Subgroups — C₃₁×#35005 #21491764

Order 7936.

2642 conjugacy classes of subgroups.

The subgroup lattice has 786 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#538	C₂	1	2	yes	maximal, complemented
2	C₃₁×#2857	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#2856	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#2847	C₂	1	2	yes	maximal, complemented
5	C₃₁×#2639	C₂	1	2	yes	maximal, complemented
6	C₃₁×#2617	C₂	1	2	yes	maximal, complemented
7	C₃₁×#2559	C₂	1	4	yes	maximal, complemented
8	C₃₁×#2557	C₂	1	4	yes	maximal, complemented
9	C₃₁×#2496	C₂	1	2	yes	maximal, complemented
10	C₃₁×#2491	C₂	1	2	yes	maximal, complemented
11	C₃₁×#2428	C₂	1	2	yes	maximal, complemented
12	C₃₁×#2422	C₂	1	2	yes	maximal, complemented
13	C₃₁×#2325	C₂	1	2	yes	maximal, complemented
14	C₄×C₃₁×#121	C₂	1	2	yes	maximal, complemented
15	C₂×C₄×C₂²⋊C₄×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂⁴×C₄×C₃₁	C₂²	1	1	yes	characteristic
17	C₃₁×#538	—	2	16	no	—
18	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
19	C₂×C₃₁×#127	C₂²	1	1	yes	characteristic, complemented
20	C₂×C₃₁×#126	C₂²	1	4	yes	—
21	C₂×C₃₁×#124	C₂²	1	4	yes	—
22	C₂×C₃₁×#123	C₂²	1	4	yes	—
23	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	—
24	C₂×C₃₁×#121	C₂²	1	2	yes	—
25	C₂×C₃₁×#121	C₂²	1	2	yes	—
26	C₂×C₃₁×#121	C₂²	1	2	yes	—
27	C₂×C₃₁×#121	C₂²	1	4	yes	—
28	C₂×C₃₁×#121	C₂²	1	2	yes	—
29	C₂×C₃₁×#121	C₂²	1	2	yes	—
30	C₂×C₃₁×#120	C₂²	1	4	yes	—
31	C₂×C₄×D₄×C₃₁	C₂²	1	4	yes	—
32	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	complemented
33	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
34	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
35	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
36	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
37	C₃₁×#400	C₂²	1	4	yes	complemented
38	C₃₁×#397	C₂²	1	4	yes	—
39	C₃₁×#397	C₂²	1	4	yes	complemented
40	C₃₁×#394	C₂²	1	4	yes	—
41	C₃₁×#394	C₂²	1	4	yes	—
42	C₃₁×#394	C₂²	1	4	yes	complemented
43	C₃₁×#393	C₂²	1	4	yes	complemented
44	C₃₁×#392	C₂²	1	4	yes	—
45	C₃₁×#391	C₂²	1	2	yes	complemented
46	C₃₁×#390	C₂²	1	2	yes	complemented
47	C₃₁×#390	C₂²	1	2	yes	complemented
48	C₃₁×#390	C₂²	1	2	yes	complemented
49	C₃₁×#390	C₂²	1	2	yes	complemented
50	C₃₁×#389	C₂²	1	2	yes	complemented
51	C₃₁×#389	C₂²	1	2	yes	complemented
52	C₃₁×#389	C₂²	1	2	yes	complemented
53	C₃₁×#388	C₂²	1	4	yes	complemented
54	C₃₁×#388	C₂²	1	4	yes	complemented
55	C₃₁×#387	C₂²	1	4	yes	complemented
56	C₃₁×#386	C₂²	1	4	yes	—
57	C₃₁×#386	C₂²	1	4	yes	—
58	C₃₁×#386	C₂²	1	4	yes	—
59	C₃₁×#386	C₂²	1	4	yes	—
60	C₃₁×#386	C₂²	1	4	yes	complemented
61	C₃₁×#385	C₂²	1	4	yes	complemented
62	C₃₁×#384	C₂²	1	1	yes	characteristic, complemented
63	C₃₁×#384	C₂²	1	1	yes	characteristic, complemented
64	C₃₁×#380	C₂²	1	2	yes	—
65	C₃₁×#380	C₂²	1	2	yes	—
66	C₃₁×#380	C₂²	1	2	yes	—
67	C₃₁×#380	C₂²	1	2	yes	—
68	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	complemented
69	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
70	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
71	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
72	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
73	C₄×C₂²⋊C₄×C₃₁	C₂²	1	4	yes	complemented
74	C₂×C₃₁×#95	C₂²	1	1	yes	characteristic
75	C₂×C₃₁×#95	C₂²	1	1	yes	characteristic
76	C₂⁵×C₃₁	C₂³	1	1	yes	characteristic
77	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
78	C₂²×D₄×C₃₁	C₂³	1	4	yes	—
79	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
80	C₂²×D₄×C₃₁	C₂³	1	4	yes	—
81	C₂²×D₄×C₃₁	C₂³	1	4	yes	—
82	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
83	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
84	C₂³×C₄×C₃₁	—	2	4	no	—
85	C₂³×C₄×C₃₁	—	4	2	no	—
86	C₂³×C₄×C₃₁	—	4	2	no	—
87	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
88	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
89	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
90	C₂³×C₄×C₃₁	C₂³	1	4	yes	—
91	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
92	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
93	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
94	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
95	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
96	C₃₁×C₄⋊Q₈	—	4	2	no	—
97	C₃₁×#127	—	4	2	no	—
98	C₃₁×#126	—	2	16	no	—
99	C₃₁×#124	—	2	16	no	—
100	C₃₁×#123	—	2	16	no	—
101	C₃₁×C₂²⋊Q₈	—	2	8	no	—
102	C₃₁×#121	—	2	8	no	—
103	C₃₁×#121	—	2	8	no	—
104	C₃₁×#121	—	2	8	no	—
105	C₃₁×#121	—	2	16	no	—
106	C₃₁×#121	—	4	4	no	—
107	C₃₁×#121	—	4	4	no	—
108	C₃₁×#120	—	2	16	no	—
109	C₄×D₄×C₃₁	—	2	16	no	—
110	C₄×D₄×C₃₁	—	4	4	no	—
111	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
112	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
113	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
114	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
115	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
116	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
117	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
118	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
119	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
120	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
121	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
122	C₂×C₂²⋊C₄×C₃₁	D₄	1	8	yes	complemented
123	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
124	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
125	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
126	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
127	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
128	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
129	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
130	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
131	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
132	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
133	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
134	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
135	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
136	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
137	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
138	C₂×C₄²×C₃₁	—	4	2	no	—
139	C₂×C₄²×C₃₁	—	4	2	no	—
140	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
141	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
142	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
143	C₂×C₄²×C₃₁	C₂³	1	4	yes	—
144	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
145	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
146	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
147	C₃₁×#95	C₂³	1	4	yes	—
148	C₃₁×#95	C₂³	1	4	yes	—
149	C₃₁×#95	C₂³	1	4	yes	—
150	C₃₁×#95	C₂³	1	2	yes	—
151	C₃₁×#95	C₂³	1	4	yes	—
152	C₃₁×#95	C₂³	1	2	yes	—
153	C₃₁×#95	C₂³	1	4	yes	—
154	C₃₁×#95	C₂³	1	2	yes	—
155	C₃₁×#95	C₂³	1	2	yes	—
156	C₃₁×#95	C₂³	1	4	yes	—
157	C₂⁴×C₃₁	—	2	2	no	—
158	C₂⁴×C₃₁	—	2	2	no	—
159	C₂⁴×C₃₁	—	4	1	no	—
160	C₂⁴×C₃₁	—	4	1	no	—
161	C₂⁴×C₃₁	—	4	1	no	—
162	C₂⁴×C₃₁	—	4	1	no	—
163	C₂⁴×C₃₁	C₂×D₄	1	4	yes	—
164	C₂⁴×C₃₁	C₂⁴	1	4	yes	—
165	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
166	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
167	C₂×Q₈×C₃₁	—	2	4	no	—
168	C₂×Q₈×C₃₁	—	4	2	no	—
169	C₂×Q₈×C₃₁	—	4	2	no	—
170	C₂×D₄×C₃₁	—	2	8	no	—
171	C₂×D₄×C₃₁	—	2	8	no	—
172	C₂×D₄×C₃₁	—	2	8	no	—
173	C₂×D₄×C₃₁	—	2	8	no	—
174	C₂×D₄×C₃₁	—	2	8	no	—
175	C₂×D₄×C₃₁	—	2	4	no	—
176	C₂×D₄×C₃₁	—	2	4	no	—
177	C₂×D₄×C₃₁	—	2	4	no	—
178	C₂×D₄×C₃₁	—	2	4	no	—
179	C₂×D₄×C₃₁	—	2	4	no	—
180	C₂×D₄×C₃₁	—	4	4	no	—
181	C₂×D₄×C₃₁	—	4	4	no	—
182	C₂×D₄×C₃₁	—	4	2	no	—
183	C₂×D₄×C₃₁	—	4	2	no	—
184	C₂×D₄×C₃₁	—	4	2	no	—
185	C₂×D₄×C₃₁	—	4	2	no	—
186	C₂×D₄×C₃₁	—	4	4	no	—
187	C₂×D₄×C₃₁	—	4	4	no	—
188	C₂²×C₄×C₃₁	—	2	2	no	—
189	C₂²×C₄×C₃₁	—	2	2	no	—
190	C₂²×C₄×C₃₁	—	2	2	no	—
191	C₂²×C₄×C₃₁	—	2	2	no	—
192	C₂²×C₄×C₃₁	—	2	4	no	—
193	C₂²×C₄×C₃₁	—	2	4	no	—
194	C₂²×C₄×C₃₁	—	2	4	no	—
195	C₂²×C₄×C₃₁	—	2	4	no	—
196	C₂²×C₄×C₃₁	—	2	8	no	—
197	C₂²×C₄×C₃₁	—	4	1	no	—
198	C₂²×C₄×C₃₁	—	4	1	no	—
199	C₂²×C₄×C₃₁	—	4	1	no	—
200	C₂²×C₄×C₃₁	—	4	1	no	—
201	C₂²×C₄×C₃₁	—	4	2	no	—
202	C₂²×C₄×C₃₁	—	4	2	no	—
203	C₂²×C₄×C₃₁	—	4	1	no	—
204	C₂²×C₄×C₃₁	—	4	1	no	—
205	C₂²×C₄×C₃₁	—	4	1	no	—
206	C₂²×C₄×C₃₁	—	4	1	no	—
207	C₂²×C₄×C₃₁	—	4	1	no	—
208	C₂²×C₄×C₃₁	—	4	1	no	—
209	C₂²×C₄×C₃₁	—	4	4	no	—
210	C₂²×C₄×C₃₁	—	4	4	no	—
211	C₂²×C₄×C₃₁	—	4	16	no	—
212	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
213	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
214	C₂²×C₄×C₃₁	#41	1	4	yes	—
215	C₂²×C₄×C₃₁	#41	1	4	yes	—
216	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
217	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
218	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
219	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
220	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
221	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
222	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
223	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
224	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
225	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
226	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
227	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
228	C₄⋊C₄×C₃₁	—	2	8	no	—
229	C₄⋊C₄×C₃₁	—	2	8	no	—
230	C₄⋊C₄×C₃₁	—	2	4	no	—
231	C₄⋊C₄×C₃₁	—	2	4	no	—
232	C₄⋊C₄×C₃₁	—	2	4	no	—
233	C₄⋊C₄×C₃₁	—	2	4	no	—
234	C₄⋊C₄×C₃₁	—	2	4	no	—
235	C₄⋊C₄×C₃₁	—	2	4	no	—
236	C₄⋊C₄×C₃₁	—	4	2	no	—
237	C₄⋊C₄×C₃₁	—	4	2	no	—
238	C₂²⋊C₄×C₃₁	—	2	8	no	—
239	C₂²⋊C₄×C₃₁	—	2	8	no	—
240	C₂²⋊C₄×C₃₁	—	2	8	no	—
241	C₂²⋊C₄×C₃₁	—	2	8	no	—
242	C₂²⋊C₄×C₃₁	—	2	8	no	—
243	C₂²⋊C₄×C₃₁	—	2	4	no	—
244	C₂²⋊C₄×C₃₁	—	2	4	no	—
245	C₂²⋊C₄×C₃₁	—	2	8	no	—
246	C₂²⋊C₄×C₃₁	—	2	8	no	—
247	C₂²⋊C₄×C₃₁	—	4	4	no	—
248	C₂²⋊C₄×C₃₁	—	4	4	no	—
249	C₂²⋊C₄×C₃₁	—	4	4	no	—
250	C₂²⋊C₄×C₃₁	—	4	4	no	—
251	C₂²⋊C₄×C₃₁	C₂×D₄	1	8	yes	—
252	C₂²⋊C₄×C₃₁	C₂×D₄	1	8	yes	—
253	C₄²×C₃₁	—	2	8	no	—
254	C₄²×C₃₁	—	2	4	no	—
255	C₄²×C₃₁	—	2	2	no	—
256	C₄²×C₃₁	—	2	2	no	—
257	C₄²×C₃₁	—	4	1	no	—
258	C₄²×C₃₁	—	4	2	no	—
259	C₄²×C₃₁	—	4	1	no	—
260	#35005	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
261	C₂³×C₃₁	—	2	1	no	—
262	C₂³×C₃₁	—	2	1	no	—
263	C₂³×C₃₁	—	2	1	no	—
264	C₂³×C₃₁	—	2	1	no	—
265	C₂³×C₃₁	—	2	8	no	—
266	C₂³×C₃₁	—	2	2	no	—
267	C₂³×C₃₁	—	2	2	no	—
268	C₂³×C₃₁	—	2	2	no	—
269	C₂³×C₃₁	—	2	2	no	—
270	C₂³×C₃₁	—	2	2	no	—
271	C₂³×C₃₁	—	2	2	no	—
272	C₂³×C₃₁	—	2	4	no	—
273	C₂³×C₃₁	—	2	4	no	—
274	C₂³×C₃₁	—	2	4	no	—
275	C₂³×C₃₁	—	2	4	no	—
276	C₂³×C₃₁	—	2	4	no	—
277	C₂³×C₃₁	—	2	4	no	—
278	C₂³×C₃₁	—	2	4	no	—
279	C₂³×C₃₁	—	4	4	no	—
280	C₂³×C₃₁	—	4	4	no	—
281	C₂³×C₃₁	—	4	4	no	—
282	C₂³×C₃₁	—	4	4	no	—
283	C₂³×C₃₁	—	4	4	no	—
284	C₂³×C₃₁	—	4	4	no	—
285	C₂³×C₃₁	C₂²×D₄	1	4	yes	—
286	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
287	C₂³×C₃₁	C₂×#41	1	2	yes	—
288	C₂³×C₃₁	C₂×#41	1	2	yes	—
289	C₂³×C₃₁	C₂⁵	1	1	yes	characteristic
290	Q₈×C₃₁	—	8	4	no	—
291	D₄×C₃₁	—	4	16	no	—
292	D₄×C₃₁	—	4	8	no	—
293	D₄×C₃₁	—	8	4	no	—
294	D₄×C₃₁	—	8	4	no	—
295	D₄×C₃₁	—	8	8	no	—
296	D₄×C₃₁	—	8	8	no	—
297	C₂×C₄×C₃₁	—	2	1	no	—
298	C₂×C₄×C₃₁	—	2	2	no	—
299	C₂×C₄×C₃₁	—	2	1	no	—
300	C₂×C₄×C₃₁	—	2	1	no	—
301	C₂×C₄×C₃₁	—	2	1	no	—
302	C₂×C₄×C₃₁	—	2	1	no	—
303	C₂×C₄×C₃₁	—	2	1	no	—
304	C₂×C₄×C₃₁	—	2	1	no	—
305	C₂×C₄×C₃₁	—	2	2	no	—
306	C₂×C₄×C₃₁	—	2	1	no	—
307	C₂×C₄×C₃₁	—	2	1	no	—
308	C₂×C₄×C₃₁	—	2	1	no	—
309	C₂×C₄×C₃₁	—	2	8	no	—
310	C₂×C₄×C₃₁	—	2	4	no	—
311	C₂×C₄×C₃₁	—	2	4	no	—
312	C₂×C₄×C₃₁	—	2	4	no	—
313	C₂×C₄×C₃₁	—	2	2	no	—
314	C₂×C₄×C₃₁	—	2	4	no	—
315	C₂×C₄×C₃₁	—	2	4	no	—
316	C₂×C₄×C₃₁	—	2	2	no	—
317	C₂×C₄×C₃₁	—	2	2	no	—
318	C₂×C₄×C₃₁	—	2	4	no	—
319	C₂×C₄×C₃₁	—	2	2	no	—
320	C₂×C₄×C₃₁	—	2	2	no	—
321	C₂×C₄×C₃₁	—	2	4	no	—
322	C₂×C₄×C₃₁	—	2	2	no	—
323	C₂×C₄×C₃₁	—	2	4	no	—
324	C₂×C₄×C₃₁	—	2	4	no	—
325	C₂×C₄×C₃₁	—	4	4	no	—
326	C₂×C₄×C₃₁	—	4	4	no	—
327	C₂×C₄×C₃₁	—	4	4	no	—
328	C₂×C₄×C₃₁	—	4	8	no	—
329	C₂×C₄×C₃₁	—	4	4	no	—
330	C₂×C₄×C₃₁	—	4	4	no	—
331	C₂×C₄×C₃₁	—	4	8	no	—
332	C₂×C₄×C₃₁	—	8	8	no	—
333	C₂×C₄×C₃₁	C₂²×D₄	1	4	yes	—
334	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
335	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
336	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
337	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
338	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
339	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
340	C₂×C₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
341	C₂×C₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
342	C₂×#538	C₂×C₃₁	1	2	yes	complemented
343	#2857	C₂×C₃₁	1	1	yes	characteristic, complemented
344	#2856	C₂×C₃₁	1	1	yes	characteristic, complemented
345	#2847	C₂×C₃₁	1	2	yes	complemented
346	#2639	C₂×C₃₁	1	2	yes	complemented
347	#2617	C₂×C₃₁	1	2	yes	complemented
348	#2559	C₂×C₃₁	1	4	yes	complemented
349	#2557	C₂×C₃₁	1	4	yes	complemented
350	#2496	C₂×C₃₁	1	2	yes	complemented
351	#2491	C₂×C₃₁	1	2	yes	complemented
352	#2428	C₂×C₃₁	1	2	yes	complemented
353	#2422	C₂×C₃₁	1	2	yes	complemented
354	#2325	C₂×C₃₁	1	2	yes	complemented
355	C₄×#121	C₂×C₃₁	1	2	yes	complemented
356	C₂×C₄×C₂²⋊C₄	C₂×C₃₁	1	1	yes	characteristic, complemented
357	C₂²×C₃₁	—	2	2	no	—
358	C₂²×C₃₁	—	2	2	no	—
359	C₂²×C₃₁	—	2	2	no	—
360	C₂²×C₃₁	—	2	2	no	—
361	C₂²×C₃₁	—	2	2	no	—
362	C₂²×C₃₁	—	2	2	no	—
363	C₂²×C₃₁	—	2	4	no	—
364	C₂²×C₃₁	—	2	4	no	—
365	C₂²×C₃₁	—	2	4	no	—
366	C₂²×C₃₁	—	4	16	no	—
367	C₂²×C₃₁	—	4	2	no	—
368	C₂²×C₃₁	—	4	2	no	—
369	C₂²×C₃₁	—	4	2	no	—
370	C₂²×C₃₁	—	4	2	no	—
371	C₂²×C₃₁	—	4	4	no	—
372	C₂²×C₃₁	—	4	4	no	—
373	C₂²×C₃₁	—	4	4	no	—
374	C₂²×C₃₁	—	4	4	no	—
375	C₂²×C₃₁	—	4	4	no	—
376	C₂²×C₃₁	—	4	4	no	—
377	C₂²×C₃₁	—	4	4	no	—
378	C₂²×C₃₁	#532	1	4	yes	—
379	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
380	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
381	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
382	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
383	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
384	C₂²×C₃₁	#585	1	1	yes	characteristic
385	C₂²×C₃₁	#585	1	1	yes	characteristic
386	C₄×C₃₁	—	2	2	no	—
387	C₄×C₃₁	—	2	4	no	—
388	C₄×C₃₁	—	2	2	no	—
389	C₄×C₃₁	—	2	2	no	—
390	C₄×C₃₁	—	2	2	no	—
391	C₄×C₃₁	—	2	2	no	—
392	C₄×C₃₁	—	4	4	no	—
393	C₄×C₃₁	—	4	2	no	—
394	C₄×C₃₁	—	4	4	no	—
395	C₄×C₃₁	—	4	4	no	—
396	C₄×C₃₁	—	4	2	no	—
397	C₄×C₃₁	#538	1	4	yes	complemented
398	C₂⁴×C₄	C₂²×C₃₁	1	1	yes	characteristic
399	#538	—	2	16	no	—
400	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
401	C₂×#127	C₂²×C₃₁	1	1	yes	characteristic, complemented
402	C₂×#126	C₂²×C₃₁	1	4	yes	—
403	C₂×#124	C₂²×C₃₁	1	4	yes	—
404	C₂×#123	C₂²×C₃₁	1	4	yes	—
405	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	—
406	C₂×#121	C₂²×C₃₁	1	2	yes	—
407	C₂×#121	C₂²×C₃₁	1	2	yes	—
408	C₂×#121	C₂²×C₃₁	1	2	yes	—
409	C₂×#121	C₂²×C₃₁	1	4	yes	—
410	C₂×#121	C₂²×C₃₁	1	2	yes	—
411	C₂×#121	C₂²×C₃₁	1	2	yes	—
412	C₂×#120	C₂²×C₃₁	1	4	yes	—
413	C₂×C₄×D₄	C₂²×C₃₁	1	4	yes	—
414	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	complemented
415	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
416	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
417	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
418	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
419	#400	C₂²×C₃₁	1	4	yes	complemented
420	#397	C₂²×C₃₁	1	4	yes	—
421	#397	C₂²×C₃₁	1	4	yes	complemented
422	#394	C₂²×C₃₁	1	4	yes	—
423	#394	C₂²×C₃₁	1	4	yes	—
424	#394	C₂²×C₃₁	1	4	yes	complemented
425	#393	C₂²×C₃₁	1	4	yes	complemented
426	#392	C₂²×C₃₁	1	4	yes	—
427	#391	C₂²×C₃₁	1	2	yes	complemented
428	#390	C₂²×C₃₁	1	2	yes	complemented
429	#390	C₂²×C₃₁	1	2	yes	complemented
430	#390	C₂²×C₃₁	1	2	yes	complemented
431	#390	C₂²×C₃₁	1	2	yes	complemented
432	#389	C₂²×C₃₁	1	2	yes	complemented
433	#389	C₂²×C₃₁	1	2	yes	complemented
434	#389	C₂²×C₃₁	1	2	yes	complemented
435	#388	C₂²×C₃₁	1	4	yes	complemented
436	#388	C₂²×C₃₁	1	4	yes	complemented
437	#387	C₂²×C₃₁	1	4	yes	complemented
438	#386	C₂²×C₃₁	1	4	yes	—
439	#386	C₂²×C₃₁	1	4	yes	—
440	#386	C₂²×C₃₁	1	4	yes	—
441	#386	C₂²×C₃₁	1	4	yes	—
442	#386	C₂²×C₃₁	1	4	yes	complemented
443	#385	C₂²×C₃₁	1	4	yes	complemented
444	#384	C₂²×C₃₁	1	1	yes	characteristic, complemented
445	#384	C₂²×C₃₁	1	1	yes	characteristic, complemented
446	#380	C₂²×C₃₁	1	2	yes	—
447	#380	C₂²×C₃₁	1	2	yes	—
448	#380	C₂²×C₃₁	1	2	yes	—
449	#380	C₂²×C₃₁	1	2	yes	—
450	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	complemented
451	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
452	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
453	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
454	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
455	C₄×C₂²⋊C₄	C₂²×C₃₁	1	4	yes	complemented
456	C₂×#95	C₂²×C₃₁	1	1	yes	characteristic
457	C₂×#95	C₂²×C₃₁	1	1	yes	characteristic
458	C₂×C₃₁	—	2	4	no	—
459	C₂×C₃₁	—	4	4	no	—
460	C₂×C₃₁	—	8	4	no	—
461	C₂×C₃₁	C₂×#532	1	1	yes	characteristic
462	C₂×C₃₁	C₂×#538	1	1	yes	characteristic
463	C₂×C₃₁	#3455	1	1	yes	characteristic
464	C₂×C₃₁	#3496	1	1	yes	characteristic
465	C₂×C₃₁	#3496	1	1	yes	characteristic
466	C₂×C₃₁	#3505	1	1	yes	characteristic
467	C₂×C₃₁	#3506	1	1	yes	characteristic
468	C₂⁵	C₂³×C₃₁	1	1	yes	characteristic
469	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
470	C₂²×D₄	C₂³×C₃₁	1	4	yes	—
471	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
472	C₂²×D₄	C₂³×C₃₁	1	4	yes	—
473	C₂²×D₄	C₂³×C₃₁	1	4	yes	—
474	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
475	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
476	C₂³×C₄	—	2	4	no	—
477	C₂³×C₄	—	4	2	no	—
478	C₂³×C₄	—	4	2	no	—
479	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
480	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
481	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
482	C₂³×C₄	C₂³×C₃₁	1	4	yes	—
483	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
484	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
485	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
486	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
487	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
488	C₄⋊Q₈	—	4	2	no	—
489	#127	—	4	2	no	—
490	#126	—	2	16	no	—
491	#124	—	2	16	no	—
492	#123	—	2	16	no	—
493	C₂²⋊Q₈	—	2	8	no	—
494	#121	—	2	8	no	—
495	#121	—	2	8	no	—
496	#121	—	2	8	no	—
497	#121	—	2	16	no	—
498	#121	—	4	4	no	—
499	#121	—	4	4	no	—
500	#120	—	2	16	no	—
501	C₄×D₄	—	2	16	no	—
502	C₄×D₄	—	4	4	no	—
503	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
504	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
505	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
506	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
507	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
508	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
509	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
510	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
511	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
512	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
513	C₂×C₂²⋊C₄	—	2	4	no	—
514	C₂×C₂²⋊C₄	D₄×C₃₁	1	8	yes	complemented
515	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
516	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
517	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
518	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
519	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
520	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
521	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
522	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
523	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
524	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
525	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
526	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
527	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
528	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
529	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
530	C₂×C₄²	—	4	2	no	—
531	C₂×C₄²	—	4	2	no	—
532	C₂×C₄²	C₂³×C₃₁	1	4	yes	—
533	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
534	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
535	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
536	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
537	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
538	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
539	#95	C₂³×C₃₁	1	2	yes	—
540	#95	C₂³×C₃₁	1	2	yes	—
541	#95	C₂³×C₃₁	1	2	yes	—
542	#95	C₂³×C₃₁	1	2	yes	—
543	#95	C₂³×C₃₁	1	4	yes	—
544	#95	C₂³×C₃₁	1	4	yes	—
545	#95	C₂³×C₃₁	1	4	yes	—
546	#95	C₂³×C₃₁	1	4	yes	—
547	#95	C₂³×C₃₁	1	4	yes	—
548	#95	C₂³×C₃₁	1	4	yes	—
549	C₃₁	#35005	1	1	yes	characteristic, direct product factor, Sylow
550	C₂⁴	—	2	2	no	—
551	C₂⁴	—	2	2	no	—
552	C₂⁴	—	4	1	no	—
553	C₂⁴	—	4	1	no	—
554	C₂⁴	—	4	1	no	—
555	C₂⁴	—	4	1	no	—
556	C₂⁴	C₂×D₄×C₃₁	1	4	yes	—
557	C₂⁴	C₂⁴×C₃₁	1	4	yes	—
558	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
559	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
560	C₂×Q₈	—	2	4	no	—
561	C₂×Q₈	—	4	2	no	—
562	C₂×Q₈	—	4	2	no	—
563	C₂×D₄	—	2	8	no	—
564	C₂×D₄	—	2	8	no	—
565	C₂×D₄	—	2	8	no	—
566	C₂×D₄	—	2	8	no	—
567	C₂×D₄	—	2	8	no	—
568	C₂×D₄	—	2	4	no	—
569	C₂×D₄	—	2	4	no	—
570	C₂×D₄	—	2	4	no	—
571	C₂×D₄	—	2	4	no	—
572	C₂×D₄	—	2	4	no	—
573	C₂×D₄	—	4	4	no	—
574	C₂×D₄	—	4	4	no	—
575	C₂×D₄	—	4	2	no	—
576	C₂×D₄	—	4	2	no	—
577	C₂×D₄	—	4	2	no	—
578	C₂×D₄	—	4	2	no	—
579	C₂×D₄	—	4	4	no	—
580	C₂×D₄	—	4	4	no	—
581	C₂²×C₄	—	2	2	no	—
582	C₂²×C₄	—	2	2	no	—
583	C₂²×C₄	—	2	2	no	—
584	C₂²×C₄	—	2	2	no	—
585	C₂²×C₄	—	2	4	no	—
586	C₂²×C₄	—	2	4	no	—
587	C₂²×C₄	—	2	4	no	—
588	C₂²×C₄	—	2	4	no	—
589	C₂²×C₄	—	2	8	no	—
590	C₂²×C₄	—	4	1	no	—
591	C₂²×C₄	—	4	1	no	—
592	C₂²×C₄	—	4	1	no	—
593	C₂²×C₄	—	4	1	no	—
594	C₂²×C₄	—	4	2	no	—
595	C₂²×C₄	—	4	2	no	—
596	C₂²×C₄	—	4	1	no	—
597	C₂²×C₄	—	4	1	no	—
598	C₂²×C₄	—	4	1	no	—
599	C₂²×C₄	—	4	1	no	—
600	C₂²×C₄	—	4	1	no	—
601	C₂²×C₄	—	4	1	no	—
602	C₂²×C₄	—	4	4	no	—
603	C₂²×C₄	—	4	4	no	—
604	C₂²×C₄	—	4	16	no	—
605	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
606	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
607	C₂²×C₄	#41×C₃₁	1	4	yes	—
608	C₂²×C₄	#41×C₃₁	1	4	yes	—
609	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
610	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
611	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
612	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
613	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
614	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
615	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
616	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
617	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
618	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
619	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
620	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
621	C₄⋊C₄	—	2	8	no	—
622	C₄⋊C₄	—	2	8	no	—
623	C₄⋊C₄	—	2	4	no	—
624	C₄⋊C₄	—	2	4	no	—
625	C₄⋊C₄	—	2	4	no	—
626	C₄⋊C₄	—	2	4	no	—
627	C₄⋊C₄	—	2	4	no	—
628	C₄⋊C₄	—	2	4	no	—
629	C₄⋊C₄	—	4	2	no	—
630	C₄⋊C₄	—	4	2	no	—
631	C₂²⋊C₄	—	2	8	no	—
632	C₂²⋊C₄	—	2	8	no	—
633	C₂²⋊C₄	—	2	8	no	—
634	C₂²⋊C₄	—	2	8	no	—
635	C₂²⋊C₄	—	2	8	no	—
636	C₂²⋊C₄	—	2	4	no	—
637	C₂²⋊C₄	—	2	4	no	—
638	C₂²⋊C₄	—	2	8	no	—
639	C₂²⋊C₄	—	2	8	no	—
640	C₂²⋊C₄	—	4	4	no	—
641	C₂²⋊C₄	—	4	4	no	—
642	C₂²⋊C₄	—	4	4	no	—
643	C₂²⋊C₄	—	4	4	no	—
644	C₂²⋊C₄	C₂×D₄×C₃₁	1	8	yes	—
645	C₂²⋊C₄	C₂×D₄×C₃₁	1	8	yes	—
646	C₄²	—	2	8	no	—
647	C₄²	—	2	4	no	—
648	C₄²	—	2	2	no	—
649	C₄²	—	2	2	no	—
650	C₄²	—	4	1	no	—
651	C₄²	—	4	2	no	—
652	C₄²	—	4	1	no	—
653	C₂³	—	2	1	no	—
654	C₂³	—	2	1	no	—
655	C₂³	—	2	1	no	—
656	C₂³	—	2	1	no	—
657	C₂³	—	2	8	no	—
658	C₂³	—	2	2	no	—
659	C₂³	—	2	2	no	—
660	C₂³	—	2	2	no	—
661	C₂³	—	2	2	no	—
662	C₂³	—	2	2	no	—
663	C₂³	—	2	2	no	—
664	C₂³	—	2	4	no	—
665	C₂³	—	2	4	no	—
666	C₂³	—	2	4	no	—
667	C₂³	—	2	4	no	—
668	C₂³	—	2	4	no	—
669	C₂³	—	2	4	no	—
670	C₂³	—	2	4	no	—
671	C₂³	—	4	4	no	—
672	C₂³	—	4	4	no	—
673	C₂³	—	4	4	no	—
674	C₂³	—	4	4	no	—
675	C₂³	—	4	4	no	—
676	C₂³	—	4	4	no	—
677	C₂³	C₂²×D₄×C₃₁	1	4	yes	—
678	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
679	C₂³	C₂×#41×C₃₁	1	2	yes	—
680	C₂³	C₂×#41×C₃₁	1	2	yes	—
681	C₂³	C₂⁵×C₃₁	1	1	yes	characteristic
682	Q₈	—	8	4	no	—
683	D₄	—	4	16	no	—
684	D₄	—	4	8	no	—
685	D₄	—	8	4	no	—
686	D₄	—	8	4	no	—
687	D₄	—	8	8	no	—
688	D₄	—	8	8	no	—
689	C₂×C₄	—	2	1	no	—
690	C₂×C₄	—	2	2	no	—
691	C₂×C₄	—	2	1	no	—
692	C₂×C₄	—	2	1	no	—
693	C₂×C₄	—	2	1	no	—
694	C₂×C₄	—	2	1	no	—
695	C₂×C₄	—	2	1	no	—
696	C₂×C₄	—	2	1	no	—
697	C₂×C₄	—	2	2	no	—
698	C₂×C₄	—	2	1	no	—
699	C₂×C₄	—	2	1	no	—
700	C₂×C₄	—	2	1	no	—
701	C₂×C₄	—	2	8	no	—
702	C₂×C₄	—	2	4	no	—
703	C₂×C₄	—	2	4	no	—
704	C₂×C₄	—	2	4	no	—
705	C₂×C₄	—	2	2	no	—
706	C₂×C₄	—	2	4	no	—
707	C₂×C₄	—	2	4	no	—
708	C₂×C₄	—	2	2	no	—
709	C₂×C₄	—	2	2	no	—
710	C₂×C₄	—	2	4	no	—
711	C₂×C₄	—	2	2	no	—
712	C₂×C₄	—	2	2	no	—
713	C₂×C₄	—	2	4	no	—
714	C₂×C₄	—	2	2	no	—
715	C₂×C₄	—	2	4	no	—
716	C₂×C₄	—	2	4	no	—
717	C₂×C₄	—	4	4	no	—
718	C₂×C₄	—	4	4	no	—
719	C₂×C₄	—	4	4	no	—
720	C₂×C₄	—	4	8	no	—
721	C₂×C₄	—	4	4	no	—
722	C₂×C₄	—	4	4	no	—
723	C₂×C₄	—	4	8	no	—
724	C₂×C₄	—	8	8	no	—
725	C₂×C₄	C₂²×D₄×C₃₁	1	4	yes	—
726	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
727	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
728	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
729	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
730	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
731	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
732	C₂×C₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
733	C₂×C₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
734	C₂²	—	2	2	no	—
735	C₂²	—	2	2	no	—
736	C₂²	—	2	2	no	—
737	C₂²	—	2	2	no	—
738	C₂²	—	2	2	no	—
739	C₂²	—	2	2	no	—
740	C₂²	—	2	4	no	—
741	C₂²	—	2	4	no	—
742	C₂²	—	2	4	no	—
743	C₂²	—	4	16	no	—
744	C₂²	—	4	2	no	—
745	C₂²	—	4	2	no	—
746	C₂²	—	4	2	no	—
747	C₂²	—	4	2	no	—
748	C₂²	—	4	4	no	—
749	C₂²	—	4	4	no	—
750	C₂²	—	4	4	no	—
751	C₂²	—	4	4	no	—
752	C₂²	—	4	4	no	—
753	C₂²	—	4	4	no	—
754	C₂²	—	4	4	no	—
755	C₂²	C₃₁×#532	1	4	yes	—
756	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
757	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
758	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
759	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
760	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
761	C₂²	C₃₁×#585	1	1	yes	characteristic
762	C₂²	C₃₁×#585	1	1	yes	characteristic
763	C₄	—	2	2	no	—
764	C₄	—	2	4	no	—
765	C₄	—	2	2	no	—
766	C₄	—	2	2	no	—
767	C₄	—	2	2	no	—
768	C₄	—	2	2	no	—
769	C₄	—	4	4	no	—
770	C₄	—	4	2	no	—
771	C₄	—	4	4	no	—
772	C₄	—	4	4	no	—
773	C₄	—	4	2	no	—
774	C₄	C₃₁×#538	1	4	yes	complemented
775	C₂	—	2	4	no	—
776	C₂	—	4	4	no	—
777	C₂	—	8	4	no	—
778	C₂	C₂×C₃₁×#532	1	1	yes	characteristic
779	C₂	C₂×C₃₁×#538	1	1	yes	characteristic
780	C₂	C₃₁×#3455	1	1	yes	characteristic
781	C₂	C₃₁×#3496	1	1	yes	characteristic
782	C₂	C₃₁×#3496	1	1	yes	characteristic
783	C₂	C₃₁×#3505	1	1	yes	characteristic
784	C₂	C₃₁×#3506	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃₁	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₃₁
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃₁×#538	C₂	semidirect
2. C₃₁×#2857	C₂	semidirect
3. C₃₁×#2856	C₂	semidirect
4. C₃₁×#2847	C₂	semidirect
5. C₃₁×#2639	C₂	semidirect
6. C₃₁×#2617	C₂	semidirect
7. C₃₁×#2559	C₂	semidirect
8. C₃₁×#2557	C₂	semidirect
9. C₃₁×#2496	C₂	semidirect
10. C₃₁×#2491	C₂	semidirect
11. C₃₁×#2428	C₂	semidirect
12. C₃₁×#2422	C₂	semidirect
13. C₃₁×#2325	C₂	semidirect
14. C₄×C₃₁×#121	C₂	semidirect
15. C₂×C₄×C₂²⋊C₄×C₃₁	C₂	semidirect
18. C₂×C₃₁×C₄⋊Q₈	C₂²	semidirect
19. C₂×C₃₁×#127	C₂²	semidirect
32. C₂×C₄×D₄×C₃₁	C₂²	semidirect
37. C₃₁×#400	C₂²	semidirect
39. C₃₁×#397	C₂²	semidirect
42. C₃₁×#394	C₂²	semidirect
43. C₃₁×#393	C₂²	semidirect
45. C₃₁×#391	C₂²	semidirect
46. C₃₁×#390	C₂²	semidirect
47. C₃₁×#390	C₂²	semidirect
48. C₃₁×#390	C₂²	semidirect
49. C₃₁×#390	C₂²	semidirect
50. C₃₁×#389	C₂²	semidirect
51. C₃₁×#389	C₂²	semidirect
52. C₃₁×#389	C₂²	semidirect
53. C₃₁×#388	C₂²	semidirect
54. C₃₁×#388	C₂²	semidirect
55. C₃₁×#387	C₂²	semidirect
60. C₃₁×#386	C₂²	semidirect
61. C₃₁×#385	C₂²	semidirect
62. C₃₁×#384	C₂²	semidirect
63. C₃₁×#384	C₂²	semidirect
68. C₄×C₄⋊C₄×C₃₁	C₂²	semidirect
73. C₄×C₂²⋊C₄×C₃₁	C₂²	semidirect
122. C₂×C₂²⋊C₄×C₃₁	D₄	semidirect
260. #35005	C₃₁	direct (N × H)
342. C₂×#538	C₂×C₃₁	semidirect
343. #2857	C₂×C₃₁	semidirect
344. #2856	C₂×C₃₁	semidirect
345. #2847	C₂×C₃₁	semidirect
346. #2639	C₂×C₃₁	semidirect
347. #2617	C₂×C₃₁	semidirect
348. #2559	C₂×C₃₁	semidirect
349. #2557	C₂×C₃₁	semidirect
350. #2496	C₂×C₃₁	semidirect
351. #2491	C₂×C₃₁	semidirect
352. #2428	C₂×C₃₁	semidirect
353. #2422	C₂×C₃₁	semidirect
354. #2325	C₂×C₃₁	semidirect
355. C₄×#121	C₂×C₃₁	semidirect
356. C₂×C₄×C₂²⋊C₄	C₂×C₃₁	semidirect
397. C₄×C₃₁	#538	semidirect
400. C₂×C₄⋊Q₈	C₂²×C₃₁	semidirect
401. C₂×#127	C₂²×C₃₁	semidirect
414. C₂×C₄×D₄	C₂²×C₃₁	semidirect
419. #400	C₂²×C₃₁	semidirect
421. #397	C₂²×C₃₁	semidirect
424. #394	C₂²×C₃₁	semidirect
425. #393	C₂²×C₃₁	semidirect
427. #391	C₂²×C₃₁	semidirect
428. #390	C₂²×C₃₁	semidirect
429. #390	C₂²×C₃₁	semidirect
430. #390	C₂²×C₃₁	semidirect
431. #390	C₂²×C₃₁	semidirect
432. #389	C₂²×C₃₁	semidirect
433. #389	C₂²×C₃₁	semidirect
434. #389	C₂²×C₃₁	semidirect
435. #388	C₂²×C₃₁	semidirect
436. #388	C₂²×C₃₁	semidirect
437. #387	C₂²×C₃₁	semidirect
442. #386	C₂²×C₃₁	semidirect
443. #385	C₂²×C₃₁	semidirect
444. #384	C₂²×C₃₁	semidirect
445. #384	C₂²×C₃₁	semidirect
450. C₄×C₄⋊C₄	C₂²×C₃₁	semidirect
455. C₄×C₂²⋊C₄	C₂²×C₃₁	semidirect
514. C₂×C₂²⋊C₄	D₄×C₃₁	semidirect
549. C₃₁	#35005	direct (N × H)
774. C₄	C₃₁×#538	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃₁×#538	2
C₃₁×#2857	2
C₃₁×#2856	2
C₃₁×#2847	2
C₃₁×#2639	2
C₃₁×#2617	2
C₃₁×#2559	2
C₃₁×#2557	2
C₃₁×#2496	2
C₃₁×#2491	2
C₃₁×#2428	2
C₃₁×#2422	2
C₃₁×#2325	2
C₄×C₃₁×#121	2
C₂×C₄×C₂²⋊C₄×C₃₁	2
#35005	31

Subgroups — C31×#35005 #21491764

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#35005 #21491764