Subgroups — C₃₁×#62251 #21519010

Order 7936.

2014 conjugacy classes of subgroups.

The subgroup lattice has 794 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3519	C₂	1	2	yes	maximal, complemented
2	C₃₁×#3341	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3339	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3338	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#3305	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3297	C₂	1	4	yes	maximal, complemented
7	C₃₁×#3295	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3287	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#3280	C₂	1	2	yes	maximal, complemented
10	D₄×D₈×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#3247	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3188	C₂	1	4	yes	maximal, complemented
13	C₃₁×#3169	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3168	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3050	C₂	1	2	yes	maximal, complemented
16	C₂×C₃₁×#466	C₂	1	2	yes	maximal, complemented
17	C₂×C₈×D₄×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₃₁×#135	C₂²	1	2	yes	complemented
19	C₂²×D₈×C₃₁	C₂²	1	2	yes	complemented
20	C₂³×C₈×C₃₁	C₂²	1	2	yes	complemented
21	C₃₁×#555	C₂²	1	2	yes	complemented
22	C₃₁×#554	C₂²	1	2	yes	—
23	C₃₁×#553	—	2	2	no	—
24	C₃₁×#553	C₂²	1	4	yes	complemented
25	C₃₁×#550	C₂²	1	2	yes	complemented
26	C₃₁×#546	—	2	4	no	—
27	C₃₁×#546	C₂²	1	4	yes	complemented
28	D₄²×C₃₁	—	2	2	no	—
29	D₄²×C₃₁	C₂²	1	2	yes	—
30	C₃₁×#540	—	2	2	no	—
31	C₃₁×#538	—	2	4	no	—
32	C₃₁×#532	C₂²	1	2	yes	complemented
33	C₃₁×#529	C₂²	1	2	yes	complemented
34	C₃₁×#525	C₂²	1	4	yes	complemented
35	C₂×C₃₁×#121	C₂²	1	4	yes	complemented
36	C₃₁×#518	—	2	2	no	—
37	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
38	C₃₁×#500	C₂²	1	1	yes	characteristic, complemented
39	C₃₁×#499	C₂²	1	1	yes	characteristic, complemented
40	C₃₁×#495	C₂²	1	1	yes	characteristic, complemented
41	C₃₁×#493	C₂²	1	1	yes	characteristic, complemented
42	C₃₁×#488	C₂²	1	2	yes	complemented
43	C₃₁×#486	C₂²	1	2	yes	complemented
44	C₃₁×#484	C₂²	1	4	yes	complemented
45	C₃₁×#482	C₂²	1	4	yes	complemented
46	C₃₁×#482	C₂²	1	4	yes	complemented
47	C₃₁×#481	C₂²	1	4	yes	complemented
48	C₃₁×#478	C₂²	1	4	yes	complemented
49	C₃₁×#477	C₂²	1	2	yes	complemented
50	C₃₁×#476	C₂²	1	2	yes	complemented
51	C₃₁×#467	C₂²	1	2	yes	complemented
52	C₃₁×#467	C₂²	1	1	yes	characteristic, complemented
53	C₃₁×#466	C₂²	1	1	yes	characteristic
54	C₃₁×#466	C₂²	1	2	yes	complemented
55	C₃₁×#466	C₂²	1	2	yes	complemented
56	C₃₁×#466	C₂²	1	2	yes	complemented
57	C₃₁×#466	C₂²	1	2	yes	complemented
58	C₃₁×#466	C₂²	1	2	yes	complemented
59	C₃₁×#466	C₂²	1	4	yes	complemented
60	C₃₁×#466	C₂²	1	4	yes	complemented
61	C₃₁×#465	C₂²	1	2	yes	complemented
62	C₃₁×#465	C₂²	1	4	yes	complemented
63	C₃₁×#465	C₂²	1	4	yes	complemented
64	C₃₁×#463	C₂²	1	4	yes	complemented
65	C₃₁×#460	C₂²	1	2	yes	complemented
66	C₃₁×#459	C₂²	1	2	yes	complemented
67	C₃₁×#450	C₂²	1	4	yes	complemented
68	C₃₁×#449	C₂²	1	4	yes	complemented
69	C₃₁×#449	C₂²	1	4	yes	complemented
70	C₃₁×#447	C₂²	1	4	yes	complemented
71	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
72	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
73	C₄×D₈×C₃₁	C₂²	1	2	yes	complemented
74	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
75	C₄×D₈×C₃₁	C₂²	1	2	yes	complemented
76	C₈×D₄×C₃₁	C₂²	1	1	yes	characteristic
77	C₈×D₄×C₃₁	C₂²	1	1	yes	characteristic
78	C₈×D₄×C₃₁	C₂²	1	2	yes	complemented
79	C₈×D₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
80	C₈×D₄×C₃₁	C₂²	1	2	yes	complemented
81	C₈×D₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
82	C₃₁×#427	C₂²	1	2	yes	complemented
83	C₂×C₃₁×#107	C₂²	1	2	yes	complemented
84	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
85	C₃₁×#416	C₂²	1	4	yes	complemented
86	C₂×C₃₁×#102	C₂²	1	4	yes	complemented
87	C₂×C₃₁×C₂²⋊C₈	C₂²	1	2	yes	complemented
88	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
89	C₂×#41×C₃₁	—	2	2	no	—
90	C₂×#41×C₃₁	C₂³	1	4	yes	—
91	C₂²×D₄×C₃₁	—	2	4	no	—
92	C₂²×D₄×C₃₁	—	2	2	no	—
93	C₂²×D₄×C₃₁	D₄	1	1	yes	characteristic
94	C₂²×D₄×C₃₁	C₂³	1	4	yes	—
95	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
96	C₃₁×#135	—	4	4	no	—
97	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
98	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
99	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
100	C₂×D₈×C₃₁	—	4	4	no	—
101	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
102	C₂×D₈×C₃₁	C₂³	1	2	yes	—
103	C₂×D₈×C₃₁	C₂³	1	2	yes	—
104	C₂×D₈×C₃₁	C₂³	1	4	yes	—
105	C₂²×C₈×C₃₁	—	4	4	no	—
106	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
107	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
108	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
109	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
110	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
111	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
112	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
113	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
114	C₃₁×#127	—	2	2	no	—
115	C₃₁×#127	C₂³	1	2	yes	—
116	C₃₁×#126	—	2	4	no	—
117	C₃₁×#126	—	2	2	no	—
118	C₃₁×#125	—	2	2	no	—
119	C₃₁×#125	C₂³	1	2	yes	—
120	C₃₁×#124	—	2	4	no	—
121	C₃₁×#124	—	2	2	no	—
122	C₃₁×#124	C₂³	1	2	yes	—
123	C₃₁×#123	—	2	4	no	—
124	C₃₁×#123	—	2	2	no	—
125	C₃₁×#123	—	2	4	no	—
126	C₃₁×#123	—	2	4	no	—
127	C₃₁×C₂²⋊Q₈	—	2	4	no	—
128	C₃₁×C₂²⋊Q₈	C₂³	1	4	yes	—
129	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
130	C₃₁×#121	—	2	4	no	—
131	C₃₁×#121	—	2	2	no	—
132	C₃₁×#121	—	2	4	no	—
133	C₃₁×#121	—	2	4	no	—
134	C₃₁×#121	—	2	2	no	—
135	C₃₁×#121	—	2	2	no	—
136	C₃₁×#121	—	2	4	no	—
137	C₃₁×#121	—	2	4	no	—
138	C₃₁×#121	C₂³	1	4	yes	—
139	C₃₁×#121	C₂³	1	4	yes	—
140	C₃₁×#121	C₂³	1	4	yes	—
141	C₃₁×#121	C₂³	1	2	yes	—
142	C₃₁×#121	C₂³	1	4	yes	—
143	C₃₁×#120	—	2	4	no	—
144	C₃₁×#120	—	2	4	no	—
145	C₃₁×#120	—	2	4	no	—
146	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
147	C₄×D₄×C₃₁	—	2	2	no	—
148	C₄×D₄×C₃₁	—	2	4	no	—
149	C₄×D₄×C₃₁	—	2	4	no	—
150	C₄×D₄×C₃₁	—	2	2	no	—
151	C₄×D₄×C₃₁	—	2	2	no	—
152	C₄×D₄×C₃₁	—	2	4	no	—
153	C₄×D₄×C₃₁	—	2	2	no	—
154	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
155	C₄×D₄×C₃₁	D₄	1	2	yes	—
156	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
157	C₄×D₄×C₃₁	C₂³	1	4	yes	—
158	C₄×D₄×C₃₁	C₂³	1	2	yes	—
159	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
160	C₄×D₄×C₃₁	C₂³	1	2	yes	—
161	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
162	C₃₁×#117	—	2	2	no	—
163	C₃₁×#117	—	2	2	no	—
164	C₃₁×#117	C₂³	1	4	yes	—
165	C₂×C₄⋊C₄×C₃₁	D₄	1	1	yes	characteristic
166	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
167	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
168	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
169	C₂×C₂²⋊C₄×C₃₁	D₄	1	2	yes	—
170	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
171	C₃₁×#107	C₂³	1	1	yes	characteristic
172	C₃₁×#107	C₂³	1	2	yes	—
173	C₃₁×#107	C₂³	1	4	yes	—
174	C₃₁×#107	C₂³	1	1	yes	characteristic
175	C₃₁×#107	C₂³	1	2	yes	—
176	C₃₁×#106	C₂³	1	4	yes	—
177	C₃₁×#106	C₂³	1	2	yes	—
178	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
179	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
180	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
181	C₃₁×#103	C₂³	1	2	yes	—
182	C₃₁×#103	C₂³	1	4	yes	—
183	C₃₁×#103	C₂³	1	2	yes	—
184	C₃₁×#102	C₂³	1	2	yes	—
185	C₃₁×#102	C₂³	1	4	yes	—
186	C₃₁×#102	C₂³	1	4	yes	—
187	C₃₁×#102	C₂³	1	4	yes	—
188	C₃₁×#102	C₂³	1	4	yes	—
189	C₃₁×#102	C₂³	1	2	yes	—
190	C₃₁×#102	C₂³	1	4	yes	—
191	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
192	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
193	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
194	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
195	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
196	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
197	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
198	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
199	C₂⁴×C₃₁	—	2	4	no	—
200	C₂⁴×C₃₁	C₂×D₄	1	2	yes	—
201	#41×C₃₁	—	4	4	no	—
202	#41×C₃₁	—	4	4	no	—
203	#41×C₃₁	—	8	4	no	—
204	C₂×Q₈×C₃₁	—	2	2	no	—
205	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
206	C₂×D₄×C₃₁	—	2	4	no	—
207	C₂×D₄×C₃₁	—	2	4	no	—
208	C₂×D₄×C₃₁	—	2	4	no	—
209	C₂×D₄×C₃₁	—	2	2	no	—
210	C₂×D₄×C₃₁	—	2	4	no	—
211	C₂×D₄×C₃₁	—	2	4	no	—
212	C₂×D₄×C₃₁	—	2	4	no	—
213	C₂×D₄×C₃₁	—	2	2	no	—
214	C₂×D₄×C₃₁	—	2	2	no	—
215	C₂×D₄×C₃₁	—	2	4	no	—
216	C₂×D₄×C₃₁	—	4	4	no	—
217	C₂×D₄×C₃₁	—	4	4	no	—
218	C₂×D₄×C₃₁	—	4	8	no	—
219	C₂×D₄×C₃₁	—	8	8	no	—
220	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
221	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
222	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
223	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
224	C₂×D₄×C₃₁	C₂⁴	1	4	yes	—
225	C₂²×C₄×C₃₁	—	2	4	no	—
226	C₂²×C₄×C₃₁	—	2	2	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	2	no	—
231	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
232	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
233	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
234	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
235	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
236	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
237	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
238	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
239	Q₁₆×C₃₁	—	2	2	no	—
240	SD₁₆×C₃₁	—	4	2	no	—
241	SD₁₆×C₃₁	—	4	4	no	—
242	D₈×C₃₁	—	2	2	no	—
243	D₈×C₃₁	—	2	4	no	—
244	D₈×C₃₁	—	4	4	no	—
245	D₈×C₃₁	—	4	2	no	—
246	C₂×C₈×C₃₁	—	2	2	no	—
247	C₂×C₈×C₃₁	—	2	4	no	—
248	C₂×C₈×C₃₁	—	2	4	no	—
249	C₂×C₈×C₃₁	—	4	2	no	—
250	C₂×C₈×C₃₁	—	4	2	no	—
251	C₂×C₈×C₃₁	—	4	2	no	—
252	C₂×C₈×C₃₁	—	4	1	no	—
253	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
254	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
255	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
256	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
257	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
258	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
259	C₄⋊C₄×C₃₁	—	2	4	no	—
260	C₄⋊C₄×C₃₁	—	2	2	no	—
261	C₄⋊C₄×C₃₁	—	2	2	no	—
262	C₄⋊C₄×C₃₁	—	2	2	no	—
263	C₄⋊C₄×C₃₁	—	2	2	no	—
264	C₄⋊C₄×C₃₁	—	2	4	no	—
265	C₄⋊C₄×C₃₁	—	2	2	no	—
266	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
267	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
268	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
269	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
270	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
271	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
272	C₂²⋊C₄×C₃₁	—	2	4	no	—
273	C₂²⋊C₄×C₃₁	—	2	4	no	—
274	C₂²⋊C₄×C₃₁	—	2	2	no	—
275	C₂²⋊C₄×C₃₁	—	2	2	no	—
276	C₂²⋊C₄×C₃₁	—	2	2	no	—
277	C₂²⋊C₄×C₃₁	—	2	4	no	—
278	C₂²⋊C₄×C₃₁	—	2	4	no	—
279	C₂²⋊C₄×C₃₁	—	2	4	no	—
280	C₂²⋊C₄×C₃₁	—	2	2	no	—
281	C₂²⋊C₄×C₃₁	—	2	4	no	—
282	C₂²⋊C₄×C₃₁	—	2	2	no	—
283	C₂²⋊C₄×C₃₁	—	2	4	no	—
284	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
285	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
286	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
287	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
288	C₄²×C₃₁	—	2	4	no	—
289	C₄²×C₃₁	—	2	2	no	—
290	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
291	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
292	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
293	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
294	#62251	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
295	C₂³×C₃₁	—	2	4	no	—
296	C₂³×C₃₁	—	2	4	no	—
297	C₂³×C₃₁	—	2	2	no	—
298	C₂³×C₃₁	—	2	4	no	—
299	C₂³×C₃₁	—	4	2	no	—
300	C₂³×C₃₁	—	4	8	no	—
301	C₂³×C₃₁	—	8	4	no	—
302	C₂³×C₃₁	—	8	4	no	—
303	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
304	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
305	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
306	Q₈×C₃₁	—	2	2	no	—
307	Q₈×C₃₁	—	2	2	no	—
308	Q₈×C₃₁	—	8	2	no	—
309	D₄×C₃₁	—	2	4	no	—
310	D₄×C₃₁	—	2	2	no	—
311	D₄×C₃₁	—	2	2	no	—
312	D₄×C₃₁	—	2	4	no	—
313	D₄×C₃₁	—	2	4	no	—
314	D₄×C₃₁	—	2	2	no	—
315	D₄×C₃₁	—	4	8	no	—
316	D₄×C₃₁	—	4	4	no	—
317	D₄×C₃₁	—	4	8	no	—
318	D₄×C₃₁	—	4	4	no	—
319	D₄×C₃₁	—	8	4	no	—
320	D₄×C₃₁	—	8	2	no	—
321	D₄×C₃₁	—	8	4	no	—
322	D₄×C₃₁	—	8	4	no	—
323	D₄×C₃₁	—	8	4	no	—
324	D₄×C₃₁	#135	1	4	yes	complemented
325	C₂×C₄×C₃₁	—	2	2	no	—
326	C₂×C₄×C₃₁	—	2	2	no	—
327	C₂×C₄×C₃₁	—	2	1	no	—
328	C₂×C₄×C₃₁	—	2	2	no	—
329	C₂×C₄×C₃₁	—	2	2	no	—
330	C₂×C₄×C₃₁	—	2	1	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	2	no	—
335	C₂×C₄×C₃₁	—	2	4	no	—
336	C₂×C₄×C₃₁	—	2	2	no	—
337	C₂×C₄×C₃₁	—	4	2	no	—
338	C₂×C₄×C₃₁	—	4	2	no	—
339	C₂×C₄×C₃₁	—	4	2	no	—
340	C₂×C₄×C₃₁	—	4	4	no	—
341	C₂×C₄×C₃₁	—	8	4	no	—
342	C₂×C₄×C₃₁	—	8	4	no	—
343	C₂×C₄×C₃₁	—	8	4	no	—
344	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
345	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
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	2	yes	—
350	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
351	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
352	C₈×C₃₁	—	2	1	no	—
353	C₈×C₃₁	—	2	2	no	—
354	C₈×C₃₁	—	2	2	no	—
355	C₈×C₃₁	—	2	1	no	—
356	C₈×C₃₁	—	2	1	no	—
357	C₈×C₃₁	H(5,𝔽₂)	1	2	yes	—
358	#3519	C₂×C₃₁	1	2	yes	complemented
359	#3341	C₂×C₃₁	1	1	yes	characteristic, complemented
360	#3339	C₂×C₃₁	1	2	yes	complemented
361	#3338	C₂×C₃₁	1	1	yes	characteristic, complemented
362	#3305	C₂×C₃₁	1	2	yes	complemented
363	#3297	C₂×C₃₁	1	4	yes	complemented
364	#3295	C₂×C₃₁	1	2	yes	complemented
365	#3287	C₂×C₃₁	1	1	yes	characteristic, complemented
366	#3280	C₂×C₃₁	1	2	yes	complemented
367	D₄×D₈	C₂×C₃₁	1	1	yes	characteristic, complemented
368	#3247	C₂×C₃₁	1	2	yes	complemented
369	#3188	C₂×C₃₁	1	4	yes	complemented
370	#3169	C₂×C₃₁	1	1	yes	characteristic, complemented
371	#3168	C₂×C₃₁	1	1	yes	characteristic, complemented
372	#3050	C₂×C₃₁	1	2	yes	complemented
373	C₂×#466	C₂×C₃₁	1	2	yes	complemented
374	C₂×C₈×D₄	C₂×C₃₁	1	1	yes	characteristic, complemented
375	C₂²×C₃₁	—	2	1	no	—
376	C₂²×C₃₁	—	2	2	no	—
377	C₂²×C₃₁	—	2	1	no	—
378	C₂²×C₃₁	—	2	2	no	—
379	C₂²×C₃₁	—	2	2	no	—
380	C₂²×C₃₁	—	2	2	no	—
381	C₂²×C₃₁	—	2	2	no	—
382	C₂²×C₃₁	—	4	8	no	—
383	C₂²×C₃₁	—	4	4	no	—
384	C₂²×C₃₁	—	4	2	no	—
385	C₂²×C₃₁	—	4	2	no	—
386	C₂²×C₃₁	—	4	4	no	—
387	C₂²×C₃₁	—	4	4	no	—
388	C₂²×C₃₁	—	4	2	no	—
389	C₂²×C₃₁	—	16	8	no	—
390	C₂²×C₃₁	C₂×#135	1	4	yes	—
391	C₂²×C₃₁	#576	1	2	yes	—
392	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
393	C₄×C₃₁	—	2	1	no	—
394	C₄×C₃₁	—	2	2	no	—
395	C₄×C₃₁	—	2	2	no	—
396	C₄×C₃₁	—	2	1	no	—
397	C₄×C₃₁	—	2	1	no	—
398	C₄×C₃₁	—	2	1	no	—
399	C₄×C₃₁	—	4	2	no	—
400	C₄×C₃₁	—	4	2	no	—
401	C₄×C₃₁	—	4	2	no	—
402	C₄×C₃₁	—	4	4	no	—
403	C₄×C₃₁	C₂×#135	1	2	yes	—
404	C₄×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
405	C₄×C₃₁	#585	1	1	yes	characteristic
406	C₂×#135	C₂²×C₃₁	1	2	yes	complemented
407	C₂²×D₈	C₂²×C₃₁	1	2	yes	complemented
408	C₂³×C₈	C₂²×C₃₁	1	2	yes	complemented
409	#555	C₂²×C₃₁	1	2	yes	complemented
410	#554	C₂²×C₃₁	1	2	yes	—
411	#553	—	2	2	no	—
412	#553	C₂²×C₃₁	1	4	yes	complemented
413	#550	C₂²×C₃₁	1	2	yes	complemented
414	#546	—	2	4	no	—
415	#546	C₂²×C₃₁	1	4	yes	complemented
416	D₄²	—	2	2	no	—
417	D₄²	C₂²×C₃₁	1	2	yes	—
418	#540	—	2	2	no	—
419	#538	—	2	4	no	—
420	#532	C₂²×C₃₁	1	2	yes	complemented
421	#529	C₂²×C₃₁	1	2	yes	complemented
422	#525	C₂²×C₃₁	1	4	yes	complemented
423	C₂×#121	C₂²×C₃₁	1	4	yes	complemented
424	#518	—	2	2	no	—
425	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
426	#500	C₂²×C₃₁	1	1	yes	characteristic, complemented
427	#499	C₂²×C₃₁	1	1	yes	characteristic, complemented
428	#495	C₂²×C₃₁	1	1	yes	characteristic, complemented
429	#493	C₂²×C₃₁	1	1	yes	characteristic, complemented
430	#488	C₂²×C₃₁	1	2	yes	complemented
431	#486	C₂²×C₃₁	1	2	yes	complemented
432	#484	C₂²×C₃₁	1	4	yes	complemented
433	#482	C₂²×C₃₁	1	4	yes	complemented
434	#482	C₂²×C₃₁	1	4	yes	complemented
435	#481	C₂²×C₃₁	1	4	yes	complemented
436	#478	C₂²×C₃₁	1	4	yes	complemented
437	#477	C₂²×C₃₁	1	2	yes	complemented
438	#476	C₂²×C₃₁	1	2	yes	complemented
439	#467	C₂²×C₃₁	1	2	yes	complemented
440	#467	C₂²×C₃₁	1	1	yes	characteristic, complemented
441	#466	C₂²×C₃₁	1	1	yes	characteristic
442	#466	C₂²×C₃₁	1	2	yes	complemented
443	#466	C₂²×C₃₁	1	2	yes	complemented
444	#466	C₂²×C₃₁	1	2	yes	complemented
445	#466	C₂²×C₃₁	1	2	yes	complemented
446	#466	C₂²×C₃₁	1	2	yes	complemented
447	#466	C₂²×C₃₁	1	4	yes	complemented
448	#466	C₂²×C₃₁	1	4	yes	complemented
449	#465	C₂²×C₃₁	1	2	yes	complemented
450	#465	C₂²×C₃₁	1	4	yes	complemented
451	#465	C₂²×C₃₁	1	4	yes	complemented
452	#463	C₂²×C₃₁	1	4	yes	complemented
453	#460	C₂²×C₃₁	1	2	yes	complemented
454	#459	C₂²×C₃₁	1	2	yes	complemented
455	#450	C₂²×C₃₁	1	4	yes	complemented
456	#449	C₂²×C₃₁	1	4	yes	complemented
457	#449	C₂²×C₃₁	1	4	yes	complemented
458	#447	C₂²×C₃₁	1	4	yes	complemented
459	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
460	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
461	C₄×D₈	C₂²×C₃₁	1	2	yes	complemented
462	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
463	C₄×D₈	C₂²×C₃₁	1	2	yes	complemented
464	C₈×D₄	C₂²×C₃₁	1	1	yes	characteristic
465	C₈×D₄	C₂²×C₃₁	1	1	yes	characteristic
466	C₈×D₄	C₂²×C₃₁	1	2	yes	complemented
467	C₈×D₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
468	C₈×D₄	C₂²×C₃₁	1	2	yes	complemented
469	C₈×D₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
470	#427	C₂²×C₃₁	1	2	yes	complemented
471	C₂×#107	C₂²×C₃₁	1	2	yes	complemented
472	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
473	#416	C₂²×C₃₁	1	4	yes	complemented
474	C₂×#102	C₂²×C₃₁	1	4	yes	complemented
475	C₂×C₂²⋊C₈	C₂²×C₃₁	1	2	yes	complemented
476	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
477	C₂×C₃₁	—	2	2	no	—
478	C₂×C₃₁	—	2	4	no	—
479	C₂×C₃₁	—	4	2	no	—
480	C₂×C₃₁	—	8	4	no	—
481	C₂×C₃₁	—	8	2	no	—
482	C₂×C₃₁	#3496	1	1	yes	characteristic
483	C₂×C₃₁	C₂²×#135	1	1	yes	characteristic
484	C₂×C₃₁	C₂×#576	1	1	yes	characteristic
485	C₂×#41	—	2	2	no	—
486	C₂×#41	C₂³×C₃₁	1	4	yes	—
487	C₂²×D₄	—	2	4	no	—
488	C₂²×D₄	—	2	2	no	—
489	C₂²×D₄	D₄×C₃₁	1	1	yes	characteristic
490	C₂²×D₄	C₂³×C₃₁	1	4	yes	—
491	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
492	#135	—	4	4	no	—
493	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
494	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
495	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
496	C₂×D₈	—	4	4	no	—
497	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
498	C₂×D₈	C₂³×C₃₁	1	2	yes	—
499	C₂×D₈	C₂³×C₃₁	1	4	yes	—
500	C₂×D₈	C₂³×C₃₁	1	2	yes	—
501	C₂²×C₈	—	4	4	no	—
502	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
503	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
504	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
505	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
506	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
507	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
508	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
509	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
510	#127	—	2	2	no	—
511	#127	C₂³×C₃₁	1	2	yes	—
512	#126	—	2	4	no	—
513	#126	—	2	2	no	—
514	#125	—	2	2	no	—
515	#125	C₂³×C₃₁	1	2	yes	—
516	#124	—	2	4	no	—
517	#124	—	2	2	no	—
518	#124	C₂³×C₃₁	1	2	yes	—
519	#123	—	2	4	no	—
520	#123	—	2	2	no	—
521	#123	—	2	4	no	—
522	#123	—	2	4	no	—
523	C₂²⋊Q₈	—	2	4	no	—
524	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
525	C₂²⋊Q₈	C₂³×C₃₁	1	4	yes	—
526	#121	—	2	4	no	—
527	#121	—	2	2	no	—
528	#121	—	2	4	no	—
529	#121	—	2	4	no	—
530	#121	—	2	2	no	—
531	#121	—	2	2	no	—
532	#121	—	2	4	no	—
533	#121	—	2	4	no	—
534	#121	C₂³×C₃₁	1	2	yes	—
535	#121	C₂³×C₃₁	1	4	yes	—
536	#121	C₂³×C₃₁	1	4	yes	—
537	#121	C₂³×C₃₁	1	4	yes	—
538	#121	C₂³×C₃₁	1	4	yes	—
539	#120	—	2	4	no	—
540	#120	—	2	4	no	—
541	#120	—	2	4	no	—
542	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
543	C₄×D₄	—	2	2	no	—
544	C₄×D₄	—	2	4	no	—
545	C₄×D₄	—	2	4	no	—
546	C₄×D₄	—	2	2	no	—
547	C₄×D₄	—	2	2	no	—
548	C₄×D₄	—	2	4	no	—
549	C₄×D₄	—	2	2	no	—
550	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
551	C₄×D₄	D₄×C₃₁	1	2	yes	—
552	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
553	C₄×D₄	C₂³×C₃₁	1	2	yes	—
554	C₄×D₄	C₂³×C₃₁	1	4	yes	—
555	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
556	C₄×D₄	C₂³×C₃₁	1	2	yes	—
557	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
558	#117	—	2	2	no	—
559	#117	—	2	2	no	—
560	#117	C₂³×C₃₁	1	4	yes	—
561	C₂×C₄⋊C₄	D₄×C₃₁	1	1	yes	characteristic
562	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
563	C₂×C₂²⋊C₄	—	2	4	no	—
564	C₂×C₂²⋊C₄	—	2	4	no	—
565	C₂×C₂²⋊C₄	D₄×C₃₁	1	2	yes	—
566	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
567	#107	C₂³×C₃₁	1	1	yes	characteristic
568	#107	C₂³×C₃₁	1	2	yes	—
569	#107	C₂³×C₃₁	1	4	yes	—
570	#107	C₂³×C₃₁	1	1	yes	characteristic
571	#107	C₂³×C₃₁	1	2	yes	—
572	#106	C₂³×C₃₁	1	4	yes	—
573	#106	C₂³×C₃₁	1	2	yes	—
574	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
575	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
576	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
577	#103	C₂³×C₃₁	1	2	yes	—
578	#103	C₂³×C₃₁	1	4	yes	—
579	#103	C₂³×C₃₁	1	2	yes	—
580	#102	C₂³×C₃₁	1	2	yes	—
581	#102	C₂³×C₃₁	1	4	yes	—
582	#102	C₂³×C₃₁	1	4	yes	—
583	#102	C₂³×C₃₁	1	4	yes	—
584	#102	C₂³×C₃₁	1	4	yes	—
585	#102	C₂³×C₃₁	1	2	yes	—
586	#102	C₂³×C₃₁	1	4	yes	—
587	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
588	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
589	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
590	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
591	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
592	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
593	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
594	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
595	C₃₁	#62251	1	1	yes	characteristic, direct product factor, Sylow
596	C₂⁴	—	2	4	no	—
597	C₂⁴	C₂×D₄×C₃₁	1	2	yes	—
598	#41	—	4	4	no	—
599	#41	—	4	4	no	—
600	#41	—	8	4	no	—
601	C₂×Q₈	—	2	2	no	—
602	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
603	C₂×D₄	—	2	4	no	—
604	C₂×D₄	—	2	4	no	—
605	C₂×D₄	—	2	4	no	—
606	C₂×D₄	—	2	2	no	—
607	C₂×D₄	—	2	4	no	—
608	C₂×D₄	—	2	4	no	—
609	C₂×D₄	—	2	4	no	—
610	C₂×D₄	—	2	2	no	—
611	C₂×D₄	—	2	2	no	—
612	C₂×D₄	—	2	4	no	—
613	C₂×D₄	—	4	4	no	—
614	C₂×D₄	—	4	4	no	—
615	C₂×D₄	—	4	8	no	—
616	C₂×D₄	—	8	8	no	—
617	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
618	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
619	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
620	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
621	C₂×D₄	C₂⁴×C₃₁	1	4	yes	—
622	C₂²×C₄	—	2	4	no	—
623	C₂²×C₄	—	2	2	no	—
624	C₂²×C₄	—	2	4	no	—
625	C₂²×C₄	—	2	4	no	—
626	C₂²×C₄	—	4	2	no	—
627	C₂²×C₄	—	4	2	no	—
628	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
629	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
630	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
631	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
632	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
633	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
634	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
635	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
636	Q₁₆	—	2	2	no	—
637	SD₁₆	—	4	2	no	—
638	SD₁₆	—	4	4	no	—
639	D₈	—	2	2	no	—
640	D₈	—	2	4	no	—
641	D₈	—	4	4	no	—
642	D₈	—	4	2	no	—
643	C₂×C₈	—	2	2	no	—
644	C₂×C₈	—	2	4	no	—
645	C₂×C₈	—	2	4	no	—
646	C₂×C₈	—	4	2	no	—
647	C₂×C₈	—	4	2	no	—
648	C₂×C₈	—	4	2	no	—
649	C₂×C₈	—	4	1	no	—
650	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
651	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
652	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
653	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
654	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
655	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
656	C₄⋊C₄	—	2	4	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	4	no	—
662	C₄⋊C₄	—	2	2	no	—
663	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
664	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
665	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
666	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
667	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
668	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
669	C₂²⋊C₄	—	2	4	no	—
670	C₂²⋊C₄	—	2	4	no	—
671	C₂²⋊C₄	—	2	2	no	—
672	C₂²⋊C₄	—	2	2	no	—
673	C₂²⋊C₄	—	2	2	no	—
674	C₂²⋊C₄	—	2	4	no	—
675	C₂²⋊C₄	—	2	4	no	—
676	C₂²⋊C₄	—	2	4	no	—
677	C₂²⋊C₄	—	2	2	no	—
678	C₂²⋊C₄	—	2	4	no	—
679	C₂²⋊C₄	—	2	2	no	—
680	C₂²⋊C₄	—	2	4	no	—
681	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
682	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
683	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
684	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
685	C₄²	—	2	4	no	—
686	C₄²	—	2	2	no	—
687	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
688	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
689	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
690	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
691	C₂³	—	2	4	no	—
692	C₂³	—	2	4	no	—
693	C₂³	—	2	2	no	—
694	C₂³	—	2	4	no	—
695	C₂³	—	4	2	no	—
696	C₂³	—	4	8	no	—
697	C₂³	—	8	4	no	—
698	C₂³	—	8	4	no	—
699	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
700	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
701	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
702	Q₈	—	2	2	no	—
703	Q₈	—	2	2	no	—
704	Q₈	—	8	2	no	—
705	D₄	—	2	4	no	—
706	D₄	—	2	2	no	—
707	D₄	—	2	2	no	—
708	D₄	—	2	4	no	—
709	D₄	—	2	4	no	—
710	D₄	—	2	2	no	—
711	D₄	—	4	8	no	—
712	D₄	—	4	4	no	—
713	D₄	—	4	8	no	—
714	D₄	—	4	4	no	—
715	D₄	—	8	4	no	—
716	D₄	—	8	2	no	—
717	D₄	—	8	4	no	—
718	D₄	—	8	4	no	—
719	D₄	—	8	4	no	—
720	D₄	C₃₁×#135	1	4	yes	complemented
721	C₂×C₄	—	2	2	no	—
722	C₂×C₄	—	2	2	no	—
723	C₂×C₄	—	2	1	no	—
724	C₂×C₄	—	2	2	no	—
725	C₂×C₄	—	2	2	no	—
726	C₂×C₄	—	2	1	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	4	no	—
732	C₂×C₄	—	2	2	no	—
733	C₂×C₄	—	4	2	no	—
734	C₂×C₄	—	4	2	no	—
735	C₂×C₄	—	4	2	no	—
736	C₂×C₄	—	4	4	no	—
737	C₂×C₄	—	8	4	no	—
738	C₂×C₄	—	8	4	no	—
739	C₂×C₄	—	8	4	no	—
740	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
741	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
742	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
743	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
744	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
745	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
746	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
747	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
748	C₈	—	2	1	no	—
749	C₈	—	2	2	no	—
750	C₈	—	2	2	no	—
751	C₈	—	2	1	no	—
752	C₈	—	2	1	no	—
753	C₈	C₃₁×H(5,𝔽₂)	1	2	yes	—
754	C₂²	—	2	1	no	—
755	C₂²	—	2	2	no	—
756	C₂²	—	2	1	no	—
757	C₂²	—	2	2	no	—
758	C₂²	—	2	2	no	—
759	C₂²	—	2	2	no	—
760	C₂²	—	2	2	no	—
761	C₂²	—	4	8	no	—
762	C₂²	—	4	4	no	—
763	C₂²	—	4	2	no	—
764	C₂²	—	4	2	no	—
765	C₂²	—	4	4	no	—
766	C₂²	—	4	4	no	—
767	C₂²	—	4	2	no	—
768	C₂²	—	16	8	no	—
769	C₂²	C₂×C₃₁×#135	1	4	yes	—
770	C₂²	C₃₁×#576	1	2	yes	—
771	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
772	C₄	—	2	1	no	—
773	C₄	—	2	2	no	—
774	C₄	—	2	2	no	—
775	C₄	—	2	1	no	—
776	C₄	—	2	1	no	—
777	C₄	—	2	1	no	—
778	C₄	—	4	2	no	—
779	C₄	—	4	2	no	—
780	C₄	—	4	2	no	—
781	C₄	—	4	4	no	—
782	C₄	C₂×C₃₁×#135	1	2	yes	—
783	C₄	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
784	C₄	C₃₁×#585	1	1	yes	characteristic
785	C₂	—	2	2	no	—
786	C₂	—	2	4	no	—
787	C₂	—	4	2	no	—
788	C₂	—	8	2	no	—
789	C₂	—	8	4	no	—
790	C₂	C₃₁×#3496	1	1	yes	characteristic
791	C₂	C₂²×C₃₁×#135	1	1	yes	characteristic
792	C₂	C₂×C₃₁×#576	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 ◁ C₂×C₄×D₄×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3519	C₂	semidirect
2. C₃₁×#3341	C₂	semidirect
3. C₃₁×#3339	C₂	semidirect
4. C₃₁×#3338	C₂	semidirect
5. C₃₁×#3305	C₂	semidirect
6. C₃₁×#3297	C₂	semidirect
7. C₃₁×#3295	C₂	semidirect
8. C₃₁×#3287	C₂	semidirect
9. C₃₁×#3280	C₂	semidirect
10. D₄×D₈×C₃₁	C₂	semidirect
11. C₃₁×#3247	C₂	semidirect
12. C₃₁×#3188	C₂	semidirect
13. C₃₁×#3169	C₂	semidirect
14. C₃₁×#3168	C₂	semidirect
15. C₃₁×#3050	C₂	semidirect
16. C₂×C₃₁×#466	C₂	semidirect
17. C₂×C₈×D₄×C₃₁	C₂	semidirect
18. C₂×C₃₁×#135	C₂²	semidirect
19. C₂²×D₈×C₃₁	C₂²	semidirect
20. C₂³×C₈×C₃₁	C₂²	semidirect
21. C₃₁×#555	C₂²	semidirect
24. C₃₁×#553	C₂²	semidirect
25. C₃₁×#550	C₂²	semidirect
27. C₃₁×#546	C₂²	semidirect
32. C₃₁×#532	C₂²	semidirect
33. C₃₁×#529	C₂²	semidirect
34. C₃₁×#525	C₂²	semidirect
35. C₂×C₃₁×#121	C₂²	semidirect
38. C₃₁×#500	C₂²	semidirect
39. C₃₁×#499	C₂²	semidirect
40. C₃₁×#495	C₂²	semidirect
41. C₃₁×#493	C₂²	semidirect
42. C₃₁×#488	C₂²	semidirect
43. C₃₁×#486	C₂²	semidirect
44. C₃₁×#484	C₂²	semidirect
45. C₃₁×#482	C₂²	semidirect
46. C₃₁×#482	C₂²	semidirect
47. C₃₁×#481	C₂²	semidirect
48. C₃₁×#478	C₂²	semidirect
49. C₃₁×#477	C₂²	semidirect
50. C₃₁×#476	C₂²	semidirect
51. C₃₁×#467	C₂²	semidirect
52. C₃₁×#467	C₂²	semidirect
54. C₃₁×#466	C₂²	semidirect
55. C₃₁×#466	C₂²	semidirect
56. C₃₁×#466	C₂²	semidirect
57. C₃₁×#466	C₂²	semidirect
58. C₃₁×#466	C₂²	semidirect
59. C₃₁×#466	C₂²	semidirect
60. C₃₁×#466	C₂²	semidirect
61. C₃₁×#465	C₂²	semidirect
62. C₃₁×#465	C₂²	semidirect
63. C₃₁×#465	C₂²	semidirect
64. C₃₁×#463	C₂²	semidirect
65. C₃₁×#460	C₂²	semidirect
66. C₃₁×#459	C₂²	semidirect
67. C₃₁×#450	C₂²	semidirect
68. C₃₁×#449	C₂²	semidirect
69. C₃₁×#449	C₂²	semidirect
70. C₃₁×#447	C₂²	semidirect
71. C₄×Q₁₆×C₃₁	C₂²	semidirect
72. C₄×SD₁₆×C₃₁	C₂²	semidirect
73. C₄×D₈×C₃₁	C₂²	semidirect
74. C₄×D₈×C₃₁	C₂²	semidirect
75. C₄×D₈×C₃₁	C₂²	semidirect
78. C₈×D₄×C₃₁	C₂²	semidirect
79. C₈×D₄×C₃₁	C₂²	semidirect
80. C₈×D₄×C₃₁	C₂²	semidirect
81. C₈×D₄×C₃₁	C₂²	semidirect
82. C₃₁×#427	C₂²	semidirect
83. C₂×C₃₁×#107	C₂²	semidirect
84. C₂×C₃₁×C₄⋊C₈	C₂²	semidirect
85. C₃₁×#416	C₂²	semidirect
86. C₂×C₃₁×#102	C₂²	semidirect
87. C₂×C₃₁×C₂²⋊C₈	C₂²	semidirect
88. C₂×C₄×C₈×C₃₁	C₂²	semidirect
294. #62251	C₃₁	direct (N × H)
324. D₄×C₃₁	#135	semidirect
358. #3519	C₂×C₃₁	semidirect
359. #3341	C₂×C₃₁	semidirect
360. #3339	C₂×C₃₁	semidirect
361. #3338	C₂×C₃₁	semidirect
362. #3305	C₂×C₃₁	semidirect
363. #3297	C₂×C₃₁	semidirect
364. #3295	C₂×C₃₁	semidirect
365. #3287	C₂×C₃₁	semidirect
366. #3280	C₂×C₃₁	semidirect
367. D₄×D₈	C₂×C₃₁	semidirect
368. #3247	C₂×C₃₁	semidirect
369. #3188	C₂×C₃₁	semidirect
370. #3169	C₂×C₃₁	semidirect
371. #3168	C₂×C₃₁	semidirect
372. #3050	C₂×C₃₁	semidirect
373. C₂×#466	C₂×C₃₁	semidirect
374. C₂×C₈×D₄	C₂×C₃₁	semidirect
406. C₂×#135	C₂²×C₃₁	semidirect
407. C₂²×D₈	C₂²×C₃₁	semidirect
408. C₂³×C₈	C₂²×C₃₁	semidirect
409. #555	C₂²×C₃₁	semidirect
412. #553	C₂²×C₃₁	semidirect
413. #550	C₂²×C₃₁	semidirect
415. #546	C₂²×C₃₁	semidirect
420. #532	C₂²×C₃₁	semidirect
421. #529	C₂²×C₃₁	semidirect
422. #525	C₂²×C₃₁	semidirect
423. C₂×#121	C₂²×C₃₁	semidirect
426. #500	C₂²×C₃₁	semidirect
427. #499	C₂²×C₃₁	semidirect
428. #495	C₂²×C₃₁	semidirect
429. #493	C₂²×C₃₁	semidirect
430. #488	C₂²×C₃₁	semidirect
431. #486	C₂²×C₃₁	semidirect
432. #484	C₂²×C₃₁	semidirect
433. #482	C₂²×C₃₁	semidirect
434. #482	C₂²×C₃₁	semidirect
435. #481	C₂²×C₃₁	semidirect
436. #478	C₂²×C₃₁	semidirect
437. #477	C₂²×C₃₁	semidirect
438. #476	C₂²×C₃₁	semidirect
439. #467	C₂²×C₃₁	semidirect
440. #467	C₂²×C₃₁	semidirect
442. #466	C₂²×C₃₁	semidirect
443. #466	C₂²×C₃₁	semidirect
444. #466	C₂²×C₃₁	semidirect
445. #466	C₂²×C₃₁	semidirect
446. #466	C₂²×C₃₁	semidirect
447. #466	C₂²×C₃₁	semidirect
448. #466	C₂²×C₃₁	semidirect
449. #465	C₂²×C₃₁	semidirect
450. #465	C₂²×C₃₁	semidirect
451. #465	C₂²×C₃₁	semidirect
452. #463	C₂²×C₃₁	semidirect
453. #460	C₂²×C₃₁	semidirect
454. #459	C₂²×C₃₁	semidirect
455. #450	C₂²×C₃₁	semidirect
456. #449	C₂²×C₃₁	semidirect
457. #449	C₂²×C₃₁	semidirect
458. #447	C₂²×C₃₁	semidirect
459. C₄×Q₁₆	C₂²×C₃₁	semidirect
460. C₄×SD₁₆	C₂²×C₃₁	semidirect
461. C₄×D₈	C₂²×C₃₁	semidirect
462. C₄×D₈	C₂²×C₃₁	semidirect
463. C₄×D₈	C₂²×C₃₁	semidirect
466. C₈×D₄	C₂²×C₃₁	semidirect
467. C₈×D₄	C₂²×C₃₁	semidirect
468. C₈×D₄	C₂²×C₃₁	semidirect
469. C₈×D₄	C₂²×C₃₁	semidirect
470. #427	C₂²×C₃₁	semidirect
471. C₂×#107	C₂²×C₃₁	semidirect
472. C₂×C₄⋊C₈	C₂²×C₃₁	semidirect
473. #416	C₂²×C₃₁	semidirect
474. C₂×#102	C₂²×C₃₁	semidirect
475. C₂×C₂²⋊C₈	C₂²×C₃₁	semidirect
476. C₂×C₄×C₈	C₂²×C₃₁	semidirect
595. C₃₁	#62251	direct (N × H)
720. D₄	C₃₁×#135	semidirect

Maximal subgroups

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

subgroup	index
C₃₁×#3519	2
C₃₁×#3341	2
C₃₁×#3339	2
C₃₁×#3338	2
C₃₁×#3305	2
C₃₁×#3297	2
C₃₁×#3295	2
C₃₁×#3287	2
C₃₁×#3280	2
D₄×D₈×C₃₁	2
C₃₁×#3247	2
C₃₁×#3188	2
C₃₁×#3169	2
C₃₁×#3168	2
C₃₁×#3050	2
C₂×C₃₁×#466	2
C₂×C₈×D₄×C₃₁	2
#62251	31

Subgroups — C31×#62251 #21519010

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#62251 #21519010