Subgroups — C₃₁×#61325 #21518084

Order 7936.

1870 conjugacy classes of subgroups.

The subgroup lattice has 814 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×#3501	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3370	C₂	1	4	yes	maximal, complemented
4	C₃₁×#3367	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3366	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3361	C₂	1	4	yes	maximal, complemented
7	C₃₁×#3360	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3358	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3136	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3131	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#3083	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3077	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3041	C₂	1	2	yes	maximal, complemented
14	C₃₁×#3036	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#2960	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#2946	C₂	1	2	yes	maximal, complemented
17	C₂×C₄×D₈×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₃₁×AGL(1,ℤ/8)	C₂²	1	2	yes	—
19	C₂²×D₈×C₃₁	C₂²	1	1	yes	characteristic
20	C₃₁×#559	C₂²	1	4	yes	complemented
21	C₃₁×#556	C₂²	1	2	yes	complemented
22	C₃₁×#555	—	2	1	no	—
23	C₃₁×#554	—	2	1	no	—
24	C₃₁×#554	—	2	2	no	—
25	C₃₁×#554	C₂²	1	2	yes	complemented
26	C₃₁×#554	C₂²	1	4	yes	complemented
27	C₃₁×#553	—	2	2	no	—
28	C₃₁×#550	C₂²	1	2	yes	complemented
29	D₄×Q₈×C₃₁	—	2	1	no	—
30	D₄×Q₈×C₃₁	C₂²	1	2	yes	complemented
31	C₃₁×#547	—	2	1	no	—
32	C₃₁×#544	C₂²	1	2	yes	—
33	C₃₁×#543	—	2	2	no	—
34	C₃₁×#538	—	2	2	no	—
35	C₃₁×#535	C₂²	1	2	yes	—
36	C₃₁×#533	C₂²	1	1	yes	characteristic
37	C₃₁×#533	C₂²	1	1	yes	characteristic
38	C₃₁×#532	C₂²	1	1	yes	characteristic
39	C₃₁×#525	—	2	2	no	—
40	C₂×C₃₁×C₂²⋊Q₈	—	2	2	no	—
41	C₃₁×#520	C₂²	1	2	yes	—
42	C₃₁×#518	C₂²	1	2	yes	—
43	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
44	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
45	C₃₁×#490	C₂²	1	4	yes	complemented
46	C₃₁×#489	C₂²	1	4	yes	complemented
47	C₃₁×#488	C₂²	1	4	yes	complemented
48	C₃₁×#488	C₂²	1	2	yes	complemented
49	C₃₁×#488	C₂²	1	2	yes	complemented
50	C₃₁×#487	C₂²	1	1	yes	characteristic, complemented
51	C₃₁×#487	C₂²	1	1	yes	characteristic, complemented
52	C₃₁×#486	C₂²	1	1	yes	characteristic, complemented
53	C₃₁×#486	C₂²	1	4	yes	complemented
54	C₃₁×#486	C₂²	1	1	yes	characteristic, complemented
55	C₃₁×#479	C₂²	1	4	yes	complemented
56	C₃₁×#478	C₂²	1	4	yes	complemented
57	C₃₁×#478	C₂²	1	4	yes	complemented
58	C₃₁×#477	C₂²	1	4	yes	complemented
59	C₃₁×#476	C₂²	1	2	yes	complemented
60	C₃₁×#474	C₂²	1	2	yes	complemented
61	C₃₁×#474	C₂²	1	4	yes	complemented
62	C₃₁×#463	C₂²	1	4	yes	—
63	C₃₁×#463	C₂²	1	4	yes	—
64	C₃₁×#463	C₂²	1	4	yes	complemented
65	C₃₁×#461	C₂²	1	2	yes	complemented
66	C₃₁×#459	C₂²	1	4	yes	—
67	C₃₁×#459	C₂²	1	4	yes	—
68	C₃₁×#459	C₂²	1	2	yes	complemented
69	C₃₁×#446	C₂²	1	2	yes	complemented
70	C₃₁×#446	C₂²	1	2	yes	complemented
71	C₈×Q₈×C₃₁	C₂²	1	2	yes	complemented
72	C₈×Q₈×C₃₁	C₂²	1	2	yes	complemented
73	C₃₁×#442	C₂²	1	4	yes	complemented
74	C₃₁×#440	C₂²	1	4	yes	complemented
75	C₄×SD₁₆×C₃₁	C₂²	1	4	yes	complemented
76	C₄×D₈×C₃₁	C₂²	1	2	yes	—
77	C₄×D₈×C₃₁	C₂²	1	2	yes	—
78	C₄×D₈×C₃₁	C₂²	1	2	yes	—
79	C₄×D₈×C₃₁	C₂²	1	2	yes	—
80	C₄×D₈×C₃₁	C₂²	1	4	yes	complemented
81	C₃₁×#428	C₂²	1	2	yes	—
82	C₂×C₃₁×#107	C₂²	1	1	yes	characteristic
83	C₃₁×#424	C₂²	1	2	yes	—
84	C₃₁×#423	C₂²	1	1	yes	characteristic
85	C₃₁×#418	C₂²	1	2	yes	—
86	C₃₁×#417	C₂²	1	2	yes	—
87	C₃₁×#416	C₂²	1	2	yes	—
88	C₃₁×#416	C₂²	1	2	yes	—
89	C₂×C₃₁×#102	C₂²	1	1	yes	characteristic
90	C₂×C₃₁×#102	C₂²	1	1	yes	characteristic
91	C₃₁×#405	C₂²	1	2	yes	—
92	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
93	C₂×#41×C₃₁	—	2	2	no	—
94	C₂×#41×C₃₁	C₂³	1	2	yes	—
95	C₂²×Q₈×C₃₁	—	2	2	no	—
96	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
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)	—	2	8	no	—
101	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
102	C₂×D₈×C₃₁	—	2	4	no	—
103	C₂×D₈×C₃₁	C₂³	1	2	yes	—
104	C₂×D₈×C₃₁	C₂³	1	2	yes	—
105	C₂×D₈×C₃₁	C₂³	1	4	yes	—
106	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
107	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
108	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
109	C₃₁×C₄⋊Q₈	—	2	2	no	—
110	C₃₁×C₄⋊Q₈	D₄	1	1	yes	characteristic
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	4	yes	—
115	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
116	C₃₁×#127	C₂³	1	4	yes	—
117	C₃₁×#127	C₂³	1	1	yes	characteristic
118	C₃₁×#126	—	2	4	no	—
119	C₃₁×#125	—	2	2	no	—
120	C₃₁×#125	D₄	1	2	yes	—
121	C₃₁×#125	C₂³	1	2	yes	—
122	C₃₁×#125	C₂³	1	4	yes	—
123	C₃₁×#124	—	2	4	no	—
124	C₃₁×#124	C₂³	1	4	yes	—
125	C₃₁×#124	C₂³	1	2	yes	—
126	C₃₁×#123	—	2	4	no	—
127	C₃₁×#123	—	2	4	no	—
128	C₃₁×C₂²⋊Q₈	—	2	2	no	—
129	C₃₁×C₂²⋊Q₈	—	2	2	no	—
130	C₃₁×C₂²⋊Q₈	—	2	4	no	—
131	C₃₁×C₂²⋊Q₈	—	2	1	no	—
132	C₃₁×C₂²⋊Q₈	—	2	1	no	—
133	C₃₁×C₂²⋊Q₈	—	2	2	no	—
134	C₃₁×C₂²⋊Q₈	—	2	4	no	—
135	C₃₁×C₂²⋊Q₈	—	2	4	no	—
136	C₃₁×C₂²⋊Q₈	—	2	4	no	—
137	C₃₁×C₂²⋊Q₈	—	2	4	no	—
138	C₃₁×C₂²⋊Q₈	—	2	4	no	—
139	C₃₁×C₂²⋊Q₈	D₄	1	2	yes	—
140	C₃₁×C₂²⋊Q₈	D₄	1	2	yes	—
141	C₃₁×#121	—	2	1	no	—
142	C₃₁×#121	—	2	1	no	—
143	C₃₁×#121	—	2	2	no	—
144	C₃₁×#121	—	2	2	no	—
145	C₃₁×#121	—	2	2	no	—
146	C₃₁×#121	—	2	4	no	—
147	C₃₁×#120	—	2	4	no	—
148	C₄×Q₈×C₃₁	—	2	1	no	—
149	C₄×Q₈×C₃₁	—	2	1	no	—
150	C₄×Q₈×C₃₁	C₂³	1	4	yes	—
151	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
152	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
153	C₄×D₄×C₃₁	—	2	2	no	—
154	C₄×D₄×C₃₁	—	2	2	no	—
155	C₄×D₄×C₃₁	—	2	4	no	—
156	C₄×D₄×C₃₁	—	2	4	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	—	2	1	no	—
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	4	yes	—
168	C₄×D₄×C₃₁	C₂³	1	4	yes	—
169	C₄×D₄×C₃₁	C₂³	1	4	yes	—
170	C₃₁×#117	—	2	2	no	—
171	C₃₁×#117	—	2	2	no	—
172	C₃₁×#117	C₂³	1	2	yes	—
173	C₃₁×#117	C₂³	1	2	yes	—
174	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
175	C₂×C₄⋊C₄×C₃₁	—	2	4	no	—
176	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
177	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
178	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
179	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
180	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
181	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
182	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
183	C₃₁×#107	C₂³	1	2	yes	—
184	C₃₁×#107	C₂³	1	2	yes	—
185	C₃₁×#107	C₂³	1	4	yes	—
186	C₃₁×#106	C₂³	1	4	yes	—
187	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
188	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
189	C₃₁×C₄⋊C₈	C₂³	1	4	yes	—
190	C₃₁×C₄⋊C₈	C₂³	1	4	yes	—
191	C₃₁×#103	C₂³	1	2	yes	—
192	C₃₁×#103	C₂³	1	2	yes	—
193	C₃₁×#103	C₂³	1	2	yes	—
194	C₃₁×#103	C₂³	1	2	yes	—
195	C₃₁×#103	C₂³	1	4	yes	—
196	C₃₁×#102	C₂³	1	2	yes	—
197	C₃₁×#102	C₂³	1	2	yes	—
198	C₃₁×#102	C₂³	1	2	yes	—
199	C₃₁×#102	C₂³	1	2	yes	—
200	C₃₁×#102	C₂³	1	2	yes	—
201	C₃₁×#102	C₂³	1	2	yes	—
202	C₃₁×#102	C₂³	1	2	yes	—
203	C₃₁×#102	C₂³	1	2	yes	—
204	C₃₁×#102	C₂³	1	4	yes	—
205	C₃₁×#102	C₂³	1	4	yes	—
206	C₃₁×#102	C₂³	1	4	yes	—
207	C₃₁×#97	C₂³	1	4	yes	—
208	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
209	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
210	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
211	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
212	C₄×C₈×C₃₁	C₂³	1	4	yes	—
213	C₂⁴×C₃₁	—	2	1	no	—
214	C₂⁴×C₃₁	—	2	1	no	—
215	#41×C₃₁	—	2	4	no	—
216	#41×C₃₁	—	2	4	no	—
217	#41×C₃₁	—	8	4	no	—
218	C₂×Q₈×C₃₁	—	2	1	no	—
219	C₂×Q₈×C₃₁	—	2	1	no	—
220	C₂×Q₈×C₃₁	—	2	4	no	—
221	C₂×Q₈×C₃₁	—	8	4	no	—
222	C₂×Q₈×C₃₁	C₂×D₄	1	2	yes	—
223	C₂×Q₈×C₃₁	C₂×D₄	1	2	yes	—
224	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
225	C₂×D₄×C₃₁	—	2	2	no	—
226	C₂×D₄×C₃₁	—	2	1	no	—
227	C₂×D₄×C₃₁	—	2	1	no	—
228	C₂×D₄×C₃₁	—	2	1	no	—
229	C₂×D₄×C₃₁	—	2	4	no	—
230	C₂×D₄×C₃₁	—	2	1	no	—
231	C₂×D₄×C₃₁	—	2	4	no	—
232	C₂×D₄×C₃₁	—	2	2	no	—
233	C₂×D₄×C₃₁	—	2	2	no	—
234	C₂×D₄×C₃₁	—	2	2	no	—
235	C₂×D₄×C₃₁	#41	1	4	yes	complemented
236	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
237	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
238	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
239	C₂²×C₄×C₃₁	—	2	1	no	—
240	C₂²×C₄×C₃₁	—	2	1	no	—
241	C₂²×C₄×C₃₁	—	2	2	no	—
242	C₂²×C₄×C₃₁	—	2	2	no	—
243	C₂²×C₄×C₃₁	—	2	2	no	—
244	C₂²×C₄×C₃₁	—	2	4	no	—
245	C₂²×C₄×C₃₁	—	2	4	no	—
246	C₂²×C₄×C₃₁	—	2	2	no	—
247	C₂²×C₄×C₃₁	—	2	4	no	—
248	C₂²×C₄×C₃₁	—	2	2	no	—
249	C₂²×C₄×C₃₁	—	8	2	no	—
250	C₂²×C₄×C₃₁	—	8	2	no	—
251	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
252	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
253	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
254	SD₁₆×C₃₁	—	2	8	no	—
255	D₈×C₃₁	—	2	4	no	—
256	D₈×C₃₁	—	2	4	no	—
257	D₈×C₃₁	—	2	8	no	—
258	M₁₆×C₃₁	—	2	4	no	—
259	C₂×C₈×C₃₁	—	2	2	no	—
260	C₂×C₈×C₃₁	—	2	2	no	—
261	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
262	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
263	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
264	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
265	C₂×C₈×C₃₁	C₂⁴	1	4	yes	—
266	C₄⋊C₄×C₃₁	—	2	1	no	—
267	C₄⋊C₄×C₃₁	—	2	2	no	—
268	C₄⋊C₄×C₃₁	—	2	1	no	—
269	C₄⋊C₄×C₃₁	—	2	4	no	—
270	C₄⋊C₄×C₃₁	—	2	4	no	—
271	C₄⋊C₄×C₃₁	—	2	4	no	—
272	C₄⋊C₄×C₃₁	—	2	4	no	—
273	C₄⋊C₄×C₃₁	—	2	1	no	—
274	C₄⋊C₄×C₃₁	—	2	1	no	—
275	C₄⋊C₄×C₃₁	—	2	1	no	—
276	C₄⋊C₄×C₃₁	—	2	2	no	—
277	C₄⋊C₄×C₃₁	—	2	1	no	—
278	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
279	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
280	C₄⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
281	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
282	C₄⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
283	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
284	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
285	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
286	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
287	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
288	C₂²⋊C₄×C₃₁	—	2	2	no	—
289	C₂²⋊C₄×C₃₁	—	2	2	no	—
290	C₂²⋊C₄×C₃₁	—	2	4	no	—
291	C₂²⋊C₄×C₃₁	—	2	4	no	—
292	C₂²⋊C₄×C₃₁	—	2	2	no	—
293	C₂²⋊C₄×C₃₁	—	2	2	no	—
294	C₂²⋊C₄×C₃₁	—	2	2	no	—
295	C₂²⋊C₄×C₃₁	—	2	4	no	—
296	C₂²⋊C₄×C₃₁	—	2	4	no	—
297	C₂²⋊C₄×C₃₁	—	2	2	no	—
298	C₂²⋊C₄×C₃₁	—	2	4	no	—
299	C₂²⋊C₄×C₃₁	—	2	2	no	—
300	C₂²⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
301	C₄²×C₃₁	—	2	4	no	—
302	C₄²×C₃₁	—	2	2	no	—
303	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
304	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
305	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
306	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
307	C₄²×C₃₁	C₂⁴	1	4	yes	—
308	#61325	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
309	C₂³×C₃₁	—	2	2	no	—
310	C₂³×C₃₁	—	2	4	no	—
311	C₂³×C₃₁	—	2	2	no	—
312	C₂³×C₃₁	—	2	2	no	—
313	C₂³×C₃₁	—	4	2	no	—
314	C₂³×C₃₁	—	8	1	no	—
315	C₂³×C₃₁	—	8	1	no	—
316	C₂³×C₃₁	—	8	1	no	—
317	C₂³×C₃₁	—	8	1	no	—
318	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
319	Q₈×C₃₁	—	2	4	no	—
320	Q₈×C₃₁	—	2	2	no	—
321	Q₈×C₃₁	—	2	2	no	—
322	Q₈×C₃₁	—	4	2	no	—
323	Q₈×C₃₁	—	4	2	no	—
324	Q₈×C₃₁	—	8	1	no	—
325	Q₈×C₃₁	—	8	4	no	—
326	D₄×C₃₁	—	2	4	no	—
327	D₄×C₃₁	—	2	2	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	—	4	4	no	—
333	D₄×C₃₁	—	4	2	no	—
334	D₄×C₃₁	—	4	2	no	—
335	D₄×C₃₁	—	8	1	no	—
336	D₄×C₃₁	—	8	4	no	—
337	D₄×C₃₁	—	8	4	no	—
338	D₄×C₃₁	C₂×#41	1	4	yes	—
339	C₂×C₄×C₃₁	—	2	2	no	—
340	C₂×C₄×C₃₁	—	2	2	no	—
341	C₂×C₄×C₃₁	—	2	2	no	—
342	C₂×C₄×C₃₁	—	2	2	no	—
343	C₂×C₄×C₃₁	—	2	2	no	—
344	C₂×C₄×C₃₁	—	2	2	no	—
345	C₂×C₄×C₃₁	—	4	1	no	—
346	C₂×C₄×C₃₁	—	4	4	no	—
347	C₂×C₄×C₃₁	—	4	4	no	—
348	C₂×C₄×C₃₁	—	4	4	no	—
349	C₂×C₄×C₃₁	—	8	4	no	—
350	C₂×C₄×C₃₁	—	8	2	no	—
351	C₂×C₄×C₃₁	—	8	2	no	—
352	C₂×C₄×C₃₁	—	8	4	no	—
353	C₂×C₄×C₃₁	—	8	4	no	—
354	C₂×C₄×C₃₁	—	8	1	no	—
355	C₂×C₄×C₃₁	—	8	1	no	—
356	C₂×C₄×C₃₁	C₂²×D₄	1	4	yes	—
357	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
358	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
359	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
360	C₂×C₄×C₃₁	C₂²×D₄	1	4	yes	—
361	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
362	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
363	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
364	C₂×C₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
365	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
366	C₈×C₃₁	—	2	1	no	—
367	C₈×C₃₁	—	2	1	no	—
368	C₈×C₃₁	—	2	4	no	—
369	C₈×C₃₁	—	2	1	no	—
370	C₈×C₃₁	—	2	1	no	—
371	#3506	C₂×C₃₁	1	1	yes	characteristic, complemented
372	#3501	C₂×C₃₁	1	1	yes	characteristic, complemented
373	#3370	C₂×C₃₁	1	4	yes	complemented
374	#3367	C₂×C₃₁	1	2	yes	complemented
375	#3366	C₂×C₃₁	1	2	yes	complemented
376	#3361	C₂×C₃₁	1	4	yes	complemented
377	#3360	C₂×C₃₁	1	2	yes	complemented
378	#3358	C₂×C₃₁	1	2	yes	complemented
379	#3136	C₂×C₃₁	1	2	yes	complemented
380	#3131	C₂×C₃₁	1	1	yes	characteristic, complemented
381	#3083	C₂×C₃₁	1	2	yes	complemented
382	#3077	C₂×C₃₁	1	1	yes	characteristic, complemented
383	#3041	C₂×C₃₁	1	2	yes	complemented
384	#3036	C₂×C₃₁	1	1	yes	characteristic, complemented
385	#2960	C₂×C₃₁	1	1	yes	characteristic, complemented
386	#2946	C₂×C₃₁	1	2	yes	complemented
387	C₂×C₄×D₈	C₂×C₃₁	1	1	yes	characteristic, complemented
388	C₂²×C₃₁	—	2	1	no	—
389	C₂²×C₃₁	—	2	1	no	—
390	C₂²×C₃₁	—	2	4	no	—
391	C₂²×C₃₁	—	4	2	no	—
392	C₂²×C₃₁	—	4	2	no	—
393	C₂²×C₃₁	—	4	2	no	—
394	C₂²×C₃₁	—	4	2	no	—
395	C₂²×C₃₁	—	4	2	no	—
396	C₂²×C₃₁	—	4	2	no	—
397	C₂²×C₃₁	—	4	2	no	—
398	C₂²×C₃₁	—	4	2	no	—
399	C₂²×C₃₁	—	8	4	no	—
400	C₂²×C₃₁	—	8	4	no	—
401	C₂²×C₃₁	#548	1	2	yes	—
402	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
403	C₄×C₃₁	—	2	1	no	—
404	C₄×C₃₁	—	2	1	no	—
405	C₄×C₃₁	—	2	4	no	—
406	C₄×C₃₁	—	2	1	no	—
407	C₄×C₃₁	—	2	4	no	—
408	C₄×C₃₁	—	4	2	no	—
409	C₄×C₃₁	—	4	2	no	—
410	C₄×C₃₁	—	4	2	no	—
411	C₄×C₃₁	—	4	2	no	—
412	C₄×C₃₁	—	4	2	no	—
413	C₄×C₃₁	#548	1	2	yes	—
414	C₄×C₃₁	#576	1	2	yes	—
415	C₄×C₃₁	C₂²×#41	1	1	yes	characteristic
416	C₄×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
417	C₂×AGL(1,ℤ/8)	C₂²×C₃₁	1	2	yes	—
418	C₂²×D₈	C₂²×C₃₁	1	1	yes	characteristic
419	#559	C₂²×C₃₁	1	4	yes	complemented
420	#556	C₂²×C₃₁	1	2	yes	complemented
421	#555	—	2	1	no	—
422	#554	—	2	1	no	—
423	#554	—	2	2	no	—
424	#554	C₂²×C₃₁	1	2	yes	complemented
425	#554	C₂²×C₃₁	1	4	yes	complemented
426	#553	—	2	2	no	—
427	#550	C₂²×C₃₁	1	2	yes	complemented
428	D₄×Q₈	—	2	1	no	—
429	D₄×Q₈	C₂²×C₃₁	1	2	yes	complemented
430	#547	—	2	1	no	—
431	#544	C₂²×C₃₁	1	2	yes	—
432	#543	—	2	2	no	—
433	#538	—	2	2	no	—
434	#535	C₂²×C₃₁	1	2	yes	—
435	#533	C₂²×C₃₁	1	1	yes	characteristic
436	#533	C₂²×C₃₁	1	1	yes	characteristic
437	#532	C₂²×C₃₁	1	1	yes	characteristic
438	#525	—	2	2	no	—
439	C₂×C₂²⋊Q₈	—	2	2	no	—
440	#520	C₂²×C₃₁	1	2	yes	—
441	#518	C₂²×C₃₁	1	2	yes	—
442	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
443	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
444	#490	C₂²×C₃₁	1	4	yes	complemented
445	#489	C₂²×C₃₁	1	4	yes	complemented
446	#488	C₂²×C₃₁	1	4	yes	complemented
447	#488	C₂²×C₃₁	1	2	yes	complemented
448	#488	C₂²×C₃₁	1	2	yes	complemented
449	#487	C₂²×C₃₁	1	1	yes	characteristic, complemented
450	#487	C₂²×C₃₁	1	1	yes	characteristic, complemented
451	#486	C₂²×C₃₁	1	1	yes	characteristic, complemented
452	#486	C₂²×C₃₁	1	4	yes	complemented
453	#486	C₂²×C₃₁	1	1	yes	characteristic, complemented
454	#479	C₂²×C₃₁	1	4	yes	complemented
455	#478	C₂²×C₃₁	1	4	yes	complemented
456	#478	C₂²×C₃₁	1	4	yes	complemented
457	#477	C₂²×C₃₁	1	4	yes	complemented
458	#476	C₂²×C₃₁	1	2	yes	complemented
459	#474	C₂²×C₃₁	1	2	yes	complemented
460	#474	C₂²×C₃₁	1	4	yes	complemented
461	#463	C₂²×C₃₁	1	4	yes	—
462	#463	C₂²×C₃₁	1	4	yes	—
463	#463	C₂²×C₃₁	1	4	yes	complemented
464	#461	C₂²×C₃₁	1	2	yes	complemented
465	#459	C₂²×C₃₁	1	4	yes	—
466	#459	C₂²×C₃₁	1	4	yes	—
467	#459	C₂²×C₃₁	1	2	yes	complemented
468	#446	C₂²×C₃₁	1	2	yes	complemented
469	#446	C₂²×C₃₁	1	2	yes	complemented
470	C₈×Q₈	C₂²×C₃₁	1	2	yes	complemented
471	C₈×Q₈	C₂²×C₃₁	1	2	yes	complemented
472	#442	C₂²×C₃₁	1	4	yes	complemented
473	#440	C₂²×C₃₁	1	4	yes	complemented
474	C₄×SD₁₆	C₂²×C₃₁	1	4	yes	complemented
475	C₄×D₈	C₂²×C₃₁	1	2	yes	—
476	C₄×D₈	C₂²×C₃₁	1	2	yes	—
477	C₄×D₈	C₂²×C₃₁	1	2	yes	—
478	C₄×D₈	C₂²×C₃₁	1	2	yes	—
479	C₄×D₈	C₂²×C₃₁	1	4	yes	complemented
480	#428	C₂²×C₃₁	1	2	yes	—
481	C₂×#107	C₂²×C₃₁	1	1	yes	characteristic
482	#424	C₂²×C₃₁	1	2	yes	—
483	#423	C₂²×C₃₁	1	1	yes	characteristic
484	#418	C₂²×C₃₁	1	2	yes	—
485	#417	C₂²×C₃₁	1	2	yes	—
486	#416	C₂²×C₃₁	1	2	yes	—
487	#416	C₂²×C₃₁	1	2	yes	—
488	C₂×#102	C₂²×C₃₁	1	1	yes	characteristic
489	C₂×#102	C₂²×C₃₁	1	1	yes	characteristic
490	#405	C₂²×C₃₁	1	2	yes	—
491	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
492	C₂×C₃₁	—	2	2	no	—
493	C₂×C₃₁	—	4	4	no	—
494	C₂×C₃₁	—	8	2	no	—
495	C₂×C₃₁	—	8	2	no	—
496	C₂×C₃₁	C₂×#548	1	1	yes	characteristic
497	C₂×C₃₁	C₂×#576	1	1	yes	characteristic
498	C₂×C₃₁	#3584	1	1	yes	characteristic
499	C₂×#41	—	2	2	no	—
500	C₂×#41	C₂³×C₃₁	1	2	yes	—
501	C₂²×Q₈	—	2	2	no	—
502	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
503	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
504	C₂³×C₄	—	2	1	no	—
505	C₂³×C₄	—	2	1	no	—
506	AGL(1,ℤ/8)	—	2	8	no	—
507	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
508	C₂×D₈	—	2	4	no	—
509	C₂×D₈	C₂³×C₃₁	1	2	yes	—
510	C₂×D₈	C₂³×C₃₁	1	2	yes	—
511	C₂×D₈	C₂³×C₃₁	1	4	yes	—
512	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
513	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
514	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
515	C₄⋊Q₈	—	2	2	no	—
516	C₄⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
517	C₄⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
518	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
519	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
520	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
521	C₄⋊Q₈	C₂³×C₃₁	1	4	yes	—
522	#127	C₂³×C₃₁	1	1	yes	characteristic
523	#127	C₂³×C₃₁	1	4	yes	—
524	#126	—	2	4	no	—
525	#125	—	2	2	no	—
526	#125	D₄×C₃₁	1	2	yes	—
527	#125	C₂³×C₃₁	1	2	yes	—
528	#125	C₂³×C₃₁	1	4	yes	—
529	#124	—	2	4	no	—
530	#124	C₂³×C₃₁	1	2	yes	—
531	#124	C₂³×C₃₁	1	4	yes	—
532	#123	—	2	4	no	—
533	#123	—	2	4	no	—
534	C₂²⋊Q₈	—	2	2	no	—
535	C₂²⋊Q₈	—	2	2	no	—
536	C₂²⋊Q₈	—	2	4	no	—
537	C₂²⋊Q₈	—	2	1	no	—
538	C₂²⋊Q₈	—	2	1	no	—
539	C₂²⋊Q₈	—	2	2	no	—
540	C₂²⋊Q₈	—	2	4	no	—
541	C₂²⋊Q₈	—	2	4	no	—
542	C₂²⋊Q₈	—	2	4	no	—
543	C₂²⋊Q₈	—	2	4	no	—
544	C₂²⋊Q₈	—	2	4	no	—
545	C₂²⋊Q₈	D₄×C₃₁	1	2	yes	—
546	C₂²⋊Q₈	D₄×C₃₁	1	2	yes	—
547	#121	—	2	1	no	—
548	#121	—	2	1	no	—
549	#121	—	2	2	no	—
550	#121	—	2	2	no	—
551	#121	—	2	2	no	—
552	#121	—	2	4	no	—
553	#120	—	2	4	no	—
554	C₄×Q₈	—	2	1	no	—
555	C₄×Q₈	—	2	1	no	—
556	C₄×Q₈	C₂³×C₃₁	1	4	yes	—
557	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
558	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
559	C₄×D₄	—	2	2	no	—
560	C₄×D₄	—	2	2	no	—
561	C₄×D₄	—	2	4	no	—
562	C₄×D₄	—	2	4	no	—
563	C₄×D₄	—	2	1	no	—
564	C₄×D₄	—	2	1	no	—
565	C₄×D₄	—	2	1	no	—
566	C₄×D₄	—	2	1	no	—
567	C₄×D₄	—	2	1	no	—
568	C₄×D₄	—	2	1	no	—
569	C₄×D₄	C₂³×C₃₁	1	2	yes	—
570	C₄×D₄	C₂³×C₃₁	1	2	yes	—
571	C₄×D₄	C₂³×C₃₁	1	2	yes	—
572	C₄×D₄	C₂³×C₃₁	1	2	yes	—
573	C₄×D₄	C₂³×C₃₁	1	4	yes	—
574	C₄×D₄	C₂³×C₃₁	1	4	yes	—
575	C₄×D₄	C₂³×C₃₁	1	4	yes	—
576	#117	—	2	2	no	—
577	#117	—	2	2	no	—
578	#117	C₂³×C₃₁	1	2	yes	—
579	#117	C₂³×C₃₁	1	2	yes	—
580	C₂×C₄⋊C₄	—	2	2	no	—
581	C₂×C₄⋊C₄	—	2	4	no	—
582	C₂×C₄⋊C₄	—	2	2	no	—
583	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
584	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
585	C₂×C₂²⋊C₄	—	2	1	no	—
586	C₂×C₂²⋊C₄	—	2	1	no	—
587	C₂×C₂²⋊C₄	—	2	4	no	—
588	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
589	#107	C₂³×C₃₁	1	2	yes	—
590	#107	C₂³×C₃₁	1	2	yes	—
591	#107	C₂³×C₃₁	1	4	yes	—
592	#106	C₂³×C₃₁	1	4	yes	—
593	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
594	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
595	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
596	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
597	#103	C₂³×C₃₁	1	2	yes	—
598	#103	C₂³×C₃₁	1	2	yes	—
599	#103	C₂³×C₃₁	1	2	yes	—
600	#103	C₂³×C₃₁	1	2	yes	—
601	#103	C₂³×C₃₁	1	4	yes	—
602	#102	C₂³×C₃₁	1	2	yes	—
603	#102	C₂³×C₃₁	1	2	yes	—
604	#102	C₂³×C₃₁	1	2	yes	—
605	#102	C₂³×C₃₁	1	2	yes	—
606	#102	C₂³×C₃₁	1	2	yes	—
607	#102	C₂³×C₃₁	1	2	yes	—
608	#102	C₂³×C₃₁	1	2	yes	—
609	#102	C₂³×C₃₁	1	2	yes	—
610	#102	C₂³×C₃₁	1	4	yes	—
611	#102	C₂³×C₃₁	1	4	yes	—
612	#102	C₂³×C₃₁	1	4	yes	—
613	#97	C₂³×C₃₁	1	4	yes	—
614	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
615	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
616	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
617	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
618	C₄×C₈	C₂³×C₃₁	1	4	yes	—
619	C₃₁	#61325	1	1	yes	characteristic, direct product factor, Sylow
620	C₂⁴	—	2	1	no	—
621	C₂⁴	—	2	1	no	—
622	#41	—	2	4	no	—
623	#41	—	2	4	no	—
624	#41	—	8	4	no	—
625	C₂×Q₈	—	2	1	no	—
626	C₂×Q₈	—	2	1	no	—
627	C₂×Q₈	—	2	4	no	—
628	C₂×Q₈	—	8	4	no	—
629	C₂×Q₈	C₂×D₄×C₃₁	1	2	yes	—
630	C₂×Q₈	C₂×D₄×C₃₁	1	2	yes	—
631	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
632	C₂×D₄	—	2	2	no	—
633	C₂×D₄	—	2	1	no	—
634	C₂×D₄	—	2	1	no	—
635	C₂×D₄	—	2	1	no	—
636	C₂×D₄	—	2	4	no	—
637	C₂×D₄	—	2	1	no	—
638	C₂×D₄	—	2	4	no	—
639	C₂×D₄	—	2	2	no	—
640	C₂×D₄	—	2	2	no	—
641	C₂×D₄	—	2	2	no	—
642	C₂×D₄	#41×C₃₁	1	4	yes	complemented
643	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
644	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
645	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
646	C₂²×C₄	—	2	1	no	—
647	C₂²×C₄	—	2	1	no	—
648	C₂²×C₄	—	2	2	no	—
649	C₂²×C₄	—	2	2	no	—
650	C₂²×C₄	—	2	2	no	—
651	C₂²×C₄	—	2	4	no	—
652	C₂²×C₄	—	2	4	no	—
653	C₂²×C₄	—	2	2	no	—
654	C₂²×C₄	—	2	4	no	—
655	C₂²×C₄	—	2	2	no	—
656	C₂²×C₄	—	8	2	no	—
657	C₂²×C₄	—	8	2	no	—
658	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
659	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
660	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
661	SD₁₆	—	2	8	no	—
662	D₈	—	2	4	no	—
663	D₈	—	2	4	no	—
664	D₈	—	2	8	no	—
665	M₁₆	—	2	4	no	—
666	C₂×C₈	—	2	2	no	—
667	C₂×C₈	—	2	2	no	—
668	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
669	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
670	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
671	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
672	C₂×C₈	C₂⁴×C₃₁	1	4	yes	—
673	C₄⋊C₄	—	2	1	no	—
674	C₄⋊C₄	—	2	2	no	—
675	C₄⋊C₄	—	2	1	no	—
676	C₄⋊C₄	—	2	4	no	—
677	C₄⋊C₄	—	2	4	no	—
678	C₄⋊C₄	—	2	4	no	—
679	C₄⋊C₄	—	2	4	no	—
680	C₄⋊C₄	—	2	1	no	—
681	C₄⋊C₄	—	2	1	no	—
682	C₄⋊C₄	—	2	1	no	—
683	C₄⋊C₄	—	2	2	no	—
684	C₄⋊C₄	—	2	1	no	—
685	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
686	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
687	C₄⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
688	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
689	C₄⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
690	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
691	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
692	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
693	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
694	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
695	C₂²⋊C₄	—	2	2	no	—
696	C₂²⋊C₄	—	2	2	no	—
697	C₂²⋊C₄	—	2	4	no	—
698	C₂²⋊C₄	—	2	4	no	—
699	C₂²⋊C₄	—	2	2	no	—
700	C₂²⋊C₄	—	2	2	no	—
701	C₂²⋊C₄	—	2	2	no	—
702	C₂²⋊C₄	—	2	4	no	—
703	C₂²⋊C₄	—	2	4	no	—
704	C₂²⋊C₄	—	2	2	no	—
705	C₂²⋊C₄	—	2	4	no	—
706	C₂²⋊C₄	—	2	2	no	—
707	C₂²⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
708	C₄²	—	2	4	no	—
709	C₄²	—	2	2	no	—
710	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
711	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
712	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
713	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
714	C₄²	C₂⁴×C₃₁	1	4	yes	—
715	C₂³	—	2	2	no	—
716	C₂³	—	2	4	no	—
717	C₂³	—	2	2	no	—
718	C₂³	—	2	2	no	—
719	C₂³	—	4	2	no	—
720	C₂³	—	8	1	no	—
721	C₂³	—	8	1	no	—
722	C₂³	—	8	1	no	—
723	C₂³	—	8	1	no	—
724	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
725	Q₈	—	2	4	no	—
726	Q₈	—	2	2	no	—
727	Q₈	—	2	2	no	—
728	Q₈	—	4	2	no	—
729	Q₈	—	4	2	no	—
730	Q₈	—	8	1	no	—
731	Q₈	—	8	4	no	—
732	D₄	—	2	4	no	—
733	D₄	—	2	2	no	—
734	D₄	—	2	2	no	—
735	D₄	—	2	2	no	—
736	D₄	—	2	2	no	—
737	D₄	—	2	2	no	—
738	D₄	—	4	4	no	—
739	D₄	—	4	2	no	—
740	D₄	—	4	2	no	—
741	D₄	—	8	1	no	—
742	D₄	—	8	4	no	—
743	D₄	—	8	4	no	—
744	D₄	C₂×#41×C₃₁	1	4	yes	—
745	C₂×C₄	—	2	2	no	—
746	C₂×C₄	—	2	2	no	—
747	C₂×C₄	—	2	2	no	—
748	C₂×C₄	—	2	2	no	—
749	C₂×C₄	—	2	2	no	—
750	C₂×C₄	—	2	2	no	—
751	C₂×C₄	—	4	1	no	—
752	C₂×C₄	—	4	4	no	—
753	C₂×C₄	—	4	4	no	—
754	C₂×C₄	—	4	4	no	—
755	C₂×C₄	—	8	4	no	—
756	C₂×C₄	—	8	2	no	—
757	C₂×C₄	—	8	2	no	—
758	C₂×C₄	—	8	4	no	—
759	C₂×C₄	—	8	4	no	—
760	C₂×C₄	—	8	1	no	—
761	C₂×C₄	—	8	1	no	—
762	C₂×C₄	C₂²×D₄×C₃₁	1	4	yes	—
763	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
764	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
765	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
766	C₂×C₄	C₂²×D₄×C₃₁	1	4	yes	—
767	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
768	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
769	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
770	C₂×C₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
771	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
772	C₈	—	2	1	no	—
773	C₈	—	2	1	no	—
774	C₈	—	2	4	no	—
775	C₈	—	2	1	no	—
776	C₈	—	2	1	no	—
777	C₂²	—	2	1	no	—
778	C₂²	—	2	1	no	—
779	C₂²	—	2	4	no	—
780	C₂²	—	4	2	no	—
781	C₂²	—	4	2	no	—
782	C₂²	—	4	2	no	—
783	C₂²	—	4	2	no	—
784	C₂²	—	4	2	no	—
785	C₂²	—	4	2	no	—
786	C₂²	—	4	2	no	—
787	C₂²	—	4	2	no	—
788	C₂²	—	8	4	no	—
789	C₂²	—	8	4	no	—
790	C₂²	C₃₁×#548	1	2	yes	—
791	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
792	C₄	—	2	1	no	—
793	C₄	—	2	4	no	—
794	C₄	—	2	1	no	—
795	C₄	—	2	1	no	—
796	C₄	—	2	4	no	—
797	C₄	—	4	2	no	—
798	C₄	—	4	2	no	—
799	C₄	—	4	2	no	—
800	C₄	—	4	2	no	—
801	C₄	—	4	2	no	—
802	C₄	C₃₁×#548	1	2	yes	—
803	C₄	C₃₁×#576	1	2	yes	—
804	C₄	C₂²×#41×C₃₁	1	1	yes	characteristic
805	C₄	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
806	C₂	—	2	2	no	—
807	C₂	—	4	4	no	—
808	C₂	—	8	2	no	—
809	C₂	—	8	2	no	—
810	C₂	C₂×C₃₁×#548	1	1	yes	characteristic
811	C₂	C₂×C₃₁×#576	1	1	yes	characteristic
812	C₂	C₃₁×#3584	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×#533 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3506	C₂	semidirect
2. C₃₁×#3501	C₂	semidirect
3. C₃₁×#3370	C₂	semidirect
4. C₃₁×#3367	C₂	semidirect
5. C₃₁×#3366	C₂	semidirect
6. C₃₁×#3361	C₂	semidirect
7. C₃₁×#3360	C₂	semidirect
8. C₃₁×#3358	C₂	semidirect
9. C₃₁×#3136	C₂	semidirect
10. C₃₁×#3131	C₂	semidirect
11. C₃₁×#3083	C₂	semidirect
12. C₃₁×#3077	C₂	semidirect
13. C₃₁×#3041	C₂	semidirect
14. C₃₁×#3036	C₂	semidirect
15. C₃₁×#2960	C₂	semidirect
16. C₃₁×#2946	C₂	semidirect
17. C₂×C₄×D₈×C₃₁	C₂	semidirect
20. C₃₁×#559	C₂²	semidirect
21. C₃₁×#556	C₂²	semidirect
25. C₃₁×#554	C₂²	semidirect
26. C₃₁×#554	C₂²	semidirect
28. C₃₁×#550	C₂²	semidirect
30. D₄×Q₈×C₃₁	C₂²	semidirect
45. C₃₁×#490	C₂²	semidirect
46. C₃₁×#489	C₂²	semidirect
47. C₃₁×#488	C₂²	semidirect
48. C₃₁×#488	C₂²	semidirect
49. C₃₁×#488	C₂²	semidirect
50. C₃₁×#487	C₂²	semidirect
51. C₃₁×#487	C₂²	semidirect
52. C₃₁×#486	C₂²	semidirect
53. C₃₁×#486	C₂²	semidirect
54. C₃₁×#486	C₂²	semidirect
55. C₃₁×#479	C₂²	semidirect
56. C₃₁×#478	C₂²	semidirect
57. C₃₁×#478	C₂²	semidirect
58. C₃₁×#477	C₂²	semidirect
59. C₃₁×#476	C₂²	semidirect
60. C₃₁×#474	C₂²	semidirect
61. C₃₁×#474	C₂²	semidirect
64. C₃₁×#463	C₂²	semidirect
65. C₃₁×#461	C₂²	semidirect
68. C₃₁×#459	C₂²	semidirect
69. C₃₁×#446	C₂²	semidirect
70. C₃₁×#446	C₂²	semidirect
71. C₈×Q₈×C₃₁	C₂²	semidirect
72. C₈×Q₈×C₃₁	C₂²	semidirect
73. C₃₁×#442	C₂²	semidirect
74. C₃₁×#440	C₂²	semidirect
75. C₄×SD₁₆×C₃₁	C₂²	semidirect
80. C₄×D₈×C₃₁	C₂²	semidirect
235. C₂×D₄×C₃₁	#41	semidirect
308. #61325	C₃₁	direct (N × H)
371. #3506	C₂×C₃₁	semidirect
372. #3501	C₂×C₃₁	semidirect
373. #3370	C₂×C₃₁	semidirect
374. #3367	C₂×C₃₁	semidirect
375. #3366	C₂×C₃₁	semidirect
376. #3361	C₂×C₃₁	semidirect
377. #3360	C₂×C₃₁	semidirect
378. #3358	C₂×C₃₁	semidirect
379. #3136	C₂×C₃₁	semidirect
380. #3131	C₂×C₃₁	semidirect
381. #3083	C₂×C₃₁	semidirect
382. #3077	C₂×C₃₁	semidirect
383. #3041	C₂×C₃₁	semidirect
384. #3036	C₂×C₃₁	semidirect
385. #2960	C₂×C₃₁	semidirect
386. #2946	C₂×C₃₁	semidirect
387. C₂×C₄×D₈	C₂×C₃₁	semidirect
419. #559	C₂²×C₃₁	semidirect
420. #556	C₂²×C₃₁	semidirect
424. #554	C₂²×C₃₁	semidirect
425. #554	C₂²×C₃₁	semidirect
427. #550	C₂²×C₃₁	semidirect
429. D₄×Q₈	C₂²×C₃₁	semidirect
444. #490	C₂²×C₃₁	semidirect
445. #489	C₂²×C₃₁	semidirect
446. #488	C₂²×C₃₁	semidirect
447. #488	C₂²×C₃₁	semidirect
448. #488	C₂²×C₃₁	semidirect
449. #487	C₂²×C₃₁	semidirect
450. #487	C₂²×C₃₁	semidirect
451. #486	C₂²×C₃₁	semidirect
452. #486	C₂²×C₃₁	semidirect
453. #486	C₂²×C₃₁	semidirect
454. #479	C₂²×C₃₁	semidirect
455. #478	C₂²×C₃₁	semidirect
456. #478	C₂²×C₃₁	semidirect
457. #477	C₂²×C₃₁	semidirect
458. #476	C₂²×C₃₁	semidirect
459. #474	C₂²×C₃₁	semidirect
460. #474	C₂²×C₃₁	semidirect
463. #463	C₂²×C₃₁	semidirect
464. #461	C₂²×C₃₁	semidirect
467. #459	C₂²×C₃₁	semidirect
468. #446	C₂²×C₃₁	semidirect
469. #446	C₂²×C₃₁	semidirect
470. C₈×Q₈	C₂²×C₃₁	semidirect
471. C₈×Q₈	C₂²×C₃₁	semidirect
472. #442	C₂²×C₃₁	semidirect
473. #440	C₂²×C₃₁	semidirect
474. C₄×SD₁₆	C₂²×C₃₁	semidirect
479. C₄×D₈	C₂²×C₃₁	semidirect
619. C₃₁	#61325	direct (N × H)
642. 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×#3501	2
C₃₁×#3370	2
C₃₁×#3367	2
C₃₁×#3366	2
C₃₁×#3361	2
C₃₁×#3360	2
C₃₁×#3358	2
C₃₁×#3136	2
C₃₁×#3131	2
C₃₁×#3083	2
C₃₁×#3077	2
C₃₁×#3041	2
C₃₁×#3036	2
C₃₁×#2960	2
C₃₁×#2946	2
C₂×C₄×D₈×C₃₁	2
#61325	31

Subgroups — C31×#61325 #21518084

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61325 #21518084