Subgroups — C₃₁×#62590 #21519349

Order 7936.

1790 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3515	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3508	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3365	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3361	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3333	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3332	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3323	C₂	1	4	yes	maximal, complemented
8	C₃₁×#3322	C₂	1	4	yes	maximal, complemented
9	C₃₁×#3237	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#3234	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3219	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3217	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3172	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3171	C₂	1	2	yes	maximal, complemented
15	C₃₁×#3142	C₂	1	2	yes	maximal, complemented
16	C₃₁×#3138	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#2971	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃₁×#559	—	2	1	no	—
19	C₃₁×#559	C₂²	1	2	yes	—
20	C₃₁×#557	C₂²	1	1	yes	characteristic, complemented
21	C₃₁×#554	C₂²	1	1	yes	characteristic, complemented
22	C₃₁×#554	C₂²	1	1	yes	characteristic, complemented
23	C₃₁×#553	C₂²	1	2	yes	—
24	C₃₁×#552	—	2	2	no	—
25	C₃₁×#552	—	2	1	no	—
26	C₃₁×#552	C₂²	1	2	yes	—
27	C₃₁×#550	—	2	1	no	—
28	C₃₁×#550	C₂²	1	2	yes	—
29	C₃₁×#547	—	2	1	no	—
30	C₃₁×#547	C₂²	1	1	yes	characteristic, complemented
31	C₃₁×#546	—	2	2	no	—
32	C₃₁×#546	C₂²	1	4	yes	—
33	C₃₁×#541	—	2	1	no	—
34	C₃₁×#540	—	2	2	no	—
35	C₃₁×#539	—	2	2	no	—
36	C₃₁×#535	—	2	1	no	—
37	C₃₁×#533	C₂²	1	1	yes	characteristic
38	C₃₁×#533	C₂²	1	1	yes	characteristic
39	C₃₁×#532	C₂²	1	2	yes	—
40	C₃₁×#532	C₂²	1	2	yes	—
41	C₂×C₃₁×#127	C₂²	1	1	yes	characteristic
42	C₃₁×#529	C₂²	1	1	yes	characteristic
43	C₃₁×#529	C₂²	1	2	yes	complemented
44	C₂×C₃₁×#125	C₂²	1	2	yes	complemented
45	C₃₁×#520	—	2	1	no	—
46	C₃₁×#518	—	2	1	no	—
47	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
48	C₃₁×#501	C₂²	1	2	yes	complemented
49	C₃₁×#501	C₂²	1	1	yes	characteristic, complemented
50	C₃₁×#497	C₂²	1	1	yes	characteristic, complemented
51	C₃₁×#496	C₂²	1	2	yes	—
52	C₃₁×#491	C₂²	1	1	yes	characteristic, complemented
53	C₃₁×#491	C₂²	1	2	yes	complemented
54	C₃₁×#490	C₂²	1	2	yes	—
55	C₃₁×#490	C₂²	1	2	yes	—
56	C₃₁×#490	C₂²	1	2	yes	—
57	C₃₁×#489	C₂²	1	1	yes	characteristic, complemented
58	C₃₁×#488	C₂²	1	4	yes	complemented
59	C₃₁×#488	C₂²	1	4	yes	complemented
60	C₃₁×#486	C₂²	1	2	yes	—
61	C₃₁×#486	C₂²	1	2	yes	—
62	C₃₁×#485	C₂²	1	4	yes	—
63	C₃₁×#481	C₂²	1	4	yes	complemented
64	C₃₁×#480	C₂²	1	4	yes	complemented
65	C₃₁×#478	C₂²	1	4	yes	complemented
66	C₃₁×#478	C₂²	1	4	yes	complemented
67	C₃₁×#477	C₂²	1	2	yes	complemented
68	C₃₁×#475	C₂²	1	2	yes	complemented
69	C₃₁×#470	C₂²	1	2	yes	—
70	C₃₁×#469	C₂²	1	4	yes	complemented
71	C₃₁×#468	C₂²	1	2	yes	—
72	C₃₁×#468	C₂²	1	4	yes	complemented
73	C₃₁×#464	C₂²	1	4	yes	complemented
74	C₃₁×#463	C₂²	1	4	yes	complemented
75	C₃₁×#460	C₂²	1	2	yes	—
76	C₃₁×#459	C₂²	1	2	yes	—
77	C₃₁×#452	C₂²	1	4	yes	complemented
78	C₃₁×#450	C₂²	1	2	yes	—
79	C₃₁×#449	C₂²	1	4	yes	complemented
80	C₃₁×#447	C₂²	1	2	yes	—
81	C₈×Q₈×C₃₁	C₂²	1	2	yes	complemented
82	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	complemented
83	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
84	C₄×SD₁₆×C₃₁	C₂²	1	4	yes	complemented
85	C₄×D₈×C₃₁	C₂²	1	4	yes	complemented
86	C₃₁×#436	C₂²	1	4	yes	—
87	C₃₁×#436	C₂²	1	2	yes	complemented
88	C₃₁×#432	C₂²	1	1	yes	characteristic
89	C₃₁×#432	C₂²	1	2	yes	complemented
90	C₃₁×#418	C₂²	1	4	yes	—
91	C₃₁×#417	C₂²	1	4	yes	complemented
92	C₃₁×#417	C₂²	1	4	yes	complemented
93	C₄×M₁₆×C₃₁	C₂²	1	1	yes	characteristic
94	C₄×M₁₆×C₃₁	C₂²	1	2	yes	complemented
95	C₂×#41×C₃₁	—	2	1	no	—
96	C₂×#41×C₃₁	—	2	2	no	—
97	C₂×#41×C₃₁	D₄	1	1	yes	characteristic
98	C₂×#41×C₃₁	C₂³	1	4	yes	—
99	C₂²×D₄×C₃₁	—	2	1	no	—
100	C₂²×D₄×C₃₁	—	2	1	no	—
101	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
102	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
103	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
104	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
105	C₂×D₈×C₃₁	C₂³	1	4	yes	—
106	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
107	C₂×M₁₆×C₃₁	C₂³	1	4	yes	—
108	C₃₁×C₄⋊Q₈	—	2	1	no	—
109	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
110	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
111	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
112	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
113	C₃₁×#127	—	2	2	no	—
114	C₃₁×#127	—	2	1	no	—
115	C₃₁×#127	—	2	1	no	—
116	C₃₁×#127	C₂³	1	2	yes	—
117	C₃₁×#127	C₂³	1	2	yes	—
118	C₃₁×#126	—	2	2	no	—
119	C₃₁×#126	—	2	2	no	—
120	C₃₁×#126	—	2	1	no	—
121	C₃₁×#126	—	2	2	no	—
122	C₃₁×#125	—	2	2	no	—
123	C₃₁×#125	—	2	2	no	—
124	C₃₁×#125	—	2	1	no	—
125	C₃₁×#125	—	2	2	no	—
126	C₃₁×#125	—	2	2	no	—
127	C₃₁×#125	—	2	1	no	—
128	C₃₁×#125	C₂³	1	2	yes	—
129	C₃₁×#125	C₂³	1	2	yes	—
130	C₃₁×#125	C₂³	1	1	yes	characteristic
131	C₃₁×#125	C₂³	1	2	yes	—
132	C₃₁×#124	—	2	2	no	—
133	C₃₁×#124	—	2	2	no	—
134	C₃₁×#124	C₂³	1	4	yes	—
135	C₃₁×#124	C₂³	1	1	yes	characteristic
136	C₃₁×#123	—	2	2	no	—
137	C₃₁×#123	—	2	1	no	—
138	C₃₁×#123	—	2	2	no	—
139	C₃₁×#123	—	2	4	no	—
140	C₃₁×#123	—	2	4	no	—
141	C₃₁×#123	—	2	2	no	—
142	C₃₁×#123	—	2	2	no	—
143	C₃₁×C₂²⋊Q₈	—	2	1	no	—
144	C₃₁×C₂²⋊Q₈	—	2	1	no	—
145	C₃₁×C₂²⋊Q₈	—	2	1	no	—
146	C₃₁×C₂²⋊Q₈	—	2	1	no	—
147	C₃₁×C₂²⋊Q₈	—	2	2	no	—
148	C₃₁×C₂²⋊Q₈	—	2	1	no	—
149	C₃₁×C₂²⋊Q₈	—	2	2	no	—
150	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
151	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
152	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
153	C₃₁×#121	—	2	2	no	—
154	C₃₁×#121	—	2	2	no	—
155	C₃₁×#121	—	2	2	no	—
156	C₃₁×#121	—	2	2	no	—
157	C₃₁×#121	—	2	4	no	—
158	C₃₁×#121	—	2	4	no	—
159	C₃₁×#121	C₂³	1	1	yes	characteristic
160	C₃₁×#121	C₂³	1	2	yes	—
161	C₃₁×#121	C₂³	1	4	yes	—
162	C₃₁×#120	—	2	4	no	—
163	C₄×Q₈×C₃₁	—	2	1	no	—
164	C₄×Q₈×C₃₁	—	2	1	no	—
165	C₄×Q₈×C₃₁	—	2	1	no	—
166	C₄×Q₈×C₃₁	—	2	1	no	—
167	C₄×Q₈×C₃₁	D₄	1	1	yes	characteristic
168	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
169	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
170	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
171	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
172	C₄×D₄×C₃₁	—	2	1	no	—
173	C₄×D₄×C₃₁	—	2	2	no	—
174	C₄×D₄×C₃₁	—	2	1	no	—
175	C₄×D₄×C₃₁	—	2	2	no	—
176	C₄×D₄×C₃₁	—	2	2	no	—
177	C₄×D₄×C₃₁	—	2	2	no	—
178	C₄×D₄×C₃₁	—	2	2	no	—
179	C₄×D₄×C₃₁	—	2	2	no	—
180	C₄×D₄×C₃₁	—	2	2	no	—
181	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
182	C₄×D₄×C₃₁	D₄	1	2	yes	—
183	C₄×D₄×C₃₁	C₂³	1	2	yes	—
184	C₄×D₄×C₃₁	C₂³	1	4	yes	—
185	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
186	C₄×D₄×C₃₁	C₂³	1	2	yes	—
187	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
188	C₃₁×#117	—	2	1	no	—
189	C₃₁×#117	—	2	2	no	—
190	C₃₁×#117	—	2	1	no	—
191	C₃₁×#117	—	2	2	no	—
192	C₃₁×#117	D₄	1	1	yes	characteristic
193	C₃₁×#117	D₄	1	2	yes	—
194	C₃₁×#117	C₂³	1	2	yes	—
195	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
196	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
197	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
198	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
199	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
200	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
201	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
202	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
203	C₃₁×#107	C₂³	1	4	yes	—
204	C₃₁×#107	C₂³	1	2	yes	—
205	C₃₁×#106	C₂³	1	4	yes	—
206	C₃₁×#106	C₂³	1	2	yes	—
207	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
208	C₃₁×C₄⋊C₈	C₂³	1	4	yes	—
209	C₃₁×#103	C₂³	1	2	yes	—
210	C₃₁×#103	C₂³	1	2	yes	—
211	C₃₁×#103	C₂³	1	4	yes	—
212	C₃₁×#103	C₂³	1	4	yes	—
213	C₃₁×#103	C₂³	1	2	yes	—
214	C₃₁×#102	C₂³	1	4	yes	—
215	C₃₁×#102	C₂³	1	4	yes	—
216	C₃₁×#102	C₂³	1	4	yes	—
217	C₃₁×#102	C₂³	1	4	yes	—
218	C₃₁×#102	C₂³	1	4	yes	—
219	C₃₁×#102	C₂³	1	4	yes	—
220	C₃₁×#102	C₂³	1	2	yes	—
221	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
222	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
223	C₃₁×#97	C₂³	1	1	yes	characteristic
224	C₃₁×#97	C₂³	1	1	yes	characteristic
225	C₃₁×#97	C₂³	1	2	yes	—
226	C₄×C₈×C₃₁	C₂³	1	2	yes	—
227	C₄×C₈×C₃₁	C₂³	1	4	yes	—
228	C₂⁴×C₃₁	—	2	2	no	—
229	#41×C₃₁	—	4	2	no	—
230	#41×C₃₁	—	4	4	no	—
231	#41×C₃₁	—	4	4	no	—
232	#41×C₃₁	—	4	4	no	—
233	#41×C₃₁	—	8	4	no	—
234	C₂×Q₈×C₃₁	—	2	1	no	—
235	C₂×Q₈×C₃₁	—	2	1	no	—
236	C₂×Q₈×C₃₁	—	2	1	no	—
237	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
238	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
239	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
240	C₂×D₄×C₃₁	—	2	2	no	—
241	C₂×D₄×C₃₁	—	2	1	no	—
242	C₂×D₄×C₃₁	—	2	4	no	—
243	C₂×D₄×C₃₁	—	2	4	no	—
244	C₂×D₄×C₃₁	—	2	2	no	—
245	C₂×D₄×C₃₁	—	2	2	no	—
246	C₂×D₄×C₃₁	—	2	2	no	—
247	C₂×D₄×C₃₁	—	2	2	no	—
248	C₂×D₄×C₃₁	—	2	2	no	—
249	C₂×D₄×C₃₁	—	4	4	no	—
250	C₂×D₄×C₃₁	—	4	4	no	—
251	C₂×D₄×C₃₁	—	8	2	no	—
252	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
253	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
254	C₂×D₄×C₃₁	C₂⁴	1	4	yes	—
255	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
256	C₂²×C₄×C₃₁	—	2	2	no	—
257	C₂²×C₄×C₃₁	—	2	2	no	—
258	C₂²×C₄×C₃₁	—	2	1	no	—
259	C₂²×C₄×C₃₁	—	2	4	no	—
260	C₂²×C₄×C₃₁	—	2	4	no	—
261	C₂²×C₄×C₃₁	—	2	2	no	—
262	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
263	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
264	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
265	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
266	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
267	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
268	Q₁₆×C₃₁	—	4	2	no	—
269	SD₁₆×C₃₁	—	4	4	no	—
270	SD₁₆×C₃₁	—	4	2	no	—
271	D₈×C₃₁	—	4	4	no	—
272	M₁₆×C₃₁	—	4	4	no	—
273	M₁₆×C₃₁	—	4	2	no	—
274	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
275	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
276	C₂×C₈×C₃₁	C₂⁴	1	4	yes	—
277	C₄⋊C₄×C₃₁	—	2	2	no	—
278	C₄⋊C₄×C₃₁	—	2	1	no	—
279	C₄⋊C₄×C₃₁	—	2	1	no	—
280	C₄⋊C₄×C₃₁	—	2	2	no	—
281	C₄⋊C₄×C₃₁	—	2	1	no	—
282	C₄⋊C₄×C₃₁	—	2	2	no	—
283	C₄⋊C₄×C₃₁	—	2	2	no	—
284	C₄⋊C₄×C₃₁	—	2	2	no	—
285	C₄⋊C₄×C₃₁	—	2	2	no	—
286	C₄⋊C₄×C₃₁	—	2	2	no	—
287	C₄⋊C₄×C₃₁	—	2	2	no	—
288	C₄⋊C₄×C₃₁	—	2	1	no	—
289	C₄⋊C₄×C₃₁	—	2	1	no	—
290	C₄⋊C₄×C₃₁	—	2	1	no	—
291	C₄⋊C₄×C₃₁	—	2	2	no	—
292	C₄⋊C₄×C₃₁	—	2	1	no	—
293	C₄⋊C₄×C₃₁	—	2	2	no	—
294	C₄⋊C₄×C₃₁	—	2	1	no	—
295	C₄⋊C₄×C₃₁	—	2	2	no	—
296	C₄⋊C₄×C₃₁	—	2	1	no	—
297	C₄⋊C₄×C₃₁	—	2	2	no	—
298	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
299	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
300	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
301	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
302	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
303	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
304	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
305	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
306	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
307	C₂²⋊C₄×C₃₁	—	2	2	no	—
308	C₂²⋊C₄×C₃₁	—	2	2	no	—
309	C₂²⋊C₄×C₃₁	—	2	2	no	—
310	C₂²⋊C₄×C₃₁	—	2	1	no	—
311	C₂²⋊C₄×C₃₁	—	2	4	no	—
312	C₂²⋊C₄×C₃₁	—	2	4	no	—
313	C₂²⋊C₄×C₃₁	—	2	1	no	—
314	C₂²⋊C₄×C₃₁	—	2	1	no	—
315	C₂²⋊C₄×C₃₁	—	2	1	no	—
316	C₂²⋊C₄×C₃₁	—	2	2	no	—
317	C₂²⋊C₄×C₃₁	—	2	4	no	—
318	C₂²⋊C₄×C₃₁	—	2	4	no	—
319	C₂²⋊C₄×C₃₁	—	2	2	no	—
320	C₂²⋊C₄×C₃₁	—	2	1	no	—
321	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
322	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
323	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
324	C₄²×C₃₁	—	2	2	no	—
325	C₄²×C₃₁	—	2	2	no	—
326	C₄²×C₃₁	—	2	2	no	—
327	C₄²×C₃₁	—	2	1	no	—
328	C₄²×C₃₁	C₂×D₄	1	2	yes	—
329	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
330	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
331	C₄²×C₃₁	C₂×D₄	1	2	yes	—
332	C₄²×C₃₁	C₂⁴	1	2	yes	—
333	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
334	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
335	#62590	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
336	C₂³×C₃₁	—	2	1	no	—
337	C₂³×C₃₁	—	2	4	no	—
338	C₂³×C₃₁	—	4	4	no	—
339	C₂³×C₃₁	—	8	2	no	—
340	C₂³×C₃₁	—	8	2	no	—
341	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
342	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
343	Q₈×C₃₁	—	2	2	no	—
344	Q₈×C₃₁	—	2	2	no	—
345	Q₈×C₃₁	—	2	2	no	—
346	Q₈×C₃₁	—	2	2	no	—
347	Q₈×C₃₁	—	4	2	no	—
348	Q₈×C₃₁	—	4	2	no	—
349	Q₈×C₃₁	—	8	1	no	—
350	D₄×C₃₁	—	2	2	no	—
351	D₄×C₃₁	—	2	2	no	—
352	D₄×C₃₁	—	2	4	no	—
353	D₄×C₃₁	—	2	4	no	—
354	D₄×C₃₁	—	4	2	no	—
355	D₄×C₃₁	—	4	4	no	—
356	D₄×C₃₁	—	4	4	no	—
357	D₄×C₃₁	—	4	4	no	—
358	D₄×C₃₁	—	4	4	no	—
359	D₄×C₃₁	—	8	2	no	—
360	D₄×C₃₁	—	8	2	no	—
361	D₄×C₃₁	—	8	1	no	—
362	D₄×C₃₁	—	8	4	no	—
363	D₄×C₃₁	—	8	4	no	—
364	C₂×C₄×C₃₁	—	2	2	no	—
365	C₂×C₄×C₃₁	—	2	2	no	—
366	C₂×C₄×C₃₁	—	2	4	no	—
367	C₂×C₄×C₃₁	—	2	1	no	—
368	C₂×C₄×C₃₁	—	2	2	no	—
369	C₂×C₄×C₃₁	—	2	2	no	—
370	C₂×C₄×C₃₁	—	2	2	no	—
371	C₂×C₄×C₃₁	—	2	2	no	—
372	C₂×C₄×C₃₁	—	2	1	no	—
373	C₂×C₄×C₃₁	—	2	1	no	—
374	C₂×C₄×C₃₁	—	4	1	no	—
375	C₂×C₄×C₃₁	—	4	2	no	—
376	C₂×C₄×C₃₁	—	4	2	no	—
377	C₂×C₄×C₃₁	—	4	4	no	—
378	C₂×C₄×C₃₁	—	4	2	no	—
379	C₂×C₄×C₃₁	—	8	2	no	—
380	C₂×C₄×C₃₁	—	8	4	no	—
381	C₂×C₄×C₃₁	—	8	4	no	—
382	C₂×C₄×C₃₁	—	8	2	no	—
383	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
384	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
385	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
386	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
387	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
388	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
389	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
390	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
391	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
392	C₈×C₃₁	—	2	2	no	—
393	C₈×C₃₁	—	2	4	no	—
394	C₈×C₃₁	—	2	2	no	—
395	#3515	C₂×C₃₁	1	1	yes	characteristic, complemented
396	#3508	C₂×C₃₁	1	1	yes	characteristic, complemented
397	#3365	C₂×C₃₁	1	2	yes	complemented
398	#3361	C₂×C₃₁	1	2	yes	complemented
399	#3333	C₂×C₃₁	1	2	yes	complemented
400	#3332	C₂×C₃₁	1	2	yes	complemented
401	#3323	C₂×C₃₁	1	4	yes	complemented
402	#3322	C₂×C₃₁	1	4	yes	complemented
403	#3237	C₂×C₃₁	1	1	yes	characteristic, complemented
404	#3234	C₂×C₃₁	1	2	yes	complemented
405	#3219	C₂×C₃₁	1	2	yes	complemented
406	#3217	C₂×C₃₁	1	1	yes	characteristic, complemented
407	#3172	C₂×C₃₁	1	1	yes	characteristic, complemented
408	#3171	C₂×C₃₁	1	2	yes	complemented
409	#3142	C₂×C₃₁	1	2	yes	complemented
410	#3138	C₂×C₃₁	1	1	yes	characteristic, complemented
411	#2971	C₂×C₃₁	1	1	yes	characteristic, complemented
412	C₂²×C₃₁	—	2	2	no	—
413	C₂²×C₃₁	—	2	1	no	—
414	C₂²×C₃₁	—	2	2	no	—
415	C₂²×C₃₁	—	2	1	no	—
416	C₂²×C₃₁	—	2	1	no	—
417	C₂²×C₃₁	—	2	2	no	—
418	C₂²×C₃₁	—	4	1	no	—
419	C₂²×C₃₁	—	4	4	no	—
420	C₂²×C₃₁	—	4	4	no	—
421	C₂²×C₃₁	—	4	1	no	—
422	C₂²×C₃₁	—	4	1	no	—
423	C₂²×C₃₁	—	4	4	no	—
424	C₂²×C₃₁	—	16	4	no	—
425	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
426	C₄×C₃₁	—	2	1	no	—
427	C₄×C₃₁	—	2	2	no	—
428	C₄×C₃₁	—	2	1	no	—
429	C₄×C₃₁	—	2	2	no	—
430	C₄×C₃₁	—	2	1	no	—
431	C₄×C₃₁	—	2	1	no	—
432	C₄×C₃₁	—	2	2	no	—
433	C₄×C₃₁	—	4	1	no	—
434	C₄×C₃₁	—	4	2	no	—
435	C₄×C₃₁	—	4	2	no	—
436	C₄×C₃₁	—	4	2	no	—
437	C₄×C₃₁	—	4	1	no	—
438	C₄×C₃₁	—	4	1	no	—
439	C₄×C₃₁	—	4	2	no	—
440	C₄×C₃₁	#575	1	2	yes	—
441	C₄×C₃₁	#585	1	2	yes	—
442	#559	—	2	1	no	—
443	#559	C₂²×C₃₁	1	2	yes	—
444	#557	C₂²×C₃₁	1	1	yes	characteristic, complemented
445	#554	C₂²×C₃₁	1	1	yes	characteristic, complemented
446	#554	C₂²×C₃₁	1	1	yes	characteristic, complemented
447	#553	C₂²×C₃₁	1	2	yes	—
448	#552	—	2	2	no	—
449	#552	—	2	1	no	—
450	#552	C₂²×C₃₁	1	2	yes	—
451	#550	—	2	1	no	—
452	#550	C₂²×C₃₁	1	2	yes	—
453	#547	—	2	1	no	—
454	#547	C₂²×C₃₁	1	1	yes	characteristic, complemented
455	#546	—	2	2	no	—
456	#546	C₂²×C₃₁	1	4	yes	—
457	#541	—	2	1	no	—
458	#540	—	2	2	no	—
459	#539	—	2	2	no	—
460	#535	—	2	1	no	—
461	#533	C₂²×C₃₁	1	1	yes	characteristic
462	#533	C₂²×C₃₁	1	1	yes	characteristic
463	#532	C₂²×C₃₁	1	2	yes	—
464	#532	C₂²×C₃₁	1	2	yes	—
465	C₂×#127	C₂²×C₃₁	1	1	yes	characteristic
466	#529	C₂²×C₃₁	1	1	yes	characteristic
467	#529	C₂²×C₃₁	1	2	yes	complemented
468	C₂×#125	C₂²×C₃₁	1	2	yes	complemented
469	#520	—	2	1	no	—
470	#518	—	2	1	no	—
471	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
472	#501	C₂²×C₃₁	1	2	yes	complemented
473	#501	C₂²×C₃₁	1	1	yes	characteristic, complemented
474	#497	C₂²×C₃₁	1	1	yes	characteristic, complemented
475	#496	C₂²×C₃₁	1	2	yes	—
476	#491	C₂²×C₃₁	1	1	yes	characteristic, complemented
477	#491	C₂²×C₃₁	1	2	yes	complemented
478	#490	C₂²×C₃₁	1	2	yes	—
479	#490	C₂²×C₃₁	1	2	yes	—
480	#490	C₂²×C₃₁	1	2	yes	—
481	#489	C₂²×C₃₁	1	1	yes	characteristic, complemented
482	#488	C₂²×C₃₁	1	4	yes	complemented
483	#488	C₂²×C₃₁	1	4	yes	complemented
484	#486	C₂²×C₃₁	1	2	yes	—
485	#486	C₂²×C₃₁	1	2	yes	—
486	#485	C₂²×C₃₁	1	4	yes	—
487	#481	C₂²×C₃₁	1	4	yes	complemented
488	#480	C₂²×C₃₁	1	4	yes	complemented
489	#478	C₂²×C₃₁	1	4	yes	complemented
490	#478	C₂²×C₃₁	1	4	yes	complemented
491	#477	C₂²×C₃₁	1	2	yes	complemented
492	#475	C₂²×C₃₁	1	2	yes	complemented
493	#470	C₂²×C₃₁	1	2	yes	—
494	#469	C₂²×C₃₁	1	4	yes	complemented
495	#468	C₂²×C₃₁	1	2	yes	—
496	#468	C₂²×C₃₁	1	4	yes	complemented
497	#464	C₂²×C₃₁	1	4	yes	complemented
498	#463	C₂²×C₃₁	1	4	yes	complemented
499	#460	C₂²×C₃₁	1	2	yes	—
500	#459	C₂²×C₃₁	1	2	yes	—
501	#452	C₂²×C₃₁	1	4	yes	complemented
502	#450	C₂²×C₃₁	1	2	yes	—
503	#449	C₂²×C₃₁	1	4	yes	complemented
504	#447	C₂²×C₃₁	1	2	yes	—
505	C₈×Q₈	C₂²×C₃₁	1	2	yes	complemented
506	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	complemented
507	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
508	C₄×SD₁₆	C₂²×C₃₁	1	4	yes	complemented
509	C₄×D₈	C₂²×C₃₁	1	4	yes	complemented
510	#436	C₂²×C₃₁	1	4	yes	—
511	#436	C₂²×C₃₁	1	2	yes	complemented
512	#432	C₂²×C₃₁	1	1	yes	characteristic
513	#432	C₂²×C₃₁	1	2	yes	complemented
514	#418	C₂²×C₃₁	1	4	yes	—
515	#417	C₂²×C₃₁	1	4	yes	complemented
516	#417	C₂²×C₃₁	1	4	yes	complemented
517	C₄×M₁₆	C₂²×C₃₁	1	1	yes	characteristic
518	C₄×M₁₆	C₂²×C₃₁	1	2	yes	complemented
519	C₂×C₃₁	—	4	2	no	—
520	C₂×C₃₁	—	4	1	no	—
521	C₂×C₃₁	—	8	1	no	—
522	C₂×C₃₁	—	8	4	no	—
523	C₂×C₃₁	#3500	1	1	yes	characteristic
524	C₂×C₃₁	C₂×#575	1	1	yes	characteristic
525	C₂×C₃₁	#3585	1	1	yes	characteristic
526	C₂×#41	—	2	1	no	—
527	C₂×#41	—	2	2	no	—
528	C₂×#41	D₄×C₃₁	1	1	yes	characteristic
529	C₂×#41	C₂³×C₃₁	1	4	yes	—
530	C₂²×D₄	—	2	1	no	—
531	C₂²×D₄	—	2	1	no	—
532	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
533	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
534	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
535	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
536	C₂×D₈	C₂³×C₃₁	1	4	yes	—
537	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
538	C₂×M₁₆	C₂³×C₃₁	1	4	yes	—
539	C₄⋊Q₈	—	2	1	no	—
540	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
541	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
542	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
543	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
544	#127	—	2	2	no	—
545	#127	—	2	1	no	—
546	#127	—	2	1	no	—
547	#127	C₂³×C₃₁	1	2	yes	—
548	#127	C₂³×C₃₁	1	2	yes	—
549	#126	—	2	2	no	—
550	#126	—	2	2	no	—
551	#126	—	2	1	no	—
552	#126	—	2	2	no	—
553	#125	—	2	2	no	—
554	#125	—	2	2	no	—
555	#125	—	2	1	no	—
556	#125	—	2	2	no	—
557	#125	—	2	2	no	—
558	#125	—	2	1	no	—
559	#125	C₂³×C₃₁	1	1	yes	characteristic
560	#125	C₂³×C₃₁	1	2	yes	—
561	#125	C₂³×C₃₁	1	2	yes	—
562	#125	C₂³×C₃₁	1	2	yes	—
563	#124	—	2	2	no	—
564	#124	—	2	2	no	—
565	#124	C₂³×C₃₁	1	1	yes	characteristic
566	#124	C₂³×C₃₁	1	4	yes	—
567	#123	—	2	2	no	—
568	#123	—	2	1	no	—
569	#123	—	2	2	no	—
570	#123	—	2	4	no	—
571	#123	—	2	4	no	—
572	#123	—	2	2	no	—
573	#123	—	2	2	no	—
574	C₂²⋊Q₈	—	2	1	no	—
575	C₂²⋊Q₈	—	2	1	no	—
576	C₂²⋊Q₈	—	2	1	no	—
577	C₂²⋊Q₈	—	2	1	no	—
578	C₂²⋊Q₈	—	2	2	no	—
579	C₂²⋊Q₈	—	2	1	no	—
580	C₂²⋊Q₈	—	2	2	no	—
581	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
582	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
583	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
584	#121	—	2	2	no	—
585	#121	—	2	2	no	—
586	#121	—	2	2	no	—
587	#121	—	2	2	no	—
588	#121	—	2	4	no	—
589	#121	—	2	4	no	—
590	#121	C₂³×C₃₁	1	1	yes	characteristic
591	#121	C₂³×C₃₁	1	2	yes	—
592	#121	C₂³×C₃₁	1	4	yes	—
593	#120	—	2	4	no	—
594	C₄×Q₈	—	2	1	no	—
595	C₄×Q₈	—	2	1	no	—
596	C₄×Q₈	—	2	1	no	—
597	C₄×Q₈	—	2	1	no	—
598	C₄×Q₈	D₄×C₃₁	1	1	yes	characteristic
599	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
600	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
601	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
602	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
603	C₄×D₄	—	2	1	no	—
604	C₄×D₄	—	2	2	no	—
605	C₄×D₄	—	2	1	no	—
606	C₄×D₄	—	2	2	no	—
607	C₄×D₄	—	2	2	no	—
608	C₄×D₄	—	2	2	no	—
609	C₄×D₄	—	2	2	no	—
610	C₄×D₄	—	2	2	no	—
611	C₄×D₄	—	2	2	no	—
612	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
613	C₄×D₄	D₄×C₃₁	1	2	yes	—
614	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
615	C₄×D₄	C₂³×C₃₁	1	2	yes	—
616	C₄×D₄	C₂³×C₃₁	1	4	yes	—
617	C₄×D₄	C₂³×C₃₁	1	2	yes	—
618	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
619	#117	—	2	1	no	—
620	#117	—	2	2	no	—
621	#117	—	2	1	no	—
622	#117	—	2	2	no	—
623	#117	D₄×C₃₁	1	1	yes	characteristic
624	#117	D₄×C₃₁	1	2	yes	—
625	#117	C₂³×C₃₁	1	2	yes	—
626	C₂×C₄⋊C₄	—	2	2	no	—
627	C₂×C₄⋊C₄	—	2	2	no	—
628	C₂×C₄⋊C₄	—	2	1	no	—
629	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
630	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
631	C₂×C₂²⋊C₄	—	2	4	no	—
632	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
633	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
634	#107	C₂³×C₃₁	1	4	yes	—
635	#107	C₂³×C₃₁	1	2	yes	—
636	#106	C₂³×C₃₁	1	4	yes	—
637	#106	C₂³×C₃₁	1	2	yes	—
638	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
639	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
640	#103	C₂³×C₃₁	1	2	yes	—
641	#103	C₂³×C₃₁	1	2	yes	—
642	#103	C₂³×C₃₁	1	4	yes	—
643	#103	C₂³×C₃₁	1	4	yes	—
644	#103	C₂³×C₃₁	1	2	yes	—
645	#102	C₂³×C₃₁	1	4	yes	—
646	#102	C₂³×C₃₁	1	4	yes	—
647	#102	C₂³×C₃₁	1	4	yes	—
648	#102	C₂³×C₃₁	1	4	yes	—
649	#102	C₂³×C₃₁	1	4	yes	—
650	#102	C₂³×C₃₁	1	4	yes	—
651	#102	C₂³×C₃₁	1	2	yes	—
652	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
653	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
654	#97	C₂³×C₃₁	1	1	yes	characteristic
655	#97	C₂³×C₃₁	1	1	yes	characteristic
656	#97	C₂³×C₃₁	1	2	yes	—
657	C₄×C₈	C₂³×C₃₁	1	2	yes	—
658	C₄×C₈	C₂³×C₃₁	1	4	yes	—
659	C₃₁	#62590	1	1	yes	characteristic, direct product factor, Sylow
660	C₂⁴	—	2	2	no	—
661	#41	—	4	2	no	—
662	#41	—	4	4	no	—
663	#41	—	4	4	no	—
664	#41	—	4	4	no	—
665	#41	—	8	4	no	—
666	C₂×Q₈	—	2	1	no	—
667	C₂×Q₈	—	2	1	no	—
668	C₂×Q₈	—	2	1	no	—
669	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
670	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
671	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
672	C₂×D₄	—	2	2	no	—
673	C₂×D₄	—	2	1	no	—
674	C₂×D₄	—	2	4	no	—
675	C₂×D₄	—	2	4	no	—
676	C₂×D₄	—	2	2	no	—
677	C₂×D₄	—	2	2	no	—
678	C₂×D₄	—	2	2	no	—
679	C₂×D₄	—	2	2	no	—
680	C₂×D₄	—	2	2	no	—
681	C₂×D₄	—	4	4	no	—
682	C₂×D₄	—	4	4	no	—
683	C₂×D₄	—	8	2	no	—
684	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
685	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
686	C₂×D₄	C₂⁴×C₃₁	1	4	yes	—
687	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
688	C₂²×C₄	—	2	2	no	—
689	C₂²×C₄	—	2	2	no	—
690	C₂²×C₄	—	2	1	no	—
691	C₂²×C₄	—	2	4	no	—
692	C₂²×C₄	—	2	4	no	—
693	C₂²×C₄	—	2	2	no	—
694	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
695	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
696	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
697	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
698	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
699	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
700	Q₁₆	—	4	2	no	—
701	SD₁₆	—	4	4	no	—
702	SD₁₆	—	4	2	no	—
703	D₈	—	4	4	no	—
704	M₁₆	—	4	4	no	—
705	M₁₆	—	4	2	no	—
706	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
707	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
708	C₂×C₈	C₂⁴×C₃₁	1	4	yes	—
709	C₄⋊C₄	—	2	2	no	—
710	C₄⋊C₄	—	2	1	no	—
711	C₄⋊C₄	—	2	1	no	—
712	C₄⋊C₄	—	2	2	no	—
713	C₄⋊C₄	—	2	1	no	—
714	C₄⋊C₄	—	2	2	no	—
715	C₄⋊C₄	—	2	2	no	—
716	C₄⋊C₄	—	2	2	no	—
717	C₄⋊C₄	—	2	2	no	—
718	C₄⋊C₄	—	2	2	no	—
719	C₄⋊C₄	—	2	2	no	—
720	C₄⋊C₄	—	2	1	no	—
721	C₄⋊C₄	—	2	1	no	—
722	C₄⋊C₄	—	2	1	no	—
723	C₄⋊C₄	—	2	2	no	—
724	C₄⋊C₄	—	2	1	no	—
725	C₄⋊C₄	—	2	2	no	—
726	C₄⋊C₄	—	2	1	no	—
727	C₄⋊C₄	—	2	2	no	—
728	C₄⋊C₄	—	2	1	no	—
729	C₄⋊C₄	—	2	2	no	—
730	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
731	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
732	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
733	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
734	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
735	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
736	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
737	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
738	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
739	C₂²⋊C₄	—	2	2	no	—
740	C₂²⋊C₄	—	2	2	no	—
741	C₂²⋊C₄	—	2	2	no	—
742	C₂²⋊C₄	—	2	1	no	—
743	C₂²⋊C₄	—	2	4	no	—
744	C₂²⋊C₄	—	2	4	no	—
745	C₂²⋊C₄	—	2	1	no	—
746	C₂²⋊C₄	—	2	1	no	—
747	C₂²⋊C₄	—	2	1	no	—
748	C₂²⋊C₄	—	2	2	no	—
749	C₂²⋊C₄	—	2	4	no	—
750	C₂²⋊C₄	—	2	4	no	—
751	C₂²⋊C₄	—	2	2	no	—
752	C₂²⋊C₄	—	2	1	no	—
753	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
754	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
755	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
756	C₄²	—	2	2	no	—
757	C₄²	—	2	2	no	—
758	C₄²	—	2	2	no	—
759	C₄²	—	2	1	no	—
760	C₄²	C₂×D₄×C₃₁	1	2	yes	—
761	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
762	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
763	C₄²	C₂×D₄×C₃₁	1	2	yes	—
764	C₄²	C₂⁴×C₃₁	1	2	yes	—
765	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
766	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
767	C₂³	—	2	1	no	—
768	C₂³	—	2	4	no	—
769	C₂³	—	4	4	no	—
770	C₂³	—	8	2	no	—
771	C₂³	—	8	2	no	—
772	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
773	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
774	Q₈	—	2	2	no	—
775	Q₈	—	2	2	no	—
776	Q₈	—	2	2	no	—
777	Q₈	—	2	2	no	—
778	Q₈	—	4	2	no	—
779	Q₈	—	4	2	no	—
780	Q₈	—	8	1	no	—
781	D₄	—	2	2	no	—
782	D₄	—	2	2	no	—
783	D₄	—	2	4	no	—
784	D₄	—	2	4	no	—
785	D₄	—	4	2	no	—
786	D₄	—	4	4	no	—
787	D₄	—	4	4	no	—
788	D₄	—	4	4	no	—
789	D₄	—	4	4	no	—
790	D₄	—	8	2	no	—
791	D₄	—	8	2	no	—
792	D₄	—	8	1	no	—
793	D₄	—	8	4	no	—
794	D₄	—	8	4	no	—
795	C₂×C₄	—	2	2	no	—
796	C₂×C₄	—	2	2	no	—
797	C₂×C₄	—	2	4	no	—
798	C₂×C₄	—	2	1	no	—
799	C₂×C₄	—	2	2	no	—
800	C₂×C₄	—	2	2	no	—
801	C₂×C₄	—	2	2	no	—
802	C₂×C₄	—	2	2	no	—
803	C₂×C₄	—	2	1	no	—
804	C₂×C₄	—	2	1	no	—
805	C₂×C₄	—	4	1	no	—
806	C₂×C₄	—	4	2	no	—
807	C₂×C₄	—	4	2	no	—
808	C₂×C₄	—	4	4	no	—
809	C₂×C₄	—	4	2	no	—
810	C₂×C₄	—	8	2	no	—
811	C₂×C₄	—	8	4	no	—
812	C₂×C₄	—	8	4	no	—
813	C₂×C₄	—	8	2	no	—
814	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
815	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
816	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
817	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
818	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
819	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
820	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
821	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
822	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
823	C₈	—	2	2	no	—
824	C₈	—	2	4	no	—
825	C₈	—	2	2	no	—
826	C₂²	—	2	2	no	—
827	C₂²	—	2	1	no	—
828	C₂²	—	2	1	no	—
829	C₂²	—	2	2	no	—
830	C₂²	—	2	2	no	—
831	C₂²	—	2	1	no	—
832	C₂²	—	4	4	no	—
833	C₂²	—	4	1	no	—
834	C₂²	—	4	1	no	—
835	C₂²	—	4	4	no	—
836	C₂²	—	4	1	no	—
837	C₂²	—	4	4	no	—
838	C₂²	—	16	4	no	—
839	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
840	C₄	—	2	2	no	—
841	C₄	—	2	1	no	—
842	C₄	—	2	1	no	—
843	C₄	—	2	2	no	—
844	C₄	—	2	1	no	—
845	C₄	—	2	2	no	—
846	C₄	—	2	1	no	—
847	C₄	—	4	2	no	—
848	C₄	—	4	1	no	—
849	C₄	—	4	1	no	—
850	C₄	—	4	2	no	—
851	C₄	—	4	2	no	—
852	C₄	—	4	1	no	—
853	C₄	—	4	2	no	—
854	C₄	C₃₁×#575	1	2	yes	—
855	C₄	C₃₁×#585	1	2	yes	—
856	C₂	—	4	1	no	—
857	C₂	—	4	2	no	—
858	C₂	—	8	4	no	—
859	C₂	—	8	1	no	—
860	C₂	C₃₁×#3500	1	1	yes	characteristic
861	C₂	C₂×C₃₁×#575	1	1	yes	characteristic
862	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 ◁ C₄×#41×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3515	C₂	semidirect
2. C₃₁×#3508	C₂	semidirect
3. C₃₁×#3365	C₂	semidirect
4. C₃₁×#3361	C₂	semidirect
5. C₃₁×#3333	C₂	semidirect
6. C₃₁×#3332	C₂	semidirect
7. C₃₁×#3323	C₂	semidirect
8. C₃₁×#3322	C₂	semidirect
9. C₃₁×#3237	C₂	semidirect
10. C₃₁×#3234	C₂	semidirect
11. C₃₁×#3219	C₂	semidirect
12. C₃₁×#3217	C₂	semidirect
13. C₃₁×#3172	C₂	semidirect
14. C₃₁×#3171	C₂	semidirect
15. C₃₁×#3142	C₂	semidirect
16. C₃₁×#3138	C₂	semidirect
17. C₃₁×#2971	C₂	semidirect
20. C₃₁×#557	C₂²	semidirect
21. C₃₁×#554	C₂²	semidirect
22. C₃₁×#554	C₂²	semidirect
30. C₃₁×#547	C₂²	semidirect
43. C₃₁×#529	C₂²	semidirect
44. C₂×C₃₁×#125	C₂²	semidirect
48. C₃₁×#501	C₂²	semidirect
49. C₃₁×#501	C₂²	semidirect
50. C₃₁×#497	C₂²	semidirect
52. C₃₁×#491	C₂²	semidirect
53. C₃₁×#491	C₂²	semidirect
57. C₃₁×#489	C₂²	semidirect
58. C₃₁×#488	C₂²	semidirect
59. C₃₁×#488	C₂²	semidirect
63. C₃₁×#481	C₂²	semidirect
64. C₃₁×#480	C₂²	semidirect
65. C₃₁×#478	C₂²	semidirect
66. C₃₁×#478	C₂²	semidirect
67. C₃₁×#477	C₂²	semidirect
68. C₃₁×#475	C₂²	semidirect
70. C₃₁×#469	C₂²	semidirect
72. C₃₁×#468	C₂²	semidirect
73. C₃₁×#464	C₂²	semidirect
74. C₃₁×#463	C₂²	semidirect
77. C₃₁×#452	C₂²	semidirect
79. C₃₁×#449	C₂²	semidirect
81. C₈×Q₈×C₃₁	C₂²	semidirect
82. C₄×Q₁₆×C₃₁	C₂²	semidirect
83. C₄×SD₁₆×C₃₁	C₂²	semidirect
84. C₄×SD₁₆×C₃₁	C₂²	semidirect
85. C₄×D₈×C₃₁	C₂²	semidirect
87. C₃₁×#436	C₂²	semidirect
89. C₃₁×#432	C₂²	semidirect
91. C₃₁×#417	C₂²	semidirect
92. C₃₁×#417	C₂²	semidirect
94. C₄×M₁₆×C₃₁	C₂²	semidirect
335. #62590	C₃₁	direct (N × H)
395. #3515	C₂×C₃₁	semidirect
396. #3508	C₂×C₃₁	semidirect
397. #3365	C₂×C₃₁	semidirect
398. #3361	C₂×C₃₁	semidirect
399. #3333	C₂×C₃₁	semidirect
400. #3332	C₂×C₃₁	semidirect
401. #3323	C₂×C₃₁	semidirect
402. #3322	C₂×C₃₁	semidirect
403. #3237	C₂×C₃₁	semidirect
404. #3234	C₂×C₃₁	semidirect
405. #3219	C₂×C₃₁	semidirect
406. #3217	C₂×C₃₁	semidirect
407. #3172	C₂×C₃₁	semidirect
408. #3171	C₂×C₃₁	semidirect
409. #3142	C₂×C₃₁	semidirect
410. #3138	C₂×C₃₁	semidirect
411. #2971	C₂×C₃₁	semidirect
444. #557	C₂²×C₃₁	semidirect
445. #554	C₂²×C₃₁	semidirect
446. #554	C₂²×C₃₁	semidirect
454. #547	C₂²×C₃₁	semidirect
467. #529	C₂²×C₃₁	semidirect
468. C₂×#125	C₂²×C₃₁	semidirect
472. #501	C₂²×C₃₁	semidirect
473. #501	C₂²×C₃₁	semidirect
474. #497	C₂²×C₃₁	semidirect
476. #491	C₂²×C₃₁	semidirect
477. #491	C₂²×C₃₁	semidirect
481. #489	C₂²×C₃₁	semidirect
482. #488	C₂²×C₃₁	semidirect
483. #488	C₂²×C₃₁	semidirect
487. #481	C₂²×C₃₁	semidirect
488. #480	C₂²×C₃₁	semidirect
489. #478	C₂²×C₃₁	semidirect
490. #478	C₂²×C₃₁	semidirect
491. #477	C₂²×C₃₁	semidirect
492. #475	C₂²×C₃₁	semidirect
494. #469	C₂²×C₃₁	semidirect
496. #468	C₂²×C₃₁	semidirect
497. #464	C₂²×C₃₁	semidirect
498. #463	C₂²×C₃₁	semidirect
501. #452	C₂²×C₃₁	semidirect
503. #449	C₂²×C₃₁	semidirect
505. C₈×Q₈	C₂²×C₃₁	semidirect
506. C₄×Q₁₆	C₂²×C₃₁	semidirect
507. C₄×SD₁₆	C₂²×C₃₁	semidirect
508. C₄×SD₁₆	C₂²×C₃₁	semidirect
509. C₄×D₈	C₂²×C₃₁	semidirect
511. #436	C₂²×C₃₁	semidirect
513. #432	C₂²×C₃₁	semidirect
515. #417	C₂²×C₃₁	semidirect
516. #417	C₂²×C₃₁	semidirect
518. C₄×M₁₆	C₂²×C₃₁	semidirect
659. C₃₁	#62590	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×#3515	2
C₃₁×#3508	2
C₃₁×#3365	2
C₃₁×#3361	2
C₃₁×#3333	2
C₃₁×#3332	2
C₃₁×#3323	2
C₃₁×#3322	2
C₃₁×#3237	2
C₃₁×#3234	2
C₃₁×#3219	2
C₃₁×#3217	2
C₃₁×#3172	2
C₃₁×#3171	2
C₃₁×#3142	2
C₃₁×#3138	2
C₃₁×#2971	2
#62590	31

Subgroups — C31×#62590 #21519349

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#62590 #21519349