Subgroups — C₃₁×#61930 #21518689

Order 7936.

1678 conjugacy classes of subgroups.

The subgroup lattice has 930 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3557	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3510	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3403	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3401	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3394	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3393	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3377	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3376	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3365	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3361	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3224	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3223	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3221	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3211	C₂	1	2	yes	maximal, complemented
15	C₃₁×#3123	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#3122	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#3121	C₂	1	2	yes	maximal, complemented
18	C₃₁×#3102	C₂	1	2	yes	maximal, complemented
19	C₃₁×#2986	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃₁×#563	—	2	2	no	—
21	C₃₁×#559	C₂²	1	2	yes	—
22	C₃₁×#559	C₂²	1	2	yes	—
23	C₃₁×#559	C₂²	1	2	yes	complemented
24	C₃₁×#557	C₂²	1	2	yes	complemented
25	C₃₁×#556	C₂²	1	2	yes	—
26	C₃₁×#556	C₂²	1	2	yes	—
27	C₃₁×#556	C₂²	1	2	yes	complemented
28	C₃₁×#554	C₂²	1	2	yes	complemented
29	C₃₁×#552	—	2	2	no	—
30	C₃₁×#551	—	2	2	no	—
31	C₃₁×#551	—	2	2	no	—
32	C₃₁×#542	—	2	2	no	—
33	C₃₁×#542	—	2	2	no	—
34	C₃₁×#542	C₂²	1	2	yes	—
35	C₃₁×#541	C₂²	1	1	yes	characteristic
36	C₃₁×#540	C₂²	1	1	yes	characteristic
37	C₃₁×#539	—	2	2	no	—
38	C₃₁×#536	C₂²	1	1	yes	characteristic
39	C₃₁×#535	C₂²	1	1	yes	characteristic
40	C₃₁×#533	C₂²	1	1	yes	characteristic
41	C₃₁×#529	—	2	2	no	—
42	C₃₁×#529	C₂²	1	2	yes	—
43	C₂×C₃₁×#124	C₂²	1	1	yes	characteristic
44	C₃₁×#519	C₂²	1	1	yes	characteristic
45	C₃₁×#518	C₂²	1	1	yes	characteristic
46	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
47	C₃₁×#497	C₂²	1	1	yes	characteristic, complemented
48	C₃₁×#496	C₂²	1	2	yes	—
49	C₃₁×#496	C₂²	1	1	yes	characteristic, complemented
50	C₃₁×#495	C₂²	1	2	yes	—
51	C₃₁×#495	C₂²	1	2	yes	—
52	C₃₁×#495	C₂²	1	2	yes	—
53	C₃₁×#494	C₂²	1	1	yes	characteristic, complemented
54	C₃₁×#492	C₂²	1	1	yes	characteristic, complemented
55	C₃₁×#491	C₂²	1	1	yes	characteristic, complemented
56	C₃₁×#491	C₂²	1	1	yes	characteristic, complemented
57	C₃₁×#489	C₂²	1	2	yes	—
58	C₃₁×#488	C₂²	1	2	yes	—
59	C₃₁×#488	C₂²	1	2	yes	—
60	C₃₁×#488	C₂²	1	1	yes	characteristic, complemented
61	C₃₁×#488	C₂²	1	1	yes	characteristic, complemented
62	C₃₁×#486	C₂²	1	2	yes	—
63	C₃₁×#485	C₂²	1	2	yes	—
64	C₃₁×#482	C₂²	1	2	yes	—
65	C₃₁×#479	C₂²	1	2	yes	complemented
66	C₃₁×#478	C₂²	1	2	yes	—
67	C₃₁×#478	C₂²	1	2	yes	—
68	C₃₁×#478	C₂²	1	2	yes	complemented
69	C₃₁×#477	C₂²	1	2	yes	complemented
70	C₃₁×#475	C₂²	1	2	yes	complemented
71	C₃₁×#464	C₂²	1	2	yes	—
72	C₃₁×#464	C₂²	1	2	yes	—
73	C₃₁×#464	C₂²	1	2	yes	—
74	C₃₁×#464	C₂²	1	2	yes	complemented
75	C₃₁×#464	C₂²	1	2	yes	complemented
76	C₃₁×#464	C₂²	1	2	yes	complemented
77	C₃₁×#464	C₂²	1	2	yes	complemented
78	C₃₁×#463	C₂²	1	2	yes	—
79	C₃₁×#463	C₂²	1	2	yes	—
80	C₃₁×#463	C₂²	1	2	yes	—
81	C₃₁×#463	C₂²	1	2	yes	complemented
82	C₃₁×#463	C₂²	1	2	yes	complemented
83	C₃₁×#462	C₂²	1	2	yes	complemented
84	C₃₁×#461	C₂²	1	2	yes	—
85	C₃₁×#461	C₂²	1	2	yes	complemented
86	C₃₁×#460	C₂²	1	2	yes	—
87	C₃₁×#459	C₂²	1	2	yes	—
88	C₃₁×#459	C₂²	1	2	yes	—
89	C₃₁×#452	C₂²	1	2	yes	—
90	C₃₁×#451	C₂²	1	2	yes	—
91	C₃₁×#450	C₂²	1	2	yes	—
92	C₃₁×#449	C₂²	1	2	yes	—
93	C₃₁×#448	C₂²	1	2	yes	—
94	C₃₁×#447	C₂²	1	2	yes	—
95	C₃₁×#446	C₂²	1	2	yes	complemented
96	C₃₁×#446	C₂²	1	2	yes	complemented
97	C₈×Q₈×C₃₁	C₂²	1	2	yes	complemented
98	C₈×Q₈×C₃₁	C₂²	1	2	yes	complemented
99	C₃₁×#442	C₂²	1	2	yes	—
100	C₃₁×#441	C₂²	1	2	yes	complemented
101	C₃₁×#440	C₂²	1	2	yes	—
102	C₃₁×#440	C₂²	1	2	yes	complemented
103	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	complemented
104	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	complemented
105	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	—
106	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
107	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
108	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
109	C₄×D₈×C₃₁	C₂²	1	2	yes	—
110	C₄×D₈×C₃₁	C₂²	1	2	yes	complemented
111	C₃₁×#433	C₂²	1	2	yes	—
112	C₃₁×#433	C₂²	1	1	yes	characteristic
113	C₃₁×#433	C₂²	1	1	yes	characteristic
114	C₃₁×#431	C₂²	1	2	yes	—
115	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
116	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
117	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
118	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
119	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
120	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
121	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
122	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
123	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
124	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
125	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
126	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
127	C₂×D₈×C₃₁	C₂³	1	2	yes	—
128	C₂×D₈×C₃₁	C₂³	1	2	yes	—
129	C₂×D₈×C₃₁	C₂³	1	2	yes	—
130	C₃₁×C₄⋊Q₈	—	2	2	no	—
131	C₃₁×C₄⋊Q₈	D₄	1	2	yes	—
132	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
133	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
134	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
135	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
136	C₃₁×#127	C₂³	1	1	yes	characteristic
137	C₃₁×#127	C₂³	1	2	yes	—
138	C₃₁×#126	—	2	2	no	—
139	C₃₁×#126	—	2	2	no	—
140	C₃₁×#126	—	2	2	no	—
141	C₃₁×#126	—	2	2	no	—
142	C₃₁×#126	—	2	2	no	—
143	C₃₁×#126	—	2	2	no	—
144	C₃₁×#126	—	2	2	no	—
145	C₃₁×#126	—	2	2	no	—
146	C₃₁×#126	—	2	2	no	—
147	C₃₁×#125	—	2	2	no	—
148	C₃₁×#125	—	2	2	no	—
149	C₃₁×#125	—	2	2	no	—
150	C₃₁×#125	D₄	1	2	yes	—
151	C₃₁×#125	C₂³	1	1	yes	characteristic
152	C₃₁×#125	C₂³	1	1	yes	characteristic
153	C₃₁×#125	C₂³	1	2	yes	—
154	C₃₁×#124	—	2	2	no	—
155	C₃₁×#124	—	2	2	no	—
156	C₃₁×#124	—	2	2	no	—
157	C₃₁×#124	—	2	2	no	—
158	C₃₁×#124	—	2	1	no	—
159	C₃₁×#124	—	2	1	no	—
160	C₃₁×#124	C₂³	1	2	yes	—
161	C₃₁×#124	C₂³	1	2	yes	—
162	C₃₁×#124	C₂³	1	2	yes	—
163	C₃₁×#124	C₂³	1	1	yes	characteristic
164	C₃₁×#124	C₂³	1	2	yes	—
165	C₃₁×#124	C₂³	1	1	yes	characteristic
166	C₃₁×#124	C₂³	1	2	yes	—
167	C₃₁×#123	—	2	2	no	—
168	C₃₁×#123	—	2	2	no	—
169	C₃₁×#123	—	2	2	no	—
170	C₃₁×#123	—	2	2	no	—
171	C₃₁×#123	—	2	2	no	—
172	C₃₁×#123	—	2	2	no	—
173	C₃₁×#123	—	2	2	no	—
174	C₃₁×#123	—	2	2	no	—
175	C₃₁×#123	—	2	2	no	—
176	C₃₁×#123	—	2	2	no	—
177	C₃₁×C₂²⋊Q₈	—	2	2	no	—
178	C₃₁×C₂²⋊Q₈	—	2	2	no	—
179	C₃₁×C₂²⋊Q₈	—	2	2	no	—
180	C₃₁×C₂²⋊Q₈	—	2	2	no	—
181	C₃₁×C₂²⋊Q₈	—	2	2	no	—
182	C₃₁×C₂²⋊Q₈	—	2	2	no	—
183	C₃₁×C₂²⋊Q₈	—	2	2	no	—
184	C₃₁×C₂²⋊Q₈	—	2	2	no	—
185	C₃₁×C₂²⋊Q₈	D₄	1	2	yes	—
186	C₃₁×C₂²⋊Q₈	D₄	1	2	yes	—
187	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
188	C₃₁×#121	—	2	2	no	—
189	C₃₁×#121	—	2	2	no	—
190	C₃₁×#121	C₂³	1	2	yes	—
191	C₃₁×#120	—	2	1	no	—
192	C₃₁×#120	—	2	1	no	—
193	C₄×Q₈×C₃₁	—	2	2	no	—
194	C₄×Q₈×C₃₁	—	2	2	no	—
195	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
196	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
197	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
198	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
199	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
200	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
201	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
202	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
203	C₄×D₄×C₃₁	—	2	2	no	—
204	C₄×D₄×C₃₁	—	2	2	no	—
205	C₄×D₄×C₃₁	—	2	2	no	—
206	C₄×D₄×C₃₁	—	2	2	no	—
207	C₄×D₄×C₃₁	—	2	2	no	—
208	C₄×D₄×C₃₁	—	2	2	no	—
209	C₄×D₄×C₃₁	C₂³	1	2	yes	—
210	C₄×D₄×C₃₁	C₂³	1	2	yes	—
211	C₄×D₄×C₃₁	C₂³	1	2	yes	—
212	C₄×D₄×C₃₁	C₂³	1	2	yes	—
213	C₄×D₄×C₃₁	C₂³	1	2	yes	—
214	C₄×D₄×C₃₁	C₂³	1	2	yes	—
215	C₃₁×#117	—	2	2	no	—
216	C₃₁×#117	—	2	2	no	—
217	C₃₁×#117	—	2	2	no	—
218	C₃₁×#117	—	2	1	no	—
219	C₃₁×#117	—	2	1	no	—
220	C₃₁×#117	—	2	1	no	—
221	C₃₁×#117	—	2	2	no	—
222	C₃₁×#117	C₂³	1	1	yes	characteristic
223	C₃₁×#117	C₂³	1	1	yes	characteristic
224	C₃₁×#117	C₂³	1	1	yes	characteristic
225	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
226	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
227	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
228	C₂×C₄²×C₃₁	—	2	1	no	—
229	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
230	C₃₁×#107	C₂³	1	2	yes	—
231	C₃₁×#107	C₂³	1	2	yes	—
232	C₃₁×#106	C₂³	1	2	yes	—
233	C₃₁×#106	C₂³	1	2	yes	—
234	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
235	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
236	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
237	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
238	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
239	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
240	C₃₁×#103	C₂³	1	2	yes	—
241	C₃₁×#103	C₂³	1	2	yes	—
242	C₃₁×#103	C₂³	1	2	yes	—
243	C₃₁×#103	C₂³	1	2	yes	—
244	C₃₁×#103	C₂³	1	2	yes	—
245	C₃₁×#103	C₂³	1	2	yes	—
246	C₃₁×#103	C₂³	1	2	yes	—
247	C₃₁×#103	C₂³	1	2	yes	—
248	C₃₁×#102	C₂³	1	2	yes	—
249	C₃₁×#102	C₂³	1	2	yes	—
250	C₃₁×#102	C₂³	1	2	yes	—
251	C₃₁×#102	C₂³	1	2	yes	—
252	C₃₁×#102	C₂³	1	2	yes	—
253	C₃₁×#102	C₂³	1	2	yes	—
254	C₃₁×#102	C₂³	1	2	yes	—
255	C₃₁×#102	C₂³	1	2	yes	—
256	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
257	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
258	C₃₁×#97	C₂³	1	1	yes	characteristic
259	C₃₁×#97	C₂³	1	2	yes	—
260	C₃₁×#97	C₂³	1	1	yes	characteristic
261	C₄×C₈×C₃₁	C₂³	1	2	yes	—
262	C₄×C₈×C₃₁	C₂³	1	2	yes	—
263	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
264	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
265	C₄×C₈×C₃₁	C₂³	1	2	yes	—
266	C₂⁴×C₃₁	—	2	1	no	—
267	#41×C₃₁	—	4	2	no	—
268	C₂×Q₈×C₃₁	—	2	1	no	—
269	C₂×Q₈×C₃₁	—	2	2	no	—
270	C₂×Q₈×C₃₁	—	4	2	no	—
271	C₂×Q₈×C₃₁	C₂×D₄	1	2	yes	—
272	C₂×Q₈×C₃₁	C₂×D₄	1	2	yes	—
273	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
274	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
275	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
276	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
277	C₂×D₄×C₃₁	—	2	1	no	—
278	C₂×D₄×C₃₁	—	2	2	no	—
279	C₂×D₄×C₃₁	—	2	1	no	—
280	C₂×D₄×C₃₁	—	2	2	no	—
281	C₂×D₄×C₃₁	—	2	2	no	—
282	C₂×D₄×C₃₁	—	2	2	no	—
283	C₂×D₄×C₃₁	—	4	2	no	—
284	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
285	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
286	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
287	C₂²×C₄×C₃₁	—	2	1	no	—
288	C₂²×C₄×C₃₁	—	2	1	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	2	no	—
294	C₂²×C₄×C₃₁	—	2	2	no	—
295	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
296	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
297	Q₁₆×C₃₁	—	4	2	no	—
298	Q₁₆×C₃₁	—	4	2	no	—
299	Q₁₆×C₃₁	—	4	2	no	—
300	SD₁₆×C₃₁	—	4	2	no	—
301	SD₁₆×C₃₁	—	4	2	no	—
302	SD₁₆×C₃₁	—	4	2	no	—
303	SD₁₆×C₃₁	—	4	2	no	—
304	SD₁₆×C₃₁	—	4	2	no	—
305	SD₁₆×C₃₁	—	4	2	no	—
306	D₈×C₃₁	—	4	2	no	—
307	D₈×C₃₁	—	4	2	no	—
308	D₈×C₃₁	—	4	2	no	—
309	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
310	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
311	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
312	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
313	C₄⋊C₄×C₃₁	—	2	2	no	—
314	C₄⋊C₄×C₃₁	—	2	2	no	—
315	C₄⋊C₄×C₃₁	—	2	2	no	—
316	C₄⋊C₄×C₃₁	—	2	2	no	—
317	C₄⋊C₄×C₃₁	—	2	2	no	—
318	C₄⋊C₄×C₃₁	—	2	2	no	—
319	C₄⋊C₄×C₃₁	—	2	2	no	—
320	C₄⋊C₄×C₃₁	—	2	2	no	—
321	C₄⋊C₄×C₃₁	—	2	2	no	—
322	C₄⋊C₄×C₃₁	—	2	2	no	—
323	C₄⋊C₄×C₃₁	—	2	2	no	—
324	C₄⋊C₄×C₃₁	—	2	2	no	—
325	C₄⋊C₄×C₃₁	—	2	2	no	—
326	C₄⋊C₄×C₃₁	—	2	2	no	—
327	C₄⋊C₄×C₃₁	—	2	2	no	—
328	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
329	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
330	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
331	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
332	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
333	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
334	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
335	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
336	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
337	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
338	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
339	C₂²⋊C₄×C₃₁	—	2	1	no	—
340	C₂²⋊C₄×C₃₁	—	2	2	no	—
341	C₂²⋊C₄×C₃₁	—	2	2	no	—
342	C₂²⋊C₄×C₃₁	—	2	2	no	—
343	C₂²⋊C₄×C₃₁	—	2	2	no	—
344	C₂²⋊C₄×C₃₁	—	2	2	no	—
345	C₂²⋊C₄×C₃₁	—	2	2	no	—
346	C₂²⋊C₄×C₃₁	—	2	2	no	—
347	C₂²⋊C₄×C₃₁	—	2	2	no	—
348	C₂²⋊C₄×C₃₁	—	2	2	no	—
349	C₂²⋊C₄×C₃₁	—	2	2	no	—
350	C₂²⋊C₄×C₃₁	—	2	2	no	—
351	C₂²⋊C₄×C₃₁	—	2	2	no	—
352	C₂²⋊C₄×C₃₁	—	2	2	no	—
353	C₂²⋊C₄×C₃₁	—	2	2	no	—
354	C₂²⋊C₄×C₃₁	—	2	2	no	—
355	C₂²⋊C₄×C₃₁	—	2	2	no	—
356	C₂²⋊C₄×C₃₁	—	2	2	no	—
357	C₂²⋊C₄×C₃₁	—	2	2	no	—
358	C₂²⋊C₄×C₃₁	—	2	2	no	—
359	C₂²⋊C₄×C₃₁	—	2	2	no	—
360	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
361	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
362	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
363	C₄²×C₃₁	—	2	2	no	—
364	C₄²×C₃₁	—	2	1	no	—
365	C₄²×C₃₁	—	2	2	no	—
366	C₄²×C₃₁	—	2	2	no	—
367	C₄²×C₃₁	—	2	2	no	—
368	C₄²×C₃₁	—	2	2	no	—
369	C₄²×C₃₁	—	2	2	no	—
370	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
371	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
372	C₄²×C₃₁	C₂⁴	1	2	yes	—
373	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
374	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
375	C₄²×C₃₁	C₂⁴	1	2	yes	—
376	#61930	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
377	C₂³×C₃₁	—	2	2	no	—
378	C₂³×C₃₁	—	2	2	no	—
379	C₂³×C₃₁	—	2	1	no	—
380	C₂³×C₃₁	—	4	2	no	—
381	C₂³×C₃₁	—	8	2	no	—
382	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
383	Q₈×C₃₁	—	2	2	no	—
384	Q₈×C₃₁	—	2	2	no	—
385	Q₈×C₃₁	—	2	2	no	—
386	Q₈×C₃₁	—	2	2	no	—
387	Q₈×C₃₁	—	2	2	no	—
388	Q₈×C₃₁	—	4	2	no	—
389	Q₈×C₃₁	—	4	2	no	—
390	Q₈×C₃₁	—	4	2	no	—
391	Q₈×C₃₁	—	8	2	no	—
392	D₄×C₃₁	—	2	2	no	—
393	D₄×C₃₁	—	2	2	no	—
394	D₄×C₃₁	—	2	2	no	—
395	D₄×C₃₁	—	2	2	no	—
396	D₄×C₃₁	—	2	2	no	—
397	D₄×C₃₁	—	4	2	no	—
398	D₄×C₃₁	—	4	2	no	—
399	D₄×C₃₁	—	8	2	no	—
400	D₄×C₃₁	—	8	2	no	—
401	D₄×C₃₁	—	8	2	no	—
402	D₄×C₃₁	—	8	2	no	—
403	C₂×C₄×C₃₁	—	2	2	no	—
404	C₂×C₄×C₃₁	—	2	2	no	—
405	C₂×C₄×C₃₁	—	2	2	no	—
406	C₂×C₄×C₃₁	—	2	1	no	—
407	C₂×C₄×C₃₁	—	2	1	no	—
408	C₂×C₄×C₃₁	—	2	1	no	—
409	C₂×C₄×C₃₁	—	2	2	no	—
410	C₂×C₄×C₃₁	—	2	2	no	—
411	C₂×C₄×C₃₁	—	4	2	no	—
412	C₂×C₄×C₃₁	—	4	2	no	—
413	C₂×C₄×C₃₁	—	4	2	no	—
414	C₂×C₄×C₃₁	—	8	2	no	—
415	C₂×C₄×C₃₁	—	8	2	no	—
416	C₂×C₄×C₃₁	—	8	2	no	—
417	C₂×C₄×C₃₁	—	8	2	no	—
418	C₂×C₄×C₃₁	—	8	2	no	—
419	C₂×C₄×C₃₁	—	8	2	no	—
420	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
421	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
422	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
423	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
424	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
425	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
426	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
427	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
428	C₈×C₃₁	—	2	2	no	—
429	C₈×C₃₁	—	2	2	no	—
430	C₈×C₃₁	—	2	2	no	—
431	C₈×C₃₁	—	2	2	no	—
432	#3557	C₂×C₃₁	1	1	yes	characteristic, complemented
433	#3510	C₂×C₃₁	1	1	yes	characteristic, complemented
434	#3403	C₂×C₃₁	1	2	yes	complemented
435	#3401	C₂×C₃₁	1	2	yes	complemented
436	#3394	C₂×C₃₁	1	2	yes	complemented
437	#3393	C₂×C₃₁	1	2	yes	complemented
438	#3377	C₂×C₃₁	1	2	yes	complemented
439	#3376	C₂×C₃₁	1	2	yes	complemented
440	#3365	C₂×C₃₁	1	2	yes	complemented
441	#3361	C₂×C₃₁	1	2	yes	complemented
442	#3224	C₂×C₃₁	1	2	yes	complemented
443	#3223	C₂×C₃₁	1	1	yes	characteristic, complemented
444	#3221	C₂×C₃₁	1	1	yes	characteristic, complemented
445	#3211	C₂×C₃₁	1	2	yes	complemented
446	#3123	C₂×C₃₁	1	1	yes	characteristic, complemented
447	#3122	C₂×C₃₁	1	1	yes	characteristic, complemented
448	#3121	C₂×C₃₁	1	2	yes	complemented
449	#3102	C₂×C₃₁	1	2	yes	complemented
450	#2986	C₂×C₃₁	1	1	yes	characteristic, complemented
451	C₂²×C₃₁	—	2	2	no	—
452	C₂²×C₃₁	—	2	1	no	—
453	C₂²×C₃₁	—	4	2	no	—
454	C₂²×C₃₁	—	4	2	no	—
455	C₂²×C₃₁	—	4	2	no	—
456	C₂²×C₃₁	—	4	2	no	—
457	C₂²×C₃₁	—	4	2	no	—
458	C₂²×C₃₁	—	4	1	no	—
459	C₂²×C₃₁	—	4	2	no	—
460	C₂²×C₃₁	—	4	2	no	—
461	C₂²×C₃₁	—	16	2	no	—
462	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
463	C₄×C₃₁	—	2	2	no	—
464	C₄×C₃₁	—	2	2	no	—
465	C₄×C₃₁	—	2	2	no	—
466	C₄×C₃₁	—	2	2	no	—
467	C₄×C₃₁	—	2	2	no	—
468	C₄×C₃₁	—	2	2	no	—
469	C₄×C₃₁	—	2	1	no	—
470	C₄×C₃₁	—	4	2	no	—
471	C₄×C₃₁	—	4	2	no	—
472	C₄×C₃₁	—	4	2	no	—
473	C₄×C₃₁	—	4	1	no	—
474	C₄×C₃₁	—	4	1	no	—
475	C₄×C₃₁	—	4	1	no	—
476	C₄×C₃₁	—	4	2	no	—
477	C₄×C₃₁	#585	1	2	yes	—
478	#563	—	2	2	no	—
479	#559	C₂²×C₃₁	1	2	yes	—
480	#559	C₂²×C₃₁	1	2	yes	—
481	#559	C₂²×C₃₁	1	2	yes	complemented
482	#557	C₂²×C₃₁	1	2	yes	complemented
483	#556	C₂²×C₃₁	1	2	yes	—
484	#556	C₂²×C₃₁	1	2	yes	—
485	#556	C₂²×C₃₁	1	2	yes	complemented
486	#554	C₂²×C₃₁	1	2	yes	complemented
487	#552	—	2	2	no	—
488	#551	—	2	2	no	—
489	#551	—	2	2	no	—
490	#542	—	2	2	no	—
491	#542	—	2	2	no	—
492	#542	C₂²×C₃₁	1	2	yes	—
493	#541	C₂²×C₃₁	1	1	yes	characteristic
494	#540	C₂²×C₃₁	1	1	yes	characteristic
495	#539	—	2	2	no	—
496	#536	C₂²×C₃₁	1	1	yes	characteristic
497	#535	C₂²×C₃₁	1	1	yes	characteristic
498	#533	C₂²×C₃₁	1	1	yes	characteristic
499	#529	—	2	2	no	—
500	#529	C₂²×C₃₁	1	2	yes	—
501	C₂×#124	C₂²×C₃₁	1	1	yes	characteristic
502	#519	C₂²×C₃₁	1	1	yes	characteristic
503	#518	C₂²×C₃₁	1	1	yes	characteristic
504	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
505	#497	C₂²×C₃₁	1	1	yes	characteristic, complemented
506	#496	C₂²×C₃₁	1	2	yes	—
507	#496	C₂²×C₃₁	1	1	yes	characteristic, complemented
508	#495	C₂²×C₃₁	1	2	yes	—
509	#495	C₂²×C₃₁	1	2	yes	—
510	#495	C₂²×C₃₁	1	2	yes	—
511	#494	C₂²×C₃₁	1	1	yes	characteristic, complemented
512	#492	C₂²×C₃₁	1	1	yes	characteristic, complemented
513	#491	C₂²×C₃₁	1	1	yes	characteristic, complemented
514	#491	C₂²×C₃₁	1	1	yes	characteristic, complemented
515	#489	C₂²×C₃₁	1	2	yes	—
516	#488	C₂²×C₃₁	1	2	yes	—
517	#488	C₂²×C₃₁	1	2	yes	—
518	#488	C₂²×C₃₁	1	1	yes	characteristic, complemented
519	#488	C₂²×C₃₁	1	1	yes	characteristic, complemented
520	#486	C₂²×C₃₁	1	2	yes	—
521	#485	C₂²×C₃₁	1	2	yes	—
522	#482	C₂²×C₃₁	1	2	yes	—
523	#479	C₂²×C₃₁	1	2	yes	complemented
524	#478	C₂²×C₃₁	1	2	yes	—
525	#478	C₂²×C₃₁	1	2	yes	—
526	#478	C₂²×C₃₁	1	2	yes	complemented
527	#477	C₂²×C₃₁	1	2	yes	complemented
528	#475	C₂²×C₃₁	1	2	yes	complemented
529	#464	C₂²×C₃₁	1	2	yes	—
530	#464	C₂²×C₃₁	1	2	yes	—
531	#464	C₂²×C₃₁	1	2	yes	—
532	#464	C₂²×C₃₁	1	2	yes	complemented
533	#464	C₂²×C₃₁	1	2	yes	complemented
534	#464	C₂²×C₃₁	1	2	yes	complemented
535	#464	C₂²×C₃₁	1	2	yes	complemented
536	#463	C₂²×C₃₁	1	2	yes	—
537	#463	C₂²×C₃₁	1	2	yes	—
538	#463	C₂²×C₃₁	1	2	yes	—
539	#463	C₂²×C₃₁	1	2	yes	complemented
540	#463	C₂²×C₃₁	1	2	yes	complemented
541	#462	C₂²×C₃₁	1	2	yes	complemented
542	#461	C₂²×C₃₁	1	2	yes	—
543	#461	C₂²×C₃₁	1	2	yes	complemented
544	#460	C₂²×C₃₁	1	2	yes	—
545	#459	C₂²×C₃₁	1	2	yes	—
546	#459	C₂²×C₃₁	1	2	yes	—
547	#452	C₂²×C₃₁	1	2	yes	—
548	#451	C₂²×C₃₁	1	2	yes	—
549	#450	C₂²×C₃₁	1	2	yes	—
550	#449	C₂²×C₃₁	1	2	yes	—
551	#448	C₂²×C₃₁	1	2	yes	—
552	#447	C₂²×C₃₁	1	2	yes	—
553	#446	C₂²×C₃₁	1	2	yes	complemented
554	#446	C₂²×C₃₁	1	2	yes	complemented
555	C₈×Q₈	C₂²×C₃₁	1	2	yes	complemented
556	C₈×Q₈	C₂²×C₃₁	1	2	yes	complemented
557	#442	C₂²×C₃₁	1	2	yes	—
558	#441	C₂²×C₃₁	1	2	yes	complemented
559	#440	C₂²×C₃₁	1	2	yes	—
560	#440	C₂²×C₃₁	1	2	yes	complemented
561	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	complemented
562	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	complemented
563	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	—
564	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
565	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
566	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
567	C₄×D₈	C₂²×C₃₁	1	2	yes	—
568	C₄×D₈	C₂²×C₃₁	1	2	yes	complemented
569	#433	C₂²×C₃₁	1	2	yes	—
570	#433	C₂²×C₃₁	1	1	yes	characteristic
571	#433	C₂²×C₃₁	1	1	yes	characteristic
572	#431	C₂²×C₃₁	1	2	yes	—
573	C₂×C₃₁	—	4	1	no	—
574	C₂×C₃₁	—	8	2	no	—
575	C₂×C₃₁	—	8	1	no	—
576	C₂×C₃₁	—	8	2	no	—
577	C₂×C₃₁	#3487	1	1	yes	characteristic
578	C₂×C₃₁	#3584	1	2	yes	—
579	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
580	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
581	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
582	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
583	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
584	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
585	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
586	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
587	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
588	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
589	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
590	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
591	C₂×D₈	C₂³×C₃₁	1	2	yes	—
592	C₂×D₈	C₂³×C₃₁	1	2	yes	—
593	C₂×D₈	C₂³×C₃₁	1	2	yes	—
594	C₄⋊Q₈	—	2	2	no	—
595	C₄⋊Q₈	D₄×C₃₁	1	2	yes	—
596	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
597	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
598	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
599	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
600	#127	C₂³×C₃₁	1	2	yes	—
601	#127	C₂³×C₃₁	1	1	yes	characteristic
602	#126	—	2	2	no	—
603	#126	—	2	2	no	—
604	#126	—	2	2	no	—
605	#126	—	2	2	no	—
606	#126	—	2	2	no	—
607	#126	—	2	2	no	—
608	#126	—	2	2	no	—
609	#126	—	2	2	no	—
610	#126	—	2	2	no	—
611	#125	—	2	2	no	—
612	#125	—	2	2	no	—
613	#125	—	2	2	no	—
614	#125	D₄×C₃₁	1	2	yes	—
615	#125	C₂³×C₃₁	1	2	yes	—
616	#125	C₂³×C₃₁	1	1	yes	characteristic
617	#125	C₂³×C₃₁	1	1	yes	characteristic
618	#124	—	2	2	no	—
619	#124	—	2	2	no	—
620	#124	—	2	2	no	—
621	#124	—	2	2	no	—
622	#124	—	2	1	no	—
623	#124	—	2	1	no	—
624	#124	C₂³×C₃₁	1	2	yes	—
625	#124	C₂³×C₃₁	1	2	yes	—
626	#124	C₂³×C₃₁	1	2	yes	—
627	#124	C₂³×C₃₁	1	2	yes	—
628	#124	C₂³×C₃₁	1	1	yes	characteristic
629	#124	C₂³×C₃₁	1	1	yes	characteristic
630	#124	C₂³×C₃₁	1	2	yes	—
631	#123	—	2	2	no	—
632	#123	—	2	2	no	—
633	#123	—	2	2	no	—
634	#123	—	2	2	no	—
635	#123	—	2	2	no	—
636	#123	—	2	2	no	—
637	#123	—	2	2	no	—
638	#123	—	2	2	no	—
639	#123	—	2	2	no	—
640	#123	—	2	2	no	—
641	C₂²⋊Q₈	—	2	2	no	—
642	C₂²⋊Q₈	—	2	2	no	—
643	C₂²⋊Q₈	—	2	2	no	—
644	C₂²⋊Q₈	—	2	2	no	—
645	C₂²⋊Q₈	—	2	2	no	—
646	C₂²⋊Q₈	—	2	2	no	—
647	C₂²⋊Q₈	—	2	2	no	—
648	C₂²⋊Q₈	—	2	2	no	—
649	C₂²⋊Q₈	D₄×C₃₁	1	2	yes	—
650	C₂²⋊Q₈	D₄×C₃₁	1	2	yes	—
651	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
652	#121	—	2	2	no	—
653	#121	—	2	2	no	—
654	#121	C₂³×C₃₁	1	2	yes	—
655	#120	—	2	1	no	—
656	#120	—	2	1	no	—
657	C₄×Q₈	—	2	2	no	—
658	C₄×Q₈	—	2	2	no	—
659	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
660	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
661	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
662	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
663	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
664	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
665	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
666	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
667	C₄×D₄	—	2	2	no	—
668	C₄×D₄	—	2	2	no	—
669	C₄×D₄	—	2	2	no	—
670	C₄×D₄	—	2	2	no	—
671	C₄×D₄	—	2	2	no	—
672	C₄×D₄	—	2	2	no	—
673	C₄×D₄	C₂³×C₃₁	1	2	yes	—
674	C₄×D₄	C₂³×C₃₁	1	2	yes	—
675	C₄×D₄	C₂³×C₃₁	1	2	yes	—
676	C₄×D₄	C₂³×C₃₁	1	2	yes	—
677	C₄×D₄	C₂³×C₃₁	1	2	yes	—
678	C₄×D₄	C₂³×C₃₁	1	2	yes	—
679	#117	—	2	2	no	—
680	#117	—	2	2	no	—
681	#117	—	2	2	no	—
682	#117	—	2	1	no	—
683	#117	—	2	1	no	—
684	#117	—	2	1	no	—
685	#117	—	2	2	no	—
686	#117	C₂³×C₃₁	1	1	yes	characteristic
687	#117	C₂³×C₃₁	1	1	yes	characteristic
688	#117	C₂³×C₃₁	1	1	yes	characteristic
689	C₂×C₄⋊C₄	—	2	2	no	—
690	C₂×C₂²⋊C₄	—	2	2	no	—
691	C₂×C₂²⋊C₄	—	2	2	no	—
692	C₂×C₄²	—	2	1	no	—
693	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
694	#107	C₂³×C₃₁	1	2	yes	—
695	#107	C₂³×C₃₁	1	2	yes	—
696	#106	C₂³×C₃₁	1	2	yes	—
697	#106	C₂³×C₃₁	1	2	yes	—
698	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
699	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
700	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
701	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
702	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
703	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
704	#103	C₂³×C₃₁	1	2	yes	—
705	#103	C₂³×C₃₁	1	2	yes	—
706	#103	C₂³×C₃₁	1	2	yes	—
707	#103	C₂³×C₃₁	1	2	yes	—
708	#103	C₂³×C₃₁	1	2	yes	—
709	#103	C₂³×C₃₁	1	2	yes	—
710	#103	C₂³×C₃₁	1	2	yes	—
711	#103	C₂³×C₃₁	1	2	yes	—
712	#102	C₂³×C₃₁	1	2	yes	—
713	#102	C₂³×C₃₁	1	2	yes	—
714	#102	C₂³×C₃₁	1	2	yes	—
715	#102	C₂³×C₃₁	1	2	yes	—
716	#102	C₂³×C₃₁	1	2	yes	—
717	#102	C₂³×C₃₁	1	2	yes	—
718	#102	C₂³×C₃₁	1	2	yes	—
719	#102	C₂³×C₃₁	1	2	yes	—
720	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
721	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
722	#97	C₂³×C₃₁	1	1	yes	characteristic
723	#97	C₂³×C₃₁	1	2	yes	—
724	#97	C₂³×C₃₁	1	1	yes	characteristic
725	C₄×C₈	C₂³×C₃₁	1	2	yes	—
726	C₄×C₈	C₂³×C₃₁	1	2	yes	—
727	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
728	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
729	C₄×C₈	C₂³×C₃₁	1	2	yes	—
730	C₃₁	#61930	1	1	yes	characteristic, direct product factor, Sylow
731	C₂⁴	—	2	1	no	—
732	#41	—	4	2	no	—
733	C₂×Q₈	—	2	1	no	—
734	C₂×Q₈	—	2	2	no	—
735	C₂×Q₈	—	4	2	no	—
736	C₂×Q₈	C₂×D₄×C₃₁	1	2	yes	—
737	C₂×Q₈	C₂×D₄×C₃₁	1	2	yes	—
738	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
739	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
740	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
741	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
742	C₂×D₄	—	2	1	no	—
743	C₂×D₄	—	2	2	no	—
744	C₂×D₄	—	2	1	no	—
745	C₂×D₄	—	2	2	no	—
746	C₂×D₄	—	2	2	no	—
747	C₂×D₄	—	2	2	no	—
748	C₂×D₄	—	4	2	no	—
749	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
750	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
751	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
752	C₂²×C₄	—	2	1	no	—
753	C₂²×C₄	—	2	1	no	—
754	C₂²×C₄	—	2	2	no	—
755	C₂²×C₄	—	2	2	no	—
756	C₂²×C₄	—	2	2	no	—
757	C₂²×C₄	—	2	2	no	—
758	C₂²×C₄	—	2	2	no	—
759	C₂²×C₄	—	2	2	no	—
760	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
761	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
762	Q₁₆	—	4	2	no	—
763	Q₁₆	—	4	2	no	—
764	Q₁₆	—	4	2	no	—
765	SD₁₆	—	4	2	no	—
766	SD₁₆	—	4	2	no	—
767	SD₁₆	—	4	2	no	—
768	SD₁₆	—	4	2	no	—
769	SD₁₆	—	4	2	no	—
770	SD₁₆	—	4	2	no	—
771	D₈	—	4	2	no	—
772	D₈	—	4	2	no	—
773	D₈	—	4	2	no	—
774	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
775	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
776	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
777	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
778	C₄⋊C₄	—	2	2	no	—
779	C₄⋊C₄	—	2	2	no	—
780	C₄⋊C₄	—	2	2	no	—
781	C₄⋊C₄	—	2	2	no	—
782	C₄⋊C₄	—	2	2	no	—
783	C₄⋊C₄	—	2	2	no	—
784	C₄⋊C₄	—	2	2	no	—
785	C₄⋊C₄	—	2	2	no	—
786	C₄⋊C₄	—	2	2	no	—
787	C₄⋊C₄	—	2	2	no	—
788	C₄⋊C₄	—	2	2	no	—
789	C₄⋊C₄	—	2	2	no	—
790	C₄⋊C₄	—	2	2	no	—
791	C₄⋊C₄	—	2	2	no	—
792	C₄⋊C₄	—	2	2	no	—
793	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
794	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
795	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
796	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
797	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
798	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
799	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
800	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
801	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
802	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
803	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
804	C₂²⋊C₄	—	2	1	no	—
805	C₂²⋊C₄	—	2	2	no	—
806	C₂²⋊C₄	—	2	2	no	—
807	C₂²⋊C₄	—	2	2	no	—
808	C₂²⋊C₄	—	2	2	no	—
809	C₂²⋊C₄	—	2	2	no	—
810	C₂²⋊C₄	—	2	2	no	—
811	C₂²⋊C₄	—	2	2	no	—
812	C₂²⋊C₄	—	2	2	no	—
813	C₂²⋊C₄	—	2	2	no	—
814	C₂²⋊C₄	—	2	2	no	—
815	C₂²⋊C₄	—	2	2	no	—
816	C₂²⋊C₄	—	2	2	no	—
817	C₂²⋊C₄	—	2	2	no	—
818	C₂²⋊C₄	—	2	2	no	—
819	C₂²⋊C₄	—	2	2	no	—
820	C₂²⋊C₄	—	2	2	no	—
821	C₂²⋊C₄	—	2	2	no	—
822	C₂²⋊C₄	—	2	2	no	—
823	C₂²⋊C₄	—	2	2	no	—
824	C₂²⋊C₄	—	2	2	no	—
825	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
826	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
827	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
828	C₄²	—	2	2	no	—
829	C₄²	—	2	1	no	—
830	C₄²	—	2	2	no	—
831	C₄²	—	2	2	no	—
832	C₄²	—	2	2	no	—
833	C₄²	—	2	2	no	—
834	C₄²	—	2	2	no	—
835	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
836	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
837	C₄²	C₂⁴×C₃₁	1	2	yes	—
838	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
839	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
840	C₄²	C₂⁴×C₃₁	1	2	yes	—
841	C₂³	—	2	2	no	—
842	C₂³	—	2	2	no	—
843	C₂³	—	2	1	no	—
844	C₂³	—	4	2	no	—
845	C₂³	—	8	2	no	—
846	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
847	Q₈	—	2	2	no	—
848	Q₈	—	2	2	no	—
849	Q₈	—	2	2	no	—
850	Q₈	—	2	2	no	—
851	Q₈	—	2	2	no	—
852	Q₈	—	4	2	no	—
853	Q₈	—	4	2	no	—
854	Q₈	—	4	2	no	—
855	Q₈	—	8	2	no	—
856	D₄	—	2	2	no	—
857	D₄	—	2	2	no	—
858	D₄	—	2	2	no	—
859	D₄	—	2	2	no	—
860	D₄	—	2	2	no	—
861	D₄	—	4	2	no	—
862	D₄	—	4	2	no	—
863	D₄	—	8	2	no	—
864	D₄	—	8	2	no	—
865	D₄	—	8	2	no	—
866	D₄	—	8	2	no	—
867	C₂×C₄	—	2	2	no	—
868	C₂×C₄	—	2	2	no	—
869	C₂×C₄	—	2	2	no	—
870	C₂×C₄	—	2	1	no	—
871	C₂×C₄	—	2	1	no	—
872	C₂×C₄	—	2	1	no	—
873	C₂×C₄	—	2	2	no	—
874	C₂×C₄	—	2	2	no	—
875	C₂×C₄	—	4	2	no	—
876	C₂×C₄	—	4	2	no	—
877	C₂×C₄	—	4	2	no	—
878	C₂×C₄	—	8	2	no	—
879	C₂×C₄	—	8	2	no	—
880	C₂×C₄	—	8	2	no	—
881	C₂×C₄	—	8	2	no	—
882	C₂×C₄	—	8	2	no	—
883	C₂×C₄	—	8	2	no	—
884	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
885	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
886	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
887	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
888	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
889	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
890	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
891	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
892	C₈	—	2	2	no	—
893	C₈	—	2	2	no	—
894	C₈	—	2	2	no	—
895	C₈	—	2	2	no	—
896	C₂²	—	2	1	no	—
897	C₂²	—	2	2	no	—
898	C₂²	—	4	1	no	—
899	C₂²	—	4	2	no	—
900	C₂²	—	4	2	no	—
901	C₂²	—	4	2	no	—
902	C₂²	—	4	2	no	—
903	C₂²	—	4	2	no	—
904	C₂²	—	4	2	no	—
905	C₂²	—	4	2	no	—
906	C₂²	—	16	2	no	—
907	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
908	C₄	—	2	1	no	—
909	C₄	—	2	2	no	—
910	C₄	—	2	2	no	—
911	C₄	—	2	2	no	—
912	C₄	—	2	2	no	—
913	C₄	—	2	2	no	—
914	C₄	—	2	2	no	—
915	C₄	—	4	1	no	—
916	C₄	—	4	1	no	—
917	C₄	—	4	1	no	—
918	C₄	—	4	2	no	—
919	C₄	—	4	2	no	—
920	C₄	—	4	2	no	—
921	C₄	—	4	2	no	—
922	C₄	C₃₁×#585	1	2	yes	—
923	C₂	—	4	1	no	—
924	C₂	—	8	2	no	—
925	C₂	—	8	1	no	—
926	C₂	—	8	2	no	—
927	C₂	C₃₁×#3487	1	1	yes	characteristic
928	C₂	C₃₁×#3584	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₃₁×#533 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3557	C₂	semidirect
2. C₃₁×#3510	C₂	semidirect
3. C₃₁×#3403	C₂	semidirect
4. C₃₁×#3401	C₂	semidirect
5. C₃₁×#3394	C₂	semidirect
6. C₃₁×#3393	C₂	semidirect
7. C₃₁×#3377	C₂	semidirect
8. C₃₁×#3376	C₂	semidirect
9. C₃₁×#3365	C₂	semidirect
10. C₃₁×#3361	C₂	semidirect
11. C₃₁×#3224	C₂	semidirect
12. C₃₁×#3223	C₂	semidirect
13. C₃₁×#3221	C₂	semidirect
14. C₃₁×#3211	C₂	semidirect
15. C₃₁×#3123	C₂	semidirect
16. C₃₁×#3122	C₂	semidirect
17. C₃₁×#3121	C₂	semidirect
18. C₃₁×#3102	C₂	semidirect
19. C₃₁×#2986	C₂	semidirect
23. C₃₁×#559	C₂²	semidirect
24. C₃₁×#557	C₂²	semidirect
27. C₃₁×#556	C₂²	semidirect
28. C₃₁×#554	C₂²	semidirect
47. C₃₁×#497	C₂²	semidirect
49. C₃₁×#496	C₂²	semidirect
53. C₃₁×#494	C₂²	semidirect
54. C₃₁×#492	C₂²	semidirect
55. C₃₁×#491	C₂²	semidirect
56. C₃₁×#491	C₂²	semidirect
60. C₃₁×#488	C₂²	semidirect
61. C₃₁×#488	C₂²	semidirect
65. C₃₁×#479	C₂²	semidirect
68. C₃₁×#478	C₂²	semidirect
69. C₃₁×#477	C₂²	semidirect
70. C₃₁×#475	C₂²	semidirect
74. C₃₁×#464	C₂²	semidirect
75. C₃₁×#464	C₂²	semidirect
76. C₃₁×#464	C₂²	semidirect
77. C₃₁×#464	C₂²	semidirect
81. C₃₁×#463	C₂²	semidirect
82. C₃₁×#463	C₂²	semidirect
83. C₃₁×#462	C₂²	semidirect
85. C₃₁×#461	C₂²	semidirect
95. C₃₁×#446	C₂²	semidirect
96. C₃₁×#446	C₂²	semidirect
97. C₈×Q₈×C₃₁	C₂²	semidirect
98. C₈×Q₈×C₃₁	C₂²	semidirect
100. C₃₁×#441	C₂²	semidirect
102. C₃₁×#440	C₂²	semidirect
103. C₄×Q₁₆×C₃₁	C₂²	semidirect
104. C₄×Q₁₆×C₃₁	C₂²	semidirect
106. C₄×SD₁₆×C₃₁	C₂²	semidirect
107. C₄×SD₁₆×C₃₁	C₂²	semidirect
108. C₄×SD₁₆×C₃₁	C₂²	semidirect
110. C₄×D₈×C₃₁	C₂²	semidirect
376. #61930	C₃₁	direct (N × H)
432. #3557	C₂×C₃₁	semidirect
433. #3510	C₂×C₃₁	semidirect
434. #3403	C₂×C₃₁	semidirect
435. #3401	C₂×C₃₁	semidirect
436. #3394	C₂×C₃₁	semidirect
437. #3393	C₂×C₃₁	semidirect
438. #3377	C₂×C₃₁	semidirect
439. #3376	C₂×C₃₁	semidirect
440. #3365	C₂×C₃₁	semidirect
441. #3361	C₂×C₃₁	semidirect
442. #3224	C₂×C₃₁	semidirect
443. #3223	C₂×C₃₁	semidirect
444. #3221	C₂×C₃₁	semidirect
445. #3211	C₂×C₃₁	semidirect
446. #3123	C₂×C₃₁	semidirect
447. #3122	C₂×C₃₁	semidirect
448. #3121	C₂×C₃₁	semidirect
449. #3102	C₂×C₃₁	semidirect
450. #2986	C₂×C₃₁	semidirect
481. #559	C₂²×C₃₁	semidirect
482. #557	C₂²×C₃₁	semidirect
485. #556	C₂²×C₃₁	semidirect
486. #554	C₂²×C₃₁	semidirect
505. #497	C₂²×C₃₁	semidirect
507. #496	C₂²×C₃₁	semidirect
511. #494	C₂²×C₃₁	semidirect
512. #492	C₂²×C₃₁	semidirect
513. #491	C₂²×C₃₁	semidirect
514. #491	C₂²×C₃₁	semidirect
518. #488	C₂²×C₃₁	semidirect
519. #488	C₂²×C₃₁	semidirect
523. #479	C₂²×C₃₁	semidirect
526. #478	C₂²×C₃₁	semidirect
527. #477	C₂²×C₃₁	semidirect
528. #475	C₂²×C₃₁	semidirect
532. #464	C₂²×C₃₁	semidirect
533. #464	C₂²×C₃₁	semidirect
534. #464	C₂²×C₃₁	semidirect
535. #464	C₂²×C₃₁	semidirect
539. #463	C₂²×C₃₁	semidirect
540. #463	C₂²×C₃₁	semidirect
541. #462	C₂²×C₃₁	semidirect
543. #461	C₂²×C₃₁	semidirect
553. #446	C₂²×C₃₁	semidirect
554. #446	C₂²×C₃₁	semidirect
555. C₈×Q₈	C₂²×C₃₁	semidirect
556. C₈×Q₈	C₂²×C₃₁	semidirect
558. #441	C₂²×C₃₁	semidirect
560. #440	C₂²×C₃₁	semidirect
561. C₄×Q₁₆	C₂²×C₃₁	semidirect
562. C₄×Q₁₆	C₂²×C₃₁	semidirect
564. C₄×SD₁₆	C₂²×C₃₁	semidirect
565. C₄×SD₁₆	C₂²×C₃₁	semidirect
566. C₄×SD₁₆	C₂²×C₃₁	semidirect
568. C₄×D₈	C₂²×C₃₁	semidirect
730. C₃₁	#61930	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃₁×#3557	2
C₃₁×#3510	2
C₃₁×#3403	2
C₃₁×#3401	2
C₃₁×#3394	2
C₃₁×#3393	2
C₃₁×#3377	2
C₃₁×#3376	2
C₃₁×#3365	2
C₃₁×#3361	2
C₃₁×#3224	2
C₃₁×#3223	2
C₃₁×#3221	2
C₃₁×#3211	2
C₃₁×#3123	2
C₃₁×#3122	2
C₃₁×#3121	2
C₃₁×#3102	2
C₃₁×#2986	2
#61930	31

Subgroups — C31×#61930 #21518689

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61930 #21518689