	2	2	no	—
532	#121	—	2	2	no	—
533	#121	—	2	2	no	—
534	#121	C₂³×C₃₁	1	4	yes	—
535	#121	C₂³×C₃₁	1	4	yes	—
536	C₄×D₄	—	2	2	no	—
537	C₄×D₄	—	2	2	no	—
538	C₄×D₄	—	2	2	no	—
539	C₄×D₄	—	2	2	no	—
540	C₄×D₄	—	2	2	no	—
541	C₄×D₄	—	2	2	no	—
542	C₄×D₄	—	2	2	no	—
543	C₄×D₄	—	2	2	no	—
544	C₄×D₄	—	2	2	no	—
545	C₄×D₄	—	2	2	no	—
546	C₄×D₄	—	2	2	no	—
547	C₄×D₄	—	2	2	no	—
548	C₄×D₄	—	2	2	no	—
549	C₄×D₄	—	2	2	no	—
550	C₄×D₄	C₂³×C₃₁	1	4	yes	—
551	C₄×D₄	C₂³×C₃₁	1	4	yes	—
552	C₂×C₄⋊C₄	—	2	1	no	—
553	C₂×C₄⋊C₄	—	2	1	no	—
554	C₂×C₄⋊C₄	—	2	1	no	—
555	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
556	C₂×C₂²⋊C₄	—	2	2	no	—
557	C₂×C₂²⋊C₄	—	2	2	no	—
558	C₂×C₂²⋊C₄	—	2	2	no	—
559	C₂×C₂²⋊C₄	—	2	2	no	—
560	C₂×C₄²	D₄×C₃₁	1	1	yes	characteristic
561	C₂×C₄²	D₄×C₃₁	1	1	yes	characteristic
562	C₂×C₄²	D₄×C₃₁	1	1	yes	characteristic
563	C₂×C₄²	D₄×C₃₁	1	1	yes	characteristic
564	C₂×C₄²	D₄×C₃₁	1	1	yes	characteristic
565	C₂×C₄²	D₄×C₃₁	1	1	yes	characteristic
566	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
567	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
568	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
569	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
570	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
571	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
572	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
573	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
574	#103	C₂³×C₃₁	1	16	yes	—
575	#102	C₂³×C₃₁	1	16	yes	—
576	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
577	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
578	#97	C₂³×C₃₁	1	4	yes	—
579	C₄×C₈	C₂³×C₃₁	1	4	yes	—
580	C₃₁	#60803	1	1	yes	characteristic, direct product factor, Sylow
581	C₂⁴	—	2	2	no	—
582	C₂⁴	—	2	2	no	—
583	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
584	#41	—	2	16	no	—
585	#41	—	4	8	no	—
586	#41	—	4	8	no	—
587	#41	—	4	8	no	—
588	#41	—	4	8	no	—
589	#41	—	4	8	no	—
590	#41	—	4	8	no	—
591	#41	—	4	8	no	—
592	C₂×Q₈	—	2	2	no	—
593	C₂×Q₈	—	2	2	no	—
594	C₂×Q₈	—	2	2	no	—
595	C₂×Q₈	—	4	4	no	—
596	C₂×Q₈	—	4	4	no	—
597	C₂×Q₈	C₂⁴×C₃₁	1	4	yes	—
598	C₂×D₄	—	2	4	no	—
599	C₂×D₄	—	2	4	no	—
600	C₂×D₄	—	2	4	no	—
601	C₂×D₄	—	2	4	no	—
602	C₂×D₄	—	2	2	no	—
603	C₂×D₄	—	2	2	no	—
604	C₂×D₄	—	2	2	no	—
605	C₂×D₄	—	2	2	no	—
606	C₂×D₄	—	2	2	no	—
607	C₂×D₄	—	2	2	no	—
608	C₂×D₄	—	2	2	no	—
609	C₂×D₄	—	2	2	no	—
610	C₂×D₄	—	2	2	no	—
611	C₂×D₄	—	2	2	no	—
612	C₂×D₄	—	2	8	no	—
613	C₂×D₄	—	4	4	no	—
614	C₂×D₄	—	4	4	no	—
615	C₂×D₄	—	4	4	no	—
616	C₂×D₄	—	4	4	no	—
617	C₂×D₄	—	4	8	no	—
618	C₂×D₄	—	4	8	no	—
619	C₂×D₄	—	4	4	no	—
620	C₂×D₄	C₂⁴×C₃₁	1	4	yes	—
621	C₂×D₄	C₂⁴×C₃₁	1	4	yes	—
622	C₂²×C₄	—	2	4	no	—
623	C₂²×C₄	—	2	4	no	—
624	C₂²×C₄	—	2	2	no	—
625	C₂²×C₄	—	2	2	no	—
626	C₂²×C₄	—	2	4	no	—
627	C₂²×C₄	—	2	4	no	—
628	C₂²×C₄	—	2	4	no	—
629	C₂²×C₄	—	2	4	no	—
630	C₂²×C₄	—	4	2	no	—
631	C₂²×C₄	—	4	8	no	—
632	C₂²×C₄	—	4	8	no	—
633	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
634	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
635	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
636	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
637	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
638	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
639	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
640	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
641	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
642	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
643	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
644	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
645	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
646	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
647	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
648	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
649	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
650	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
651	SD₁₆	—	4	16	no	—
652	D₈	—	4	16	no	—
653	M₁₆	—	2	8	no	—
654	C₂×C₈	C₂⁴×C₃₁	1	8	yes	—
655	C₄⋊C₄	—	2	2	no	—
656	C₄⋊C₄	—	2	2	no	—
657	C₄⋊C₄	—	2	2	no	—
658	C₄⋊C₄	—	2	2	no	—
659	C₄⋊C₄	—	2	2	no	—
660	C₄⋊C₄	—	2	2	no	—
661	C₄⋊C₄	—	2	2	no	—
662	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
663	C₂²⋊C₄	—	2	4	no	—
664	C₂²⋊C₄	—	2	4	no	—
665	C₂²⋊C₄	—	2	4	no	—
666	C₂²⋊C₄	—	2	4	no	—
667	C₂²⋊C₄	—	2	4	no	—
668	C₂²⋊C₄	—	2	4	no	—
669	C₂²⋊C₄	—	2	4	no	—
670	C₂²⋊C₄	—	2	4	no	—
671	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
672	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
673	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
674	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
675	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
676	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
677	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
678	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
679	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
680	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
681	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
682	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
683	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
684	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
685	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
686	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
687	C₂³	—	2	2	no	—
688	C₂³	—	2	2	no	—
689	C₂³	—	2	4	no	—
690	C₂³	—	2	4	no	—
691	C₂³	—	4	1	no	—
692	C₂³	—	4	4	no	—
693	C₂³	—	4	4	no	—
694	C₂³	—	4	4	no	—
695	C₂³	—	4	4	no	—
696	C₂³	—	4	4	no	—
697	C₂³	—	4	4	no	—
698	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
699	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
700	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
701	Q₈	—	2	8	no	—
702	Q₈	—	4	4	no	—
703	Q₈	—	4	4	no	—
704	Q₈	—	4	4	no	—
705	D₄	—	2	8	no	—
706	D₄	—	2	8	no	—
707	D₄	—	4	4	no	—
708	D₄	—	4	4	no	—
709	D₄	—	4	4	no	—
710	D₄	—	4	4	no	—
711	D₄	—	4	8	no	—
712	D₄	—	4	8	no	—
713	D₄	—	4	8	no	—
714	D₄	—	4	8	no	—
715	D₄	—	4	4	no	—
716	D₄	—	4	4	no	—
717	D₄	—	4	4	no	—
718	D₄	—	4	4	no	—
719	D₄	—	4	4	no	—
720	D₄	—	4	4	no	—
721	C₂×C₄	—	2	2	no	—
722	C₂×C₄	—	2	2	no	—
723	C₂×C₄	—	2	2	no	—
724	C₂×C₄	—	2	2	no	—
725	C₂×C₄	—	2	2	no	—
726	C₂×C₄	—	2	2	no	—
727	C₂×C₄	—	2	2	no	—
728	C₂×C₄	—	2	2	no	—
729	C₂×C₄	—	2	2	no	—
730	C₂×C₄	—	2	2	no	—
731	C₂×C₄	—	2	2	no	—
732	C₂×C₄	—	2	2	no	—
733	C₂×C₄	—	2	2	no	—
734	C₂×C₄	—	2	4	no	—
735	C₂×C₄	—	2	4	no	—
736	C₂×C₄	—	4	1	no	—
737	C₂×C₄	—	4	1	no	—
738	C₂×C₄	—	4	1	no	—
739	C₂×C₄	—	4	8	no	—
740	C₂×C₄	—	4	8	no	—
741	C₂×C₄	—	4	4	no	—
742	C₂×C₄	—	4	4	no	—
743	C₂×C₄	—	4	8	no	—
744	C₂×C₄	—	4	8	no	—
745	C₂×C₄	C₃₁×AGL(1,ℤ/8)	1	4	yes	complemented
746	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
747	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
748	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
749	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
750	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
751	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
752	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
753	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
754	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
755	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
756	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
757	C₂×C₄	C₃₁×H(5,𝔽₂)	1	4	yes	—
758	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
759	C₈	—	2	8	no	—
760	C₂²	—	2	1	no	—
761	C₂²	—	2	1	no	—
762	C₂²	—	2	1	no	—
763	C₂²	—	2	1	no	—
764	C₂²	—	2	1	no	—
765	C₂²	—	2	1	no	—
766	C₂²	—	2	1	no	—
767	C₂²	—	4	4	no	—
768	C₂²	—	4	4	no	—
769	C₂²	—	4	4	no	—
770	C₂²	—	4	4	no	—
771	C₂²	—	4	4	no	—
772	C₂²	—	4	4	no	—
773	C₂²	—	4	4	no	—
774	C₂²	—	8	8	no	—
775	C₂²	—	8	8	no	—
776	C₂²	C₃₁×#535	1	2	yes	—
777	C₂²	C₂×C₃₁×AGL(1,ℤ/8)	1	2	yes	—
778	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
779	C₄	—	2	1	no	—
780	C₄	—	2	1	no	—
781	C₄	—	2	1	no	—
782	C₄	—	2	1	no	—
783	C₄	—	2	1	no	—
784	C₄	—	2	1	no	—
785	C₄	—	2	1	no	—
786	C₄	—	4	4	no	—
787	C₄	—	4	4	no	—
788	C₄	C₃₁×#535	1	2	yes	—
789	C₄	C₂×C₃₁×AGL(1,ℤ/8)	1	2	yes	—
790	C₄	C₂×C₃₁×AGL(1,ℤ/8)	1	2	yes	—
791	C₄	C₃₁×#575	1	2	yes	—
792	C₄	C₂×C₃₁×H(5,𝔽₂)	1	2	yes	—
793	C₂	—	2	2	no	—
794	C₂	—	2	2	no	—
795	C₂	—	4	1	no	—
796	C₂	—	8	4	no	—
797	C₂	—	8	4	no	—
798	C₂	C₂×C₃₁×#535	1	1	yes	characteristic
799	C₂	C₂²×C₃₁×AGL(1,ℤ/8)	1	1	yes	characteristic
800	C₂	C₂×C₃₁×#575	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 ◁ C₂²×C₄²×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃₁×#532	C₂	semidirect
2. C₂×C₃₁×#532	C₂	semidirect
3. C₃₁×#3214	C₂	semidirect
4. C₃₁×#3213	C₂	semidirect
5. C₃₁×#3207	C₂	semidirect
6. C₃₁×#3206	C₂	semidirect
7. C₃₁×#3205	C₂	semidirect
8. C₃₁×#3151	C₂	semidirect
9. C₃₁×#3141	C₂	semidirect
10. C₃₁×#3036	C₂	semidirect
11. C₃₁×#3006	C₂	semidirect
12. C₃₁×#2920	C₂	semidirect
15. C₂×C₃₁×AGL(1,ℤ/8)	C₂²	semidirect
28. C₃₁×#532	C₂²	semidirect
29. C₃₁×#532	C₂²	semidirect
30. C₃₁×#532	C₂²	semidirect
31. C₃₁×#532	C₂²	semidirect
32. C₂×C₃₁×C₄⋊Q₈	C₂²	semidirect
33. C₂×C₃₁×C₄⋊Q₈	C₂²	semidirect
34. C₂×C₃₁×#127	C₂²	semidirect
35. C₂×C₃₁×#127	C₂²	semidirect
37. C₂×C₃₁×#124	C₂²	semidirect
45. C₂×C₄×D₄×C₃₁	C₂²	semidirect
47. C₃₁×#496	C₂²	semidirect
48. C₃₁×#493	C₂²	semidirect
49. C₃₁×#492	C₂²	semidirect
50. C₃₁×#489	C₂²	semidirect
51. C₃₁×#487	C₂²	semidirect
52. C₃₁×#486	C₂²	semidirect
53. C₃₁×#463	C₂²	semidirect
54. C₃₁×#461	C₂²	semidirect
55. C₃₁×#459	C₂²	semidirect
56. C₃₁×#449	C₂²	semidirect
57. C₃₁×#448	C₂²	semidirect
58. C₃₁×#447	C₂²	semidirect
59. C₃₁×#432	C₂²	semidirect
60. C₃₁×#432	C₂²	semidirect
61. C₃₁×#431	C₂²	semidirect
62. C₃₁×#431	C₂²	semidirect
63. C₃₁×#423	C₂²	semidirect
64. C₃₁×#417	C₂²	semidirect
66. C₄×M₁₆×C₃₁	C₂²	semidirect
286. #60803	C₃₁	direct (N × H)
345. C₂×C₄×C₃₁	AGL(1,ℤ/8)	semidirect
360. C₂×#532	C₂×C₃₁	semidirect
361. C₂×#532	C₂×C₃₁	semidirect
362. #3214	C₂×C₃₁	semidirect
363. #3213	C₂×C₃₁	semidirect
364. #3207	C₂×C₃₁	semidirect
365. #3206	C₂×C₃₁	semidirect
366. #3205	C₂×C₃₁	semidirect
367. #3151	C₂×C₃₁	semidirect
368. #3141	C₂×C₃₁	semidirect
369. #3036	C₂×C₃₁	semidirect
370. #3006	C₂×C₃₁	semidirect
371. #2920	C₂×C₃₁	semidirect
407. C₂×AGL(1,ℤ/8)	C₂²×C₃₁	semidirect
420. #532	C₂²×C₃₁	semidirect
421. #532	C₂²×C₃₁	semidirect
422. #532	C₂²×C₃₁	semidirect
423. #532	C₂²×C₃₁	semidirect
424. C₂×C₄⋊Q₈	C₂²×C₃₁	semidirect
425. C₂×C₄⋊Q₈	C₂²×C₃₁	semidirect
426. C₂×#127	C₂²×C₃₁	semidirect
427. C₂×#127	C₂²×C₃₁	semidirect
429. C₂×#124	C₂²×C₃₁	semidirect
437. C₂×C₄×D₄	C₂²×C₃₁	semidirect
439. #496	C₂²×C₃₁	semidirect
440. #493	C₂²×C₃₁	semidirect
441. #492	C₂²×C₃₁	semidirect
442. #489	C₂²×C₃₁	semidirect
443. #487	C₂²×C₃₁	semidirect
444. #486	C₂²×C₃₁	semidirect
445. #463	C₂²×C₃₁	semidirect
446. #461	C₂²×C₃₁	semidirect
447. #459	C₂²×C₃₁	semidirect
448. #449	C₂²×C₃₁	semidirect
449. #448	C₂²×C₃₁	semidirect
450. #447	C₂²×C₃₁	semidirect
451. #432	C₂²×C₃₁	semidirect
452. #432	C₂²×C₃₁	semidirect
453. #431	C₂²×C₃₁	semidirect
454. #431	C₂²×C₃₁	semidirect
455. #423	C₂²×C₃₁	semidirect
456. #417	C₂²×C₃₁	semidirect
458. C₄×M₁₆	C₂²×C₃₁	semidirect
580. C₃₁	#60803	direct (N × H)
745. C₂×C₄	C₃₁×AGL(1,ℤ/8)	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃₁×#532	2
C₃₁×#3214	2
C₃₁×#3213	2
C₃₁×#3207	2
C₃₁×#3206	2
C₃₁×#3205	2
C₃₁×#3151	2
C₃₁×#3141	2
C₃₁×#3036	2
C₃₁×#3006	2
C₃₁×#2920	2
#60803	31

Subgroups — C31×#60803 #21517562

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#60803 #21517562