Subgroups — C₃₁×#61210 #21517969

Order 7936.

2014 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3507	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3499	C₂	1	1	yes	maximal, characteristic
3	C₃₁×#3331	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3328	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3315	C₂	1	4	yes	maximal, complemented
6	C₃₁×#3312	C₂	1	4	yes	maximal, complemented
7	C₃₁×#3302	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3299	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3139	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#3097	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3076	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3059	C₂	1	2	yes	maximal, complemented
13	C₂×C₃₁×#462	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3011	C₂	1	2	yes	maximal, complemented
15	C₄×C₃₁×#137	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#2935	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#2898	C₂	1	2	yes	maximal, complemented
18	C₂×C₃₁×2₋¹⁺⁴	C₂²	1	2	yes	—
19	C₂×C₃₁×#137	C₂²	1	1	yes	characteristic
20	C₂²×Q₁₆×C₃₁	C₂²	1	2	yes	—
21	C₂×C₃₁×#131	C₂²	1	2	yes	—
22	C₃₁×#559	—	2	1	no	—
23	C₃₁×#557	—	2	1	no	—
24	C₃₁×#556	—	2	2	no	—
25	C₃₁×#556	C₂²	1	2	yes	—
26	C₃₁×#554	C₂²	1	2	yes	—
27	C₃₁×#552	C₂²	1	4	yes	—
28	D₄×Q₈×C₃₁	C₂²	1	2	yes	—
29	D₄×Q₈×C₃₁	C₂²	1	2	yes	—
30	C₃₁×#547	—	2	2	no	—
31	C₃₁×#547	—	2	2	no	—
32	C₃₁×#547	C₂²	1	2	yes	—
33	C₃₁×#547	C₂²	1	2	yes	—
34	C₃₁×#539	—	2	2	no	—
35	C₃₁×#536	—	2	2	no	—
36	C₃₁×#536	C₂²	1	2	yes	—
37	C₃₁×#536	C₂²	1	2	yes	—
38	C₃₁×#533	C₂²	1	1	yes	characteristic
39	C₃₁×#532	—	2	1	no	—
40	C₃₁×#532	C₂²	1	1	yes	characteristic
41	C₂×C₃₁×C₄⋊Q₈	—	2	1	no	—
42	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
43	C₃₁×#529	—	2	2	no	—
44	C₃₁×#520	C₂²	1	2	yes	—
45	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
46	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
47	C₃₁×#491	C₂²	1	4	yes	—
48	C₃₁×#487	C₂²	1	2	yes	—
49	C₃₁×#487	C₂²	1	2	yes	—
50	C₃₁×#485	C₂²	1	4	yes	—
51	C₃₁×#485	C₂²	1	4	yes	—
52	C₃₁×#484	C₂²	1	4	yes	—
53	C₃₁×#483	C₂²	1	4	yes	—
54	C₃₁×#479	C₂²	1	2	yes	—
55	C₃₁×#478	C₂²	1	2	yes	—
56	C₃₁×#477	C₂²	1	1	yes	characteristic
57	C₃₁×#476	C₂²	1	1	yes	characteristic
58	C₃₁×#475	C₂²	1	1	yes	characteristic
59	C₃₁×#474	C₂²	1	1	yes	characteristic
60	C₃₁×#470	C₂²	1	4	yes	—
61	C₃₁×#470	C₂²	1	4	yes	—
62	C₃₁×#467	C₂²	1	4	yes	—
63	C₃₁×#467	C₂²	1	4	yes	—
64	C₃₁×#462	C₂²	1	2	yes	—
65	C₃₁×#462	C₂²	1	2	yes	—
66	C₃₁×#462	C₂²	1	4	yes	—
67	C₃₁×#452	C₂²	1	4	yes	—
68	C₃₁×#452	C₂²	1	4	yes	—
69	C₃₁×#451	C₂²	1	4	yes	—
70	C₃₁×#451	C₂²	1	4	yes	—
71	C₃₁×#441	C₂²	1	2	yes	—
72	C₃₁×#440	C₂²	1	2	yes	—
73	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	—
74	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	—
75	C₃₁×#436	C₂²	1	2	yes	—
76	C₃₁×#435	C₂²	1	4	yes	—
77	C₈×D₄×C₃₁	C₂²	1	2	yes	—
78	C₃₁×#428	C₂²	1	1	yes	characteristic
79	C₃₁×#427	C₂²	1	2	yes	—
80	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
81	C₃₁×#419	C₂²	1	2	yes	—
82	C₃₁×#419	C₂²	1	2	yes	—
83	C₃₁×#419	C₂²	1	4	yes	—
84	C₃₁×#419	C₂²	1	1	yes	characteristic
85	C₃₁×#417	C₂²	1	4	yes	—
86	C₃₁×#417	C₂²	1	1	yes	characteristic
87	C₃₁×#416	C₂²	1	2	yes	—
88	C₃₁×#416	C₂²	1	4	yes	—
89	C₂×C₃₁×#103	C₂²	1	2	yes	—
90	C₂×C₃₁×#103	C₂²	1	4	yes	—
91	C₃₁×#408	C₂²	1	2	yes	—
92	C₄×M₁₆×C₃₁	C₂²	1	1	yes	characteristic
93	C₃₁×2₋¹⁺⁴	—	2	8	no	—
94	C₃₁×2₋¹⁺⁴	—	4	4	no	—
95	C₂×#41×C₃₁	—	2	2	no	—
96	C₂×#41×C₃₁	—	2	4	no	—
97	C₂×#41×C₃₁	C₂³	1	4	yes	—
98	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
99	C₂×#41×C₃₁	C₂³	1	2	yes	—
100	C₂²×Q₈×C₃₁	—	2	2	no	—
101	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
102	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
103	C₂²×Q₈×C₃₁	C₂³	1	4	yes	—
104	C₃₁×#137	—	2	4	no	—
105	C₂×Q₁₆×C₃₁	—	4	4	no	—
106	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
107	C₂×Q₁₆×C₃₁	C₂³	1	4	yes	—
108	C₂×Q₁₆×C₃₁	C₂³	1	4	yes	—
109	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
110	C₃₁×#131	—	4	4	no	—
111	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
112	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
113	C₂×M₁₆×C₃₁	C₂³	1	4	yes	—
114	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
115	C₂²×C₈×C₃₁	C₂³	1	4	yes	—
116	C₃₁×C₄⋊Q₈	—	2	2	no	—
117	C₃₁×C₄⋊Q₈	—	2	2	no	—
118	C₃₁×C₄⋊Q₈	—	2	2	no	—
119	C₃₁×C₄⋊Q₈	—	2	2	no	—
120	C₃₁×C₄⋊Q₈	—	2	1	no	—
121	C₃₁×C₄⋊Q₈	—	2	1	no	—
122	C₃₁×C₄⋊Q₈	D₄	1	1	yes	characteristic
123	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
124	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
125	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
126	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
127	C₃₁×#127	D₄	1	1	yes	characteristic
128	C₃₁×#126	—	2	4	no	—
129	C₃₁×#126	—	2	4	no	—
130	C₃₁×#125	—	2	2	no	—
131	C₃₁×#125	—	2	4	no	—
132	C₃₁×#125	C₂³	1	2	yes	—
133	C₃₁×#124	—	2	2	no	—
134	C₃₁×#124	—	2	2	no	—
135	C₃₁×#124	—	2	2	no	—
136	C₃₁×#124	D₄	1	2	yes	—
137	C₃₁×#123	—	2	4	no	—
138	C₃₁×#123	—	2	4	no	—
139	C₃₁×#123	—	2	4	no	—
140	C₃₁×#123	—	2	4	no	—
141	C₃₁×#123	—	2	4	no	—
142	C₃₁×C₂²⋊Q₈	—	2	1	no	—
143	C₃₁×C₂²⋊Q₈	—	2	1	no	—
144	C₃₁×C₂²⋊Q₈	—	2	4	no	—
145	C₃₁×C₂²⋊Q₈	—	2	4	no	—
146	C₃₁×C₂²⋊Q₈	—	2	4	no	—
147	C₃₁×C₂²⋊Q₈	C₂³	1	4	yes	—
148	C₃₁×C₂²⋊Q₈	C₂³	1	4	yes	—
149	C₃₁×C₂²⋊Q₈	C₂³	1	4	yes	—
150	C₃₁×C₂²⋊Q₈	C₂³	1	4	yes	—
151	C₃₁×#121	—	2	2	no	—
152	C₃₁×#121	—	2	2	no	—
153	C₃₁×#121	D₄	1	2	yes	—
154	C₃₁×#121	D₄	1	2	yes	—
155	C₄×Q₈×C₃₁	—	2	2	no	—
156	C₄×Q₈×C₃₁	—	2	2	no	—
157	C₄×Q₈×C₃₁	—	2	1	no	—
158	C₄×Q₈×C₃₁	—	2	1	no	—
159	C₄×Q₈×C₃₁	—	2	1	no	—
160	C₄×Q₈×C₃₁	—	2	1	no	—
161	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
162	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
163	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
164	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
165	C₄×D₄×C₃₁	—	2	4	no	—
166	C₄×D₄×C₃₁	—	2	2	no	—
167	C₄×D₄×C₃₁	—	2	2	no	—
168	C₄×D₄×C₃₁	—	2	2	no	—
169	C₄×D₄×C₃₁	—	2	2	no	—
170	C₄×D₄×C₃₁	—	2	1	no	—
171	C₄×D₄×C₃₁	—	2	1	no	—
172	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
173	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
174	C₄×D₄×C₃₁	C₂³	1	2	yes	—
175	C₄×D₄×C₃₁	C₂³	1	2	yes	—
176	C₃₁×#117	—	2	4	no	—
177	C₃₁×#117	—	2	1	no	—
178	C₃₁×#117	C₂³	1	2	yes	—
179	C₃₁×#117	C₂³	1	4	yes	—
180	C₃₁×#117	C₂³	1	1	yes	characteristic
181	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
182	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
183	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
184	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
185	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
186	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
187	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
188	C₂×C₄²×C₃₁	—	2	1	no	—
189	C₂×C₄²×C₃₁	—	2	1	no	—
190	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
191	C₃₁×#107	C₂³	1	2	yes	—
192	C₃₁×#107	C₂³	1	2	yes	—
193	C₃₁×#107	C₂³	1	2	yes	—
194	C₃₁×#106	C₂³	1	2	yes	—
195	C₃₁×#106	C₂³	1	2	yes	—
196	C₃₁×#106	C₂³	1	2	yes	—
197	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
198	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
199	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
200	C₃₁×#103	C₂³	1	2	yes	—
201	C₃₁×#103	C₂³	1	4	yes	—
202	C₃₁×#103	C₂³	1	2	yes	—
203	C₃₁×#103	C₂³	1	4	yes	—
204	C₃₁×#103	C₂³	1	4	yes	—
205	C₃₁×#103	C₂³	1	2	yes	—
206	C₃₁×#103	C₂³	1	4	yes	—
207	C₃₁×#103	C₂³	1	2	yes	—
208	C₃₁×#103	C₂³	1	2	yes	—
209	C₃₁×#103	C₂³	1	4	yes	—
210	C₃₁×#103	C₂³	1	4	yes	—
211	C₃₁×#102	C₂³	1	2	yes	—
212	C₃₁×#102	C₂³	1	2	yes	—
213	C₃₁×#102	C₂³	1	2	yes	—
214	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
215	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
216	C₃₁×#97	C₂³	1	2	yes	—
217	C₄×C₈×C₃₁	C₂³	1	2	yes	—
218	#41×C₃₁	—	2	4	no	—
219	#41×C₃₁	—	2	4	no	—
220	#41×C₃₁	—	2	2	no	—
221	#41×C₃₁	—	2	8	no	—
222	#41×C₃₁	—	4	4	no	—
223	#41×C₃₁	—	4	8	no	—
224	#41×C₃₁	—	4	16	no	—
225	#41×C₃₁	#41	1	4	yes	—
226	C₂×Q₈×C₃₁	—	2	1	no	—
227	C₂×Q₈×C₃₁	—	2	1	no	—
228	C₂×Q₈×C₃₁	—	2	4	no	—
229	C₂×Q₈×C₃₁	—	2	2	no	—
230	C₂×Q₈×C₃₁	—	2	1	no	—
231	C₂×Q₈×C₃₁	—	2	8	no	—
232	C₂×Q₈×C₃₁	—	2	2	no	—
233	C₂×Q₈×C₃₁	—	2	4	no	—
234	C₂×Q₈×C₃₁	—	2	2	no	—
235	C₂×Q₈×C₃₁	—	2	4	no	—
236	C₂×Q₈×C₃₁	—	4	4	no	—
237	C₂×Q₈×C₃₁	—	4	8	no	—
238	C₂×Q₈×C₃₁	C₂×D₄	1	2	yes	—
239	C₂×Q₈×C₃₁	C₂⁴	1	4	yes	—
240	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
241	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
242	C₂×D₄×C₃₁	—	2	1	no	—
243	C₂×D₄×C₃₁	—	2	4	no	—
244	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
245	C₂×D₄×C₃₁	C₂×D₄	1	4	yes	—
246	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
247	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
248	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
249	C₂²×C₄×C₃₁	—	2	1	no	—
250	C₂²×C₄×C₃₁	—	2	1	no	—
251	C₂²×C₄×C₃₁	—	2	2	no	—
252	C₂²×C₄×C₃₁	—	2	4	no	—
253	C₂²×C₄×C₃₁	—	2	1	no	—
254	C₂²×C₄×C₃₁	—	2	4	no	—
255	C₂²×C₄×C₃₁	—	2	1	no	—
256	C₂²×C₄×C₃₁	—	2	1	no	—
257	C₂²×C₄×C₃₁	—	2	4	no	—
258	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
259	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
260	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
261	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
262	Q₁₆×C₃₁	—	2	4	no	—
263	Q₁₆×C₃₁	—	4	4	no	—
264	Q₁₆×C₃₁	—	4	4	no	—
265	SD₁₆×C₃₁	—	2	4	no	—
266	M₁₆×C₃₁	—	2	2	no	—
267	M₁₆×C₃₁	—	2	2	no	—
268	M₁₆×C₃₁	—	4	4	no	—
269	C₂×C₈×C₃₁	—	2	4	no	—
270	C₂×C₈×C₃₁	—	4	4	no	—
271	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
272	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
273	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
274	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
275	C₄⋊C₄×C₃₁	—	2	2	no	—
276	C₄⋊C₄×C₃₁	—	2	2	no	—
277	C₄⋊C₄×C₃₁	—	2	2	no	—
278	C₄⋊C₄×C₃₁	—	2	2	no	—
279	C₄⋊C₄×C₃₁	—	2	2	no	—
280	C₄⋊C₄×C₃₁	—	2	2	no	—
281	C₄⋊C₄×C₃₁	—	2	4	no	—
282	C₄⋊C₄×C₃₁	—	2	4	no	—
283	C₄⋊C₄×C₃₁	—	2	1	no	—
284	C₄⋊C₄×C₃₁	—	2	4	no	—
285	C₄⋊C₄×C₃₁	—	2	2	no	—
286	C₄⋊C₄×C₃₁	—	2	1	no	—
287	C₄⋊C₄×C₃₁	—	2	1	no	—
288	C₄⋊C₄×C₃₁	—	2	4	no	—
289	C₄⋊C₄×C₃₁	—	2	1	no	—
290	C₄⋊C₄×C₃₁	—	2	2	no	—
291	C₄⋊C₄×C₃₁	—	2	1	no	—
292	C₄⋊C₄×C₃₁	—	2	4	no	—
293	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
294	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
295	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
296	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
297	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
298	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
299	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
300	C₂²⋊C₄×C₃₁	—	2	4	no	—
301	C₂²⋊C₄×C₃₁	—	2	2	no	—
302	C₂²⋊C₄×C₃₁	—	2	1	no	—
303	C₂²⋊C₄×C₃₁	—	2	4	no	—
304	C₂²⋊C₄×C₃₁	—	2	4	no	—
305	C₂²⋊C₄×C₃₁	—	2	4	no	—
306	C₂²⋊C₄×C₃₁	—	2	4	no	—
307	C₂²⋊C₄×C₃₁	—	2	1	no	—
308	C₂²⋊C₄×C₃₁	—	2	1	no	—
309	C₂²⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
310	C₂²⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
311	C₄²×C₃₁	—	2	2	no	—
312	C₄²×C₃₁	—	2	1	no	—
313	C₄²×C₃₁	—	2	1	no	—
314	C₄²×C₃₁	—	2	1	no	—
315	C₄²×C₃₁	—	2	2	no	—
316	C₄²×C₃₁	—	2	4	no	—
317	C₄²×C₃₁	—	2	2	no	—
318	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
319	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
320	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
321	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
322	#61210	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
323	C₂³×C₃₁	—	2	1	no	—
324	C₂³×C₃₁	C₂²×D₄	1	4	yes	—
325	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
326	Q₈×C₃₁	—	2	4	no	—
327	Q₈×C₃₁	—	2	1	no	—
328	Q₈×C₃₁	—	2	2	no	—
329	Q₈×C₃₁	—	2	4	no	—
330	Q₈×C₃₁	—	2	2	no	—
331	Q₈×C₃₁	—	2	4	no	—
332	Q₈×C₃₁	—	4	8	no	—
333	Q₈×C₃₁	—	4	2	no	—
334	Q₈×C₃₁	—	4	4	no	—
335	Q₈×C₃₁	—	4	2	no	—
336	Q₈×C₃₁	—	8	1	no	—
337	Q₈×C₃₁	C₂×#41	1	2	yes	—
338	D₄×C₃₁	—	2	4	no	—
339	D₄×C₃₁	—	2	8	no	—
340	D₄×C₃₁	—	2	4	no	—
341	D₄×C₃₁	—	2	4	no	—
342	D₄×C₃₁	—	2	1	no	—
343	D₄×C₃₁	—	4	2	no	—
344	D₄×C₃₁	—	4	8	no	—
345	D₄×C₃₁	C₂×#41	1	2	yes	—
346	C₂×C₄×C₃₁	—	2	1	no	—
347	C₂×C₄×C₃₁	—	2	4	no	—
348	C₂×C₄×C₃₁	—	2	2	no	—
349	C₂×C₄×C₃₁	—	2	4	no	—
350	C₂×C₄×C₃₁	—	2	4	no	—
351	C₂×C₄×C₃₁	—	2	2	no	—
352	C₂×C₄×C₃₁	—	2	2	no	—
353	C₂×C₄×C₃₁	—	2	1	no	—
354	C₂×C₄×C₃₁	—	2	1	no	—
355	C₂×C₄×C₃₁	—	2	2	no	—
356	C₂×C₄×C₃₁	—	2	2	no	—
357	C₂×C₄×C₃₁	—	2	4	no	—
358	C₂×C₄×C₃₁	—	4	1	no	—
359	C₂×C₄×C₃₁	—	4	8	no	—
360	C₂×C₄×C₃₁	—	4	8	no	—
361	C₂×C₄×C₃₁	—	4	2	no	—
362	C₂×C₄×C₃₁	—	4	2	no	—
363	C₂×C₄×C₃₁	—	4	4	no	—
364	C₂×C₄×C₃₁	—	4	2	no	—
365	C₂×C₄×C₃₁	—	8	1	no	—
366	C₂×C₄×C₃₁	—	8	4	no	—
367	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
368	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
369	C₂×C₄×C₃₁	C₂²×D₄	1	4	yes	—
370	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
371	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
372	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
373	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
374	C₂×C₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
375	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
376	C₈×C₃₁	—	2	2	no	—
377	C₈×C₃₁	—	2	2	no	—
378	C₈×C₃₁	—	2	2	no	—
379	C₈×C₃₁	—	2	2	no	—
380	#3507	C₂×C₃₁	1	1	yes	characteristic, complemented
381	#3499	C₂×C₃₁	1	1	yes	characteristic
382	#3331	C₂×C₃₁	1	2	yes	complemented
383	#3328	C₂×C₃₁	1	2	yes	complemented
384	#3315	C₂×C₃₁	1	4	yes	complemented
385	#3312	C₂×C₃₁	1	4	yes	complemented
386	#3302	C₂×C₃₁	1	2	yes	complemented
387	#3299	C₂×C₃₁	1	2	yes	complemented
388	#3139	C₂×C₃₁	1	1	yes	characteristic, complemented
389	#3097	C₂×C₃₁	1	2	yes	complemented
390	#3076	C₂×C₃₁	1	1	yes	characteristic, complemented
391	#3059	C₂×C₃₁	1	2	yes	complemented
392	C₂×#462	C₂×C₃₁	1	1	yes	characteristic, complemented
393	#3011	C₂×C₃₁	1	2	yes	complemented
394	C₄×#137	C₂×C₃₁	1	1	yes	characteristic, complemented
395	#2935	C₂×C₃₁	1	1	yes	characteristic, complemented
396	#2898	C₂×C₃₁	1	2	yes	complemented
397	C₂²×C₃₁	—	2	1	no	—
398	C₂²×C₃₁	—	2	1	no	—
399	C₂²×C₃₁	—	2	4	no	—
400	C₂²×C₃₁	—	2	2	no	—
401	C₂²×C₃₁	—	2	4	no	—
402	C₂²×C₃₁	—	2	4	no	—
403	C₂²×C₃₁	—	4	1	no	—
404	C₂²×C₃₁	—	4	1	no	—
405	C₂²×C₃₁	#546	1	2	yes	—
406	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
407	C₄×C₃₁	—	2	1	no	—
408	C₄×C₃₁	—	2	1	no	—
409	C₄×C₃₁	—	2	2	no	—
410	C₄×C₃₁	—	2	4	no	—
411	C₄×C₃₁	—	2	1	no	—
412	C₄×C₃₁	—	4	1	no	—
413	C₄×C₃₁	—	4	2	no	—
414	C₄×C₃₁	—	4	2	no	—
415	C₄×C₃₁	—	4	4	no	—
416	C₄×C₃₁	—	4	2	no	—
417	C₄×C₃₁	—	4	1	no	—
418	C₄×C₃₁	—	4	2	no	—
419	C₄×C₃₁	#546	1	2	yes	—
420	C₄×C₃₁	#578	1	2	yes	—
421	C₄×C₃₁	C₂²×#41	1	1	yes	characteristic
422	C₄×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
423	C₂×2₋¹⁺⁴	C₂²×C₃₁	1	2	yes	—
424	C₂×#137	C₂²×C₃₁	1	1	yes	characteristic
425	C₂²×Q₁₆	C₂²×C₃₁	1	2	yes	—
426	C₂×#131	C₂²×C₃₁	1	2	yes	—
427	#559	—	2	1	no	—
428	#557	—	2	1	no	—
429	#556	—	2	2	no	—
430	#556	C₂²×C₃₁	1	2	yes	—
431	#554	C₂²×C₃₁	1	2	yes	—
432	#552	C₂²×C₃₁	1	4	yes	—
433	D₄×Q₈	C₂²×C₃₁	1	2	yes	—
434	D₄×Q₈	C₂²×C₃₁	1	2	yes	—
435	#547	—	2	2	no	—
436	#547	—	2	2	no	—
437	#547	C₂²×C₃₁	1	2	yes	—
438	#547	C₂²×C₃₁	1	2	yes	—
439	#539	—	2	2	no	—
440	#536	—	2	2	no	—
441	#536	C₂²×C₃₁	1	2	yes	—
442	#536	C₂²×C₃₁	1	2	yes	—
443	#533	C₂²×C₃₁	1	1	yes	characteristic
444	#532	—	2	1	no	—
445	#532	C₂²×C₃₁	1	1	yes	characteristic
446	C₂×C₄⋊Q₈	—	2	1	no	—
447	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
448	#529	—	2	2	no	—
449	#520	C₂²×C₃₁	1	2	yes	—
450	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
451	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
452	#491	C₂²×C₃₁	1	4	yes	—
453	#487	C₂²×C₃₁	1	2	yes	—
454	#487	C₂²×C₃₁	1	2	yes	—
455	#485	C₂²×C₃₁	1	4	yes	—
456	#485	C₂²×C₃₁	1	4	yes	—
457	#484	C₂²×C₃₁	1	4	yes	—
458	#483	C₂²×C₃₁	1	4	yes	—
459	#479	C₂²×C₃₁	1	2	yes	—
460	#478	C₂²×C₃₁	1	2	yes	—
461	#477	C₂²×C₃₁	1	1	yes	characteristic
462	#476	C₂²×C₃₁	1	1	yes	characteristic
463	#475	C₂²×C₃₁	1	1	yes	characteristic
464	#474	C₂²×C₃₁	1	1	yes	characteristic
465	#470	C₂²×C₃₁	1	4	yes	—
466	#470	C₂²×C₃₁	1	4	yes	—
467	#467	C₂²×C₃₁	1	4	yes	—
468	#467	C₂²×C₃₁	1	4	yes	—
469	#462	C₂²×C₃₁	1	2	yes	—
470	#462	C₂²×C₃₁	1	2	yes	—
471	#462	C₂²×C₃₁	1	4	yes	—
472	#452	C₂²×C₃₁	1	4	yes	—
473	#452	C₂²×C₃₁	1	4	yes	—
474	#451	C₂²×C₃₁	1	4	yes	—
475	#451	C₂²×C₃₁	1	4	yes	—
476	#441	C₂²×C₃₁	1	2	yes	—
477	#440	C₂²×C₃₁	1	2	yes	—
478	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	—
479	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	—
480	#436	C₂²×C₃₁	1	2	yes	—
481	#435	C₂²×C₃₁	1	4	yes	—
482	C₈×D₄	C₂²×C₃₁	1	2	yes	—
483	#428	C₂²×C₃₁	1	1	yes	characteristic
484	#427	C₂²×C₃₁	1	2	yes	—
485	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
486	#419	C₂²×C₃₁	1	4	yes	—
487	#419	C₂²×C₃₁	1	2	yes	—
488	#419	C₂²×C₃₁	1	2	yes	—
489	#419	C₂²×C₃₁	1	1	yes	characteristic
490	#417	C₂²×C₃₁	1	4	yes	—
491	#417	C₂²×C₃₁	1	1	yes	characteristic
492	#416	C₂²×C₃₁	1	2	yes	—
493	#416	C₂²×C₃₁	1	4	yes	—
494	C₂×#103	C₂²×C₃₁	1	2	yes	—
495	C₂×#103	C₂²×C₃₁	1	4	yes	—
496	#408	C₂²×C₃₁	1	2	yes	—
497	C₄×M₁₆	C₂²×C₃₁	1	1	yes	characteristic
498	C₂×C₃₁	—	2	2	no	—
499	C₂×C₃₁	—	4	4	no	—
500	C₂×C₃₁	—	4	2	no	—
501	C₂×C₃₁	C₂×#546	1	1	yes	characteristic
502	C₂×C₃₁	C₂×#578	1	1	yes	characteristic
503	C₂×C₃₁	#3586	1	1	yes	characteristic
504	2₋¹⁺⁴	—	2	8	no	—
505	2₋¹⁺⁴	—	4	4	no	—
506	C₂×#41	—	2	2	no	—
507	C₂×#41	—	2	4	no	—
508	C₂×#41	C₂³×C₃₁	1	4	yes	—
509	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
510	C₂×#41	C₂³×C₃₁	1	2	yes	—
511	C₂²×Q₈	—	2	2	no	—
512	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
513	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
514	C₂²×Q₈	C₂³×C₃₁	1	4	yes	—
515	#137	—	2	4	no	—
516	C₂×Q₁₆	—	4	4	no	—
517	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
518	C₂×Q₁₆	C₂³×C₃₁	1	4	yes	—
519	C₂×Q₁₆	C₂³×C₃₁	1	4	yes	—
520	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
521	#131	—	4	4	no	—
522	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
523	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
524	C₂×M₁₆	C₂³×C₃₁	1	4	yes	—
525	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
526	C₂²×C₈	C₂³×C₃₁	1	4	yes	—
527	C₄⋊Q₈	—	2	2	no	—
528	C₄⋊Q₈	—	2	2	no	—
529	C₄⋊Q₈	—	2	2	no	—
530	C₄⋊Q₈	—	2	2	no	—
531	C₄⋊Q₈	—	2	1	no	—
532	C₄⋊Q₈	—	2	1	no	—
533	C₄⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
534	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
535	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
536	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
537	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
538	#127	D₄×C₃₁	1	1	yes	characteristic
539	#126	—	2	4	no	—
540	#126	—	2	4	no	—
541	#125	—	2	2	no	—
542	#125	—	2	4	no	—
543	#125	C₂³×C₃₁	1	2	yes	—
544	#124	—	2	2	no	—
545	#124	—	2	2	no	—
546	#124	—	2	2	no	—
547	#124	D₄×C₃₁	1	2	yes	—
548	#123	—	2	4	no	—
549	#123	—	2	4	no	—
550	#123	—	2	4	no	—
551	#123	—	2	4	no	—
552	#123	—	2	4	no	—
553	C₂²⋊Q₈	—	2	1	no	—
554	C₂²⋊Q₈	—	2	1	no	—
555	C₂²⋊Q₈	—	2	4	no	—
556	C₂²⋊Q₈	—	2	4	no	—
557	C₂²⋊Q₈	—	2	4	no	—
558	C₂²⋊Q₈	C₂³×C₃₁	1	4	yes	—
559	C₂²⋊Q₈	C₂³×C₃₁	1	4	yes	—
560	C₂²⋊Q₈	C₂³×C₃₁	1	4	yes	—
561	C₂²⋊Q₈	C₂³×C₃₁	1	4	yes	—
562	#121	—	2	2	no	—
563	#121	—	2	2	no	—
564	#121	D₄×C₃₁	1	2	yes	—
565	#121	D₄×C₃₁	1	2	yes	—
566	C₄×Q₈	—	2	2	no	—
567	C₄×Q₈	—	2	2	no	—
568	C₄×Q₈	—	2	1	no	—
569	C₄×Q₈	—	2	1	no	—
570	C₄×Q₈	—	2	1	no	—
571	C₄×Q₈	—	2	1	no	—
572	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
573	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
574	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
575	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
576	C₄×D₄	—	2	4	no	—
577	C₄×D₄	—	2	2	no	—
578	C₄×D₄	—	2	2	no	—
579	C₄×D₄	—	2	2	no	—
580	C₄×D₄	—	2	2	no	—
581	C₄×D₄	—	2	1	no	—
582	C₄×D₄	—	2	1	no	—
583	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
584	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
585	C₄×D₄	C₂³×C₃₁	1	2	yes	—
586	C₄×D₄	C₂³×C₃₁	1	2	yes	—
587	#117	—	2	4	no	—
588	#117	—	2	1	no	—
589	#117	C₂³×C₃₁	1	1	yes	characteristic
590	#117	C₂³×C₃₁	1	2	yes	—
591	#117	C₂³×C₃₁	1	4	yes	—
592	C₂×C₄⋊C₄	—	2	1	no	—
593	C₂×C₄⋊C₄	—	2	1	no	—
594	C₂×C₄⋊C₄	—	2	1	no	—
595	C₂×C₄⋊C₄	—	2	2	no	—
596	C₂×C₄⋊C₄	—	2	2	no	—
597	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
598	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
599	C₂×C₄²	—	2	1	no	—
600	C₂×C₄²	—	2	1	no	—
601	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
602	#107	C₂³×C₃₁	1	2	yes	—
603	#107	C₂³×C₃₁	1	2	yes	—
604	#107	C₂³×C₃₁	1	2	yes	—
605	#106	C₂³×C₃₁	1	2	yes	—
606	#106	C₂³×C₃₁	1	2	yes	—
607	#106	C₂³×C₃₁	1	2	yes	—
608	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
609	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
610	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
611	#103	C₂³×C₃₁	1	2	yes	—
612	#103	C₂³×C₃₁	1	4	yes	—
613	#103	C₂³×C₃₁	1	2	yes	—
614	#103	C₂³×C₃₁	1	4	yes	—
615	#103	C₂³×C₃₁	1	4	yes	—
616	#103	C₂³×C₃₁	1	2	yes	—
617	#103	C₂³×C₃₁	1	4	yes	—
618	#103	C₂³×C₃₁	1	2	yes	—
619	#103	C₂³×C₃₁	1	2	yes	—
620	#103	C₂³×C₃₁	1	4	yes	—
621	#103	C₂³×C₃₁	1	4	yes	—
622	#102	C₂³×C₃₁	1	2	yes	—
623	#102	C₂³×C₃₁	1	2	yes	—
624	#102	C₂³×C₃₁	1	2	yes	—
625	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
626	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
627	#97	C₂³×C₃₁	1	2	yes	—
628	C₄×C₈	C₂³×C₃₁	1	2	yes	—
629	C₃₁	#61210	1	1	yes	characteristic, direct product factor, Sylow
630	#41	—	2	4	no	—
631	#41	—	2	4	no	—
632	#41	—	2	2	no	—
633	#41	—	2	8	no	—
634	#41	—	4	4	no	—
635	#41	—	4	8	no	—
636	#41	—	4	16	no	—
637	#41	#41×C₃₁	1	4	yes	—
638	C₂×Q₈	—	2	1	no	—
639	C₂×Q₈	—	2	1	no	—
640	C₂×Q₈	—	2	4	no	—
641	C₂×Q₈	—	2	2	no	—
642	C₂×Q₈	—	2	1	no	—
643	C₂×Q₈	—	2	8	no	—
644	C₂×Q₈	—	2	2	no	—
645	C₂×Q₈	—	2	4	no	—
646	C₂×Q₈	—	2	2	no	—
647	C₂×Q₈	—	2	4	no	—
648	C₂×Q₈	—	4	4	no	—
649	C₂×Q₈	—	4	8	no	—
650	C₂×Q₈	C₂×D₄×C₃₁	1	2	yes	—
651	C₂×Q₈	C₂⁴×C₃₁	1	4	yes	—
652	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
653	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
654	C₂×D₄	—	2	1	no	—
655	C₂×D₄	—	2	4	no	—
656	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
657	C₂×D₄	C₂×D₄×C₃₁	1	4	yes	—
658	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
659	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
660	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
661	C₂²×C₄	—	2	1	no	—
662	C₂²×C₄	—	2	1	no	—
663	C₂²×C₄	—	2	2	no	—
664	C₂²×C₄	—	2	4	no	—
665	C₂²×C₄	—	2	1	no	—
666	C₂²×C₄	—	2	4	no	—
667	C₂²×C₄	—	2	1	no	—
668	C₂²×C₄	—	2	1	no	—
669	C₂²×C₄	—	2	4	no	—
670	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
671	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
672	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
673	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
674	Q₁₆	—	2	4	no	—
675	Q₁₆	—	4	4	no	—
676	Q₁₆	—	4	4	no	—
677	SD₁₆	—	2	4	no	—
678	M₁₆	—	2	2	no	—
679	M₁₆	—	2	2	no	—
680	M₁₆	—	4	4	no	—
681	C₂×C₈	—	2	4	no	—
682	C₂×C₈	—	4	4	no	—
683	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
684	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
685	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
686	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
687	C₄⋊C₄	—	2	2	no	—
688	C₄⋊C₄	—	2	2	no	—
689	C₄⋊C₄	—	2	2	no	—
690	C₄⋊C₄	—	2	2	no	—
691	C₄⋊C₄	—	2	2	no	—
692	C₄⋊C₄	—	2	2	no	—
693	C₄⋊C₄	—	2	4	no	—
694	C₄⋊C₄	—	2	4	no	—
695	C₄⋊C₄	—	2	1	no	—
696	C₄⋊C₄	—	2	4	no	—
697	C₄⋊C₄	—	2	2	no	—
698	C₄⋊C₄	—	2	1	no	—
699	C₄⋊C₄	—	2	1	no	—
700	C₄⋊C₄	—	2	4	no	—
701	C₄⋊C₄	—	2	1	no	—
702	C₄⋊C₄	—	2	2	no	—
703	C₄⋊C₄	—	2	1	no	—
704	C₄⋊C₄	—	2	4	no	—
705	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
706	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
707	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
708	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
709	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
710	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
711	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
712	C₂²⋊C₄	—	2	4	no	—
713	C₂²⋊C₄	—	2	2	no	—
714	C₂²⋊C₄	—	2	1	no	—
715	C₂²⋊C₄	—	2	4	no	—
716	C₂²⋊C₄	—	2	4	no	—
717	C₂²⋊C₄	—	2	4	no	—
718	C₂²⋊C₄	—	2	4	no	—
719	C₂²⋊C₄	—	2	1	no	—
720	C₂²⋊C₄	—	2	1	no	—
721	C₂²⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
722	C₂²⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
723	C₄²	—	2	2	no	—
724	C₄²	—	2	1	no	—
725	C₄²	—	2	1	no	—
726	C₄²	—	2	1	no	—
727	C₄²	—	2	2	no	—
728	C₄²	—	2	4	no	—
729	C₄²	—	2	2	no	—
730	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
731	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
732	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
733	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
734	C₂³	—	2	1	no	—
735	C₂³	C₂²×D₄×C₃₁	1	4	yes	—
736	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
737	Q₈	—	2	4	no	—
738	Q₈	—	2	1	no	—
739	Q₈	—	2	2	no	—
740	Q₈	—	2	4	no	—
741	Q₈	—	2	2	no	—
742	Q₈	—	2	4	no	—
743	Q₈	—	4	8	no	—
744	Q₈	—	4	2	no	—
745	Q₈	—	4	4	no	—
746	Q₈	—	4	2	no	—
747	Q₈	—	8	1	no	—
748	Q₈	C₂×#41×C₃₁	1	2	yes	—
749	D₄	—	2	4	no	—
750	D₄	—	2	8	no	—
751	D₄	—	2	4	no	—
752	D₄	—	2	4	no	—
753	D₄	—	2	1	no	—
754	D₄	—	4	2	no	—
755	D₄	—	4	8	no	—
756	D₄	C₂×#41×C₃₁	1	2	yes	—
757	C₂×C₄	—	2	1	no	—
758	C₂×C₄	—	2	4	no	—
759	C₂×C₄	—	2	2	no	—
760	C₂×C₄	—	2	4	no	—
761	C₂×C₄	—	2	4	no	—
762	C₂×C₄	—	2	2	no	—
763	C₂×C₄	—	2	2	no	—
764	C₂×C₄	—	2	1	no	—
765	C₂×C₄	—	2	1	no	—
766	C₂×C₄	—	2	2	no	—
767	C₂×C₄	—	2	2	no	—
768	C₂×C₄	—	2	4	no	—
769	C₂×C₄	—	4	1	no	—
770	C₂×C₄	—	4	8	no	—
771	C₂×C₄	—	4	8	no	—
772	C₂×C₄	—	4	2	no	—
773	C₂×C₄	—	4	2	no	—
774	C₂×C₄	—	4	4	no	—
775	C₂×C₄	—	4	2	no	—
776	C₂×C₄	—	8	1	no	—
777	C₂×C₄	—	8	4	no	—
778	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
779	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
780	C₂×C₄	C₂²×D₄×C₃₁	1	4	yes	—
781	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
782	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
783	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
784	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
785	C₂×C₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
786	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
787	C₈	—	2	2	no	—
788	C₈	—	2	2	no	—
789	C₈	—	2	2	no	—
790	C₈	—	2	2	no	—
791	C₂²	—	2	1	no	—
792	C₂²	—	2	1	no	—
793	C₂²	—	2	2	no	—
794	C₂²	—	2	4	no	—
795	C₂²	—	2	4	no	—
796	C₂²	—	2	4	no	—
797	C₂²	—	4	1	no	—
798	C₂²	—	4	1	no	—
799	C₂²	C₃₁×#546	1	2	yes	—
800	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
801	C₄	—	2	2	no	—
802	C₄	—	2	4	no	—
803	C₄	—	2	1	no	—
804	C₄	—	2	1	no	—
805	C₄	—	2	1	no	—
806	C₄	—	4	4	no	—
807	C₄	—	4	2	no	—
808	C₄	—	4	1	no	—
809	C₄	—	4	2	no	—
810	C₄	—	4	1	no	—
811	C₄	—	4	2	no	—
812	C₄	—	4	2	no	—
813	C₄	C₃₁×#546	1	2	yes	—
814	C₄	C₃₁×#578	1	2	yes	—
815	C₄	C₂²×#41×C₃₁	1	1	yes	characteristic
816	C₄	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
817	C₂	—	2	2	no	—
818	C₂	—	4	4	no	—
819	C₂	—	4	2	no	—
820	C₂	C₂×C₃₁×#546	1	1	yes	characteristic
821	C₂	C₂×C₃₁×#578	1	1	yes	characteristic
822	C₂	C₃₁×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
prime radical	C₃₁×#3499	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₃₁×#532 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3507	C₂	semidirect
3. C₃₁×#3331	C₂	semidirect
4. C₃₁×#3328	C₂	semidirect
5. C₃₁×#3315	C₂	semidirect
6. C₃₁×#3312	C₂	semidirect
7. C₃₁×#3302	C₂	semidirect
8. C₃₁×#3299	C₂	semidirect
9. C₃₁×#3139	C₂	semidirect
10. C₃₁×#3097	C₂	semidirect
11. C₃₁×#3076	C₂	semidirect
12. C₃₁×#3059	C₂	semidirect
13. C₂×C₃₁×#462	C₂	semidirect
14. C₃₁×#3011	C₂	semidirect
15. C₄×C₃₁×#137	C₂	semidirect
16. C₃₁×#2935	C₂	semidirect
17. C₃₁×#2898	C₂	semidirect
322. #61210	C₃₁	direct (N × H)
380. #3507	C₂×C₃₁	semidirect
382. #3331	C₂×C₃₁	semidirect
383. #3328	C₂×C₃₁	semidirect
384. #3315	C₂×C₃₁	semidirect
385. #3312	C₂×C₃₁	semidirect
386. #3302	C₂×C₃₁	semidirect
387. #3299	C₂×C₃₁	semidirect
388. #3139	C₂×C₃₁	semidirect
389. #3097	C₂×C₃₁	semidirect
390. #3076	C₂×C₃₁	semidirect
391. #3059	C₂×C₃₁	semidirect
392. C₂×#462	C₂×C₃₁	semidirect
393. #3011	C₂×C₃₁	semidirect
394. C₄×#137	C₂×C₃₁	semidirect
395. #2935	C₂×C₃₁	semidirect
396. #2898	C₂×C₃₁	semidirect
629. C₃₁	#61210	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×#3507	2
C₃₁×#3499	2
C₃₁×#3331	2
C₃₁×#3328	2
C₃₁×#3315	2
C₃₁×#3312	2
C₃₁×#3302	2
C₃₁×#3299	2
C₃₁×#3139	2
C₃₁×#3097	2
C₃₁×#3076	2
C₃₁×#3059	2
C₂×C₃₁×#462	2
C₃₁×#3011	2
C₄×C₃₁×#137	2
C₃₁×#2935	2
C₃₁×#2898	2
#61210	31

Subgroups — C31×#61210 #21517969

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61210 #21517969