Subgroups — C₃₁×#34415 #21491174

Order 7936.

2766 conjugacy classes of subgroups.

The subgroup lattice has 762 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#535	C₂	1	1	yes	maximal, characteristic
2	C₃₁×#2379	C₂	1	2	yes	maximal, complemented
3	C₃₁×#2375	C₂	1	2	yes	maximal, complemented
4	C₃₁×#2372	C₂	1	2	yes	maximal, complemented
5	C₃₁×#2363	C₂	1	2	yes	maximal, complemented
6	C₃₁×#2361	C₂	1	2	yes	maximal, complemented
7	C₃₁×#2358	C₂	1	2	yes	maximal, complemented
8	C₃₁×#2346	C₂	1	2	yes	maximal, complemented
9	D₄×C₂²⋊C₄×C₃₁	C₂	1	2	yes	maximal, complemented
10	C₃₁×#2328	C₂	1	4	yes	maximal, complemented
11	C₃₁×#2324	C₂	1	2	yes	maximal, complemented
12	C₃₁×#2321	C₂	1	4	yes	maximal, complemented
13	C₃₁×#2311	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×C₃₁×#121	C₂	1	2	yes	maximal, complemented
15	C₃₁×#2297	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#41×C₃₁	C₂²	1	1	yes	characteristic
17	C₂³×D₄×C₃₁	C₂²	1	1	yes	characteristic
18	C₃₁×#535	C₄	1	16	yes	complemented
19	C₂×C₃₁×#127	C₂²	1	2	yes	—
20	C₂×C₃₁×#124	C₂²	1	2	yes	—
21	C₂×C₃₁×#121	C₂²	1	2	yes	—
22	C₂×C₃₁×#121	C₂²	1	2	yes	—
23	C₂×C₃₁×#120	C₂²	1	2	yes	—
24	C₂×C₃₁×#120	C₂²	1	2	yes	—
25	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
26	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
27	C₂×C₄×D₄×C₃₁	C₂²	1	4	yes	complemented
28	C₂×C₄×D₄×C₃₁	C₂²	1	4	yes	complemented
29	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
30	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic, complemented
31	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic, complemented
32	C₂²×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
33	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	4	yes	—
34	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic, complemented
35	C₃₁×#391	C₂²	1	2	yes	complemented
36	C₃₁×#391	C₂²	1	1	yes	characteristic, complemented
37	C₃₁×#391	C₂²	1	1	yes	characteristic, complemented
38	C₃₁×#390	C₂²	1	2	yes	—
39	C₃₁×#390	C₂²	1	2	yes	—
40	C₃₁×#390	C₂²	1	2	yes	—
41	C₃₁×#390	C₂²	1	1	yes	characteristic
42	C₃₁×#390	C₂²	1	1	yes	characteristic
43	C₃₁×#390	C₂²	1	4	yes	complemented
44	C₃₁×#390	C₂²	1	4	yes	complemented
45	C₃₁×#389	C₂²	1	2	yes	complemented
46	C₃₁×#389	C₂²	1	2	yes	complemented
47	C₃₁×#388	C₂²	1	4	yes	—
48	C₃₁×#388	C₂²	1	4	yes	—
49	C₃₁×#388	C₂²	1	4	yes	complemented
50	C₃₁×#388	C₂²	1	4	yes	complemented
51	C₃₁×#388	C₂²	1	4	yes	complemented
52	C₃₁×#388	C₂²	1	4	yes	complemented
53	C₃₁×#386	C₂²	1	2	yes	—
54	C₃₁×#386	C₂²	1	2	yes	—
55	C₃₁×#386	C₂²	1	4	yes	—
56	C₃₁×#386	C₂²	1	4	yes	—
57	C₃₁×#386	C₂²	1	2	yes	complemented
58	C₃₁×#386	C₂²	1	4	yes	complemented
59	C₃₁×#386	C₂²	1	4	yes	complemented
60	C₃₁×#386	C₂²	1	2	yes	complemented
61	C₃₁×#386	C₂²	1	4	yes	complemented
62	C₃₁×#386	C₂²	1	4	yes	complemented
63	C₃₁×#385	C₂²	1	4	yes	complemented
64	C₃₁×#385	C₂²	1	4	yes	complemented
65	C₃₁×#382	C₂²	1	4	yes	complemented
66	C₃₁×#380	C₂²	1	2	yes	—
67	C₃₁×#380	C₂²	1	2	yes	complemented
68	C₃₁×#379	C₂²	1	4	yes	—
69	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	complemented
70	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	complemented
71	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
72	C₄×C₂²⋊C₄×C₃₁	C₂²	1	4	yes	complemented
73	C₄×C₂²⋊C₄×C₃₁	C₂²	1	4	yes	complemented
74	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	complemented
75	C₃₁×#376	C₂²	1	4	yes	complemented
76	C₂⁵×C₃₁	C₂³	1	2	yes	—
77	C₂×#41×C₃₁	—	4	2	no	—
78	C₂×#41×C₃₁	—	4	2	no	—
79	C₂×#41×C₃₁	C₂×C₄	1	8	yes	complemented
80	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
81	C₂²×D₄×C₃₁	—	4	2	no	—
82	C₂²×D₄×C₃₁	—	4	2	no	—
83	C₂²×D₄×C₃₁	C₂×C₄	1	8	yes	complemented
84	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
85	C₂²×D₄×C₃₁	C₂³	1	4	yes	—
86	C₂²×D₄×C₃₁	C₂³	1	4	yes	—
87	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
88	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
89	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
90	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
91	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
92	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
93	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
94	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
95	C₂³×C₄×C₃₁	C₂³	1	4	yes	—
96	C₂³×C₄×C₃₁	C₂³	1	4	yes	—
97	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
98	C₃₁×#127	C₂×C₄	1	16	yes	complemented
99	C₃₁×#124	C₂×C₄	1	16	yes	complemented
100	C₃₁×#121	C₂×C₄	1	16	yes	complemented
101	C₃₁×#121	C₂×C₄	1	16	yes	complemented
102	C₃₁×#120	C₂×C₄	1	16	yes	complemented
103	C₃₁×#120	C₂×C₄	1	16	yes	complemented
104	C₄×D₄×C₃₁	—	4	8	no	—
105	C₄×D₄×C₃₁	—	4	4	no	—
106	C₄×D₄×C₃₁	—	4	4	no	—
107	C₄×D₄×C₃₁	—	4	8	no	—
108	C₃₁×#117	—	4	2	no	—
109	C₃₁×#117	—	4	2	no	—
110	C₃₁×#117	C₂×C₄	1	8	yes	complemented
111	C₂×C₄⋊C₄×C₃₁	—	4	2	no	—
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	2	yes	—
115	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
116	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
117	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
118	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
119	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
120	C₂×C₂²⋊C₄×C₃₁	—	4	8	no	—
121	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
122	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
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	2	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	2	yes	—
133	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
134	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
135	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
136	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
137	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
138	C₂×C₄²×C₃₁	—	4	2	no	—
139	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
140	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
141	C₂×C₄²×C₃₁	C₂³	1	4	yes	—
142	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
143	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
144	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
145	C₂×C₄²×C₃₁	C₂³	1	4	yes	—
146	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
147	C₃₁×#95	C₂³	1	2	yes	—
148	C₃₁×#95	C₂³	1	4	yes	—
149	C₃₁×#95	C₂³	1	4	yes	—
150	C₃₁×#95	C₂³	1	4	yes	—
151	C₃₁×#95	C₂³	1	2	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	4	yes	—
156	C₃₁×#95	C₂³	1	4	yes	—
157	C₂⁴×C₃₁	—	4	4	no	—
158	C₂⁴×C₃₁	—	4	2	no	—
159	C₂⁴×C₃₁	—	4	2	no	—
160	C₂⁴×C₃₁	—	4	4	no	—
161	C₂⁴×C₃₁	C₂²×C₄	1	8	yes	—
162	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
163	C₂⁴×C₃₁	C₂⁴	1	4	yes	—
164	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
165	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
166	#41×C₃₁	—	4	16	no	—
167	C₂×Q₈×C₃₁	—	4	1	no	—
168	C₂×Q₈×C₃₁	—	4	1	no	—
169	C₂×Q₈×C₃₁	C₂²×C₄	1	4	yes	—
170	C₂×D₄×C₃₁	—	2	4	no	—
171	C₂×D₄×C₃₁	—	2	4	no	—
172	C₂×D₄×C₃₁	—	4	16	no	—
173	C₂×D₄×C₃₁	—	4	4	no	—
174	C₂×D₄×C₃₁	—	4	4	no	—
175	C₂×D₄×C₃₁	—	4	2	no	—
176	C₂×D₄×C₃₁	—	4	2	no	—
177	C₂×D₄×C₃₁	—	4	4	no	—
178	C₂×D₄×C₃₁	—	4	4	no	—
179	C₂×D₄×C₃₁	—	4	1	no	—
180	C₂×D₄×C₃₁	—	4	1	no	—
181	C₂×D₄×C₃₁	—	4	1	no	—
182	C₂×D₄×C₃₁	—	4	1	no	—
183	C₂×D₄×C₃₁	—	4	1	no	—
184	C₂×D₄×C₃₁	—	4	1	no	—
185	C₂×D₄×C₃₁	C₂²×C₄	1	8	yes	—
186	C₂×D₄×C₃₁	C₂²×C₄	1	4	yes	—
187	C₂×D₄×C₃₁	C₂²×C₄	1	4	yes	—
188	C₂×D₄×C₃₁	C₂²×C₄	1	16	yes	—
189	C₂×D₄×C₃₁	C₂²×C₄	1	16	yes	—
190	C₂×D₄×C₃₁	C₂²×C₄	1	8	yes	—
191	C₂×D₄×C₃₁	C₂²×C₄	1	4	yes	—
192	C₂²×C₄×C₃₁	—	2	2	no	—
193	C₂²×C₄×C₃₁	—	2	2	no	—
194	C₂²×C₄×C₃₁	—	2	2	no	—
195	C₂²×C₄×C₃₁	—	2	2	no	—
196	C₂²×C₄×C₃₁	—	2	2	no	—
197	C₂²×C₄×C₃₁	—	2	2	no	—
198	C₂²×C₄×C₃₁	—	2	4	no	—
199	C₂²×C₄×C₃₁	—	2	8	no	—
200	C₂²×C₄×C₃₁	—	4	2	no	—
201	C₂²×C₄×C₃₁	—	4	2	no	—
202	C₂²×C₄×C₃₁	—	4	4	no	—
203	C₂²×C₄×C₃₁	—	4	2	no	—
204	C₂²×C₄×C₃₁	—	4	4	no	—
205	C₂²×C₄×C₃₁	—	4	4	no	—
206	C₂²×C₄×C₃₁	—	4	4	no	—
207	C₂²×C₄×C₃₁	—	4	4	no	—
208	C₂²×C₄×C₃₁	—	4	4	no	—
209	C₂²×C₄×C₃₁	C₂²×C₄	1	4	yes	—
210	C₂²×C₄×C₃₁	C₂²×C₄	1	4	yes	—
211	C₂²×C₄×C₃₁	C₂²×C₄	1	4	yes	—
212	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
213	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
214	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
215	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
216	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
217	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
218	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
219	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
220	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
221	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
222	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
223	C₄⋊C₄×C₃₁	—	2	4	no	—
224	C₄⋊C₄×C₃₁	—	2	4	no	—
225	C₄⋊C₄×C₃₁	—	4	2	no	—
226	C₄⋊C₄×C₃₁	—	4	1	no	—
227	C₄⋊C₄×C₃₁	—	4	1	no	—
228	C₄⋊C₄×C₃₁	—	4	4	no	—
229	C₄⋊C₄×C₃₁	—	4	4	no	—
230	C₄⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
231	C₂²⋊C₄×C₃₁	—	2	4	no	—
232	C₂²⋊C₄×C₃₁	—	2	8	no	—
233	C₂²⋊C₄×C₃₁	—	2	4	no	—
234	C₂²⋊C₄×C₃₁	—	4	4	no	—
235	C₂²⋊C₄×C₃₁	—	4	4	no	—
236	C₂²⋊C₄×C₃₁	—	4	2	no	—
237	C₂²⋊C₄×C₃₁	—	4	4	no	—
238	C₂²⋊C₄×C₃₁	—	4	2	no	—
239	C₂²⋊C₄×C₃₁	—	4	2	no	—
240	C₂²⋊C₄×C₃₁	—	4	2	no	—
241	C₂²⋊C₄×C₃₁	—	4	4	no	—
242	C₂²⋊C₄×C₃₁	—	4	4	no	—
243	C₂²⋊C₄×C₃₁	—	4	4	no	—
244	C₂²⋊C₄×C₃₁	—	4	4	no	—
245	C₂²⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
246	C₂²⋊C₄×C₃₁	C₂²×C₄	1	16	yes	—
247	C₂²⋊C₄×C₃₁	C₂²×C₄	1	16	yes	—
248	C₄²×C₃₁	—	2	4	no	—
249	C₄²×C₃₁	—	2	4	no	—
250	C₄²×C₃₁	—	2	8	no	—
251	C₄²×C₃₁	—	4	1	no	—
252	C₄²×C₃₁	—	4	1	no	—
253	C₄²×C₃₁	—	4	4	no	—
254	C₄²×C₃₁	—	4	2	no	—
255	C₄²×C₃₁	C₂²×C₄	1	8	yes	—
256	#34415	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
257	C₂³×C₃₁	—	2	2	no	—
258	C₂³×C₃₁	—	2	4	no	—
259	C₂³×C₃₁	—	2	2	no	—
260	C₂³×C₃₁	—	2	1	no	—
261	C₂³×C₃₁	—	2	1	no	—
262	C₂³×C₃₁	—	2	2	no	—
263	C₂³×C₃₁	—	2	4	no	—
264	C₂³×C₃₁	—	2	4	no	—
265	C₂³×C₃₁	—	2	4	no	—
266	C₂³×C₃₁	—	2	1	no	—
267	C₂³×C₃₁	—	2	1	no	—
268	C₂³×C₃₁	—	2	1	no	—
269	C₂³×C₃₁	—	2	1	no	—
270	C₂³×C₃₁	—	2	2	no	—
271	C₂³×C₃₁	—	2	4	no	—
272	C₂³×C₃₁	—	2	2	no	—
273	C₂³×C₃₁	—	2	2	no	—
274	C₂³×C₃₁	—	2	4	no	—
275	C₂³×C₃₁	—	4	8	no	—
276	C₂³×C₃₁	—	4	16	no	—
277	C₂³×C₃₁	—	8	8	no	—
278	C₂³×C₃₁	—	8	4	no	—
279	C₂³×C₃₁	—	8	4	no	—
280	C₂³×C₃₁	C₂³×C₄	1	2	yes	—
281	C₂³×C₃₁	C₂³×C₄	1	8	yes	—
282	C₂³×C₃₁	C₂³×C₄	1	2	yes	—
283	C₂³×C₃₁	C₂³×C₄	1	2	yes	—
284	C₂³×C₃₁	C₂⁵	1	1	yes	characteristic
285	Q₈×C₃₁	—	4	4	no	—
286	D₄×C₃₁	—	2	16	no	—
287	D₄×C₃₁	—	4	8	no	—
288	D₄×C₃₁	—	4	16	no	—
289	D₄×C₃₁	—	4	16	no	—
290	D₄×C₃₁	—	4	4	no	—
291	D₄×C₃₁	—	4	4	no	—
292	D₄×C₃₁	—	4	4	no	—
293	C₂×C₄×C₃₁	—	2	2	no	—
294	C₂×C₄×C₃₁	—	2	4	no	—
295	C₂×C₄×C₃₁	—	2	1	no	—
296	C₂×C₄×C₃₁	—	2	1	no	—
297	C₂×C₄×C₃₁	—	2	1	no	—
298	C₂×C₄×C₃₁	—	2	1	no	—
299	C₂×C₄×C₃₁	—	2	1	no	—
300	C₂×C₄×C₃₁	—	2	1	no	—
301	C₂×C₄×C₃₁	—	2	4	no	—
302	C₂×C₄×C₃₁	—	2	2	no	—
303	C₂×C₄×C₃₁	—	2	8	no	—
304	C₂×C₄×C₃₁	—	2	8	no	—
305	C₂×C₄×C₃₁	—	2	8	no	—
306	C₂×C₄×C₃₁	—	2	2	no	—
307	C₂×C₄×C₃₁	—	2	2	no	—
308	C₂×C₄×C₃₁	—	2	4	no	—
309	C₂×C₄×C₃₁	—	2	2	no	—
310	C₂×C₄×C₃₁	—	2	4	no	—
311	C₂×C₄×C₃₁	—	2	2	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	2	no	—
316	C₂×C₄×C₃₁	—	2	4	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	—	4	8	no	—
322	C₂×C₄×C₃₁	—	8	8	no	—
323	C₂×C₄×C₃₁	—	8	4	no	—
324	C₂×C₄×C₃₁	—	8	8	no	—
325	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
326	C₂×C₄×C₃₁	C₂³×C₄	1	8	yes	—
327	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
328	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
329	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
330	C₂×C₄×C₃₁	H(5,𝔽₂)	1	4	yes	—
331	C₂×C₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
332	C₂×C₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
333	C₂×#535	C₂×C₃₁	1	1	yes	characteristic
334	#2379	C₂×C₃₁	1	2	yes	complemented
335	#2375	C₂×C₃₁	1	2	yes	complemented
336	#2372	C₂×C₃₁	1	2	yes	complemented
337	#2363	C₂×C₃₁	1	2	yes	complemented
338	#2361	C₂×C₃₁	1	2	yes	complemented
339	#2358	C₂×C₃₁	1	2	yes	complemented
340	#2346	C₂×C₃₁	1	2	yes	complemented
341	D₄×C₂²⋊C₄	C₂×C₃₁	1	2	yes	complemented
342	#2328	C₂×C₃₁	1	4	yes	complemented
343	#2324	C₂×C₃₁	1	2	yes	complemented
344	#2321	C₂×C₃₁	1	4	yes	complemented
345	#2311	C₂×C₃₁	1	1	yes	characteristic, complemented
346	C₄×#121	C₂×C₃₁	1	2	yes	complemented
347	#2297	C₂×C₃₁	1	1	yes	characteristic, complemented
348	C₂²×C₃₁	—	2	2	no	—
349	C₂²×C₃₁	—	2	2	no	—
350	C₂²×C₃₁	—	2	2	no	—
351	C₂²×C₃₁	—	2	8	no	—
352	C₂²×C₃₁	—	2	4	no	—
353	C₂²×C₃₁	—	2	4	no	—
354	C₂²×C₃₁	—	2	8	no	—
355	C₂²×C₃₁	—	2	8	no	—
356	C₂²×C₃₁	—	2	4	no	—
357	C₂²×C₃₁	—	4	2	no	—
358	C₂²×C₃₁	—	4	4	no	—
359	C₂²×C₃₁	—	4	2	no	—
360	C₂²×C₃₁	—	4	4	no	—
361	C₂²×C₃₁	—	4	2	no	—
362	C₂²×C₃₁	—	4	1	no	—
363	C₂²×C₃₁	—	4	4	no	—
364	C₂²×C₃₁	—	4	1	no	—
365	C₂²×C₃₁	—	4	1	no	—
366	C₂²×C₃₁	—	4	1	no	—
367	C₂²×C₃₁	—	4	1	no	—
368	C₂²×C₃₁	—	4	4	no	—
369	C₂²×C₃₁	—	4	1	no	—
370	C₂²×C₃₁	—	8	16	no	—
371	C₂²×C₃₁	C₂⁴×C₄	1	1	yes	characteristic
372	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
373	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
374	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	2	yes	—
375	C₂²×C₃₁	#585	1	2	yes	—
376	C₄×C₃₁	—	2	2	no	—
377	C₄×C₃₁	—	2	2	no	—
378	C₄×C₃₁	—	2	2	no	—
379	C₄×C₃₁	—	2	8	no	—
380	C₄×C₃₁	—	2	4	no	—
381	C₄×C₃₁	—	4	2	no	—
382	C₄×C₃₁	—	4	4	no	—
383	C₄×C₃₁	—	4	4	no	—
384	C₄×C₃₁	—	4	2	no	—
385	C₄×C₃₁	—	4	2	no	—
386	C₄×C₃₁	#518	1	4	yes	—
387	C₂²×#41	C₂²×C₃₁	1	1	yes	characteristic
388	C₂³×D₄	C₂²×C₃₁	1	1	yes	characteristic
389	#535	C₄×C₃₁	1	16	yes	complemented
390	C₂×#127	C₂²×C₃₁	1	2	yes	—
391	C₂×#124	C₂²×C₃₁	1	2	yes	—
392	C₂×#121	C₂²×C₃₁	1	2	yes	—
393	C₂×#121	C₂²×C₃₁	1	2	yes	—
394	C₂×#120	C₂²×C₃₁	1	2	yes	—
395	C₂×#120	C₂²×C₃₁	1	2	yes	—
396	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
397	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
398	C₂×C₄×D₄	C₂²×C₃₁	1	4	yes	complemented
399	C₂×C₄×D₄	C₂²×C₃₁	1	4	yes	complemented
400	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
401	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic, complemented
402	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic, complemented
403	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
404	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	4	yes	—
405	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic, complemented
406	#391	C₂²×C₃₁	1	2	yes	complemented
407	#391	C₂²×C₃₁	1	1	yes	characteristic, complemented
408	#391	C₂²×C₃₁	1	1	yes	characteristic, complemented
409	#390	C₂²×C₃₁	1	2	yes	—
410	#390	C₂²×C₃₁	1	2	yes	—
411	#390	C₂²×C₃₁	1	2	yes	—
412	#390	C₂²×C₃₁	1	1	yes	characteristic
413	#390	C₂²×C₃₁	1	1	yes	characteristic
414	#390	C₂²×C₃₁	1	4	yes	complemented
415	#390	C₂²×C₃₁	1	4	yes	complemented
416	#389	C₂²×C₃₁	1	2	yes	complemented
417	#389	C₂²×C₃₁	1	2	yes	complemented
418	#388	C₂²×C₃₁	1	4	yes	—
419	#388	C₂²×C₃₁	1	4	yes	—
420	#388	C₂²×C₃₁	1	4	yes	complemented
421	#388	C₂²×C₃₁	1	4	yes	complemented
422	#388	C₂²×C₃₁	1	4	yes	complemented
423	#388	C₂²×C₃₁	1	4	yes	complemented
424	#386	C₂²×C₃₁	1	2	yes	—
425	#386	C₂²×C₃₁	1	2	yes	—
426	#386	C₂²×C₃₁	1	4	yes	—
427	#386	C₂²×C₃₁	1	4	yes	—
428	#386	C₂²×C₃₁	1	2	yes	complemented
429	#386	C₂²×C₃₁	1	4	yes	complemented
430	#386	C₂²×C₃₁	1	4	yes	complemented
431	#386	C₂²×C₃₁	1	2	yes	complemented
432	#386	C₂²×C₃₁	1	4	yes	complemented
433	#386	C₂²×C₃₁	1	4	yes	complemented
434	#385	C₂²×C₃₁	1	4	yes	complemented
435	#385	C₂²×C₃₁	1	4	yes	complemented
436	#382	C₂²×C₃₁	1	4	yes	complemented
437	#380	C₂²×C₃₁	1	2	yes	—
438	#380	C₂²×C₃₁	1	2	yes	complemented
439	#379	C₂²×C₃₁	1	4	yes	—
440	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	complemented
441	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	complemented
442	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
443	C₄×C₂²⋊C₄	C₂²×C₃₁	1	4	yes	complemented
444	C₄×C₂²⋊C₄	C₂²×C₃₁	1	4	yes	complemented
445	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	complemented
446	#376	C₂²×C₃₁	1	4	yes	complemented
447	C₂×C₃₁	—	4	2	no	—
448	C₂×C₃₁	—	4	2	no	—
449	C₂×C₃₁	—	4	8	no	—
450	C₂×C₃₁	—	4	2	no	—
451	C₂×C₃₁	C₂×#518	1	1	yes	characteristic
452	C₂×C₃₁	C₄×H(5,𝔽₂)	1	2	yes	—
453	C₂×C₃₁	#3542	1	2	yes	—
454	C₂×C₃₁	#3549	1	1	yes	characteristic
455	C₂×C₃₁	#3551	1	1	yes	characteristic
456	C₂⁵	C₂³×C₃₁	1	2	yes	—
457	C₂×#41	—	4	2	no	—
458	C₂×#41	—	4	2	no	—
459	C₂×#41	C₂×C₄×C₃₁	1	8	yes	complemented
460	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
461	C₂²×D₄	—	4	2	no	—
462	C₂²×D₄	—	4	2	no	—
463	C₂²×D₄	C₂×C₄×C₃₁	1	8	yes	complemented
464	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
465	C₂²×D₄	C₂³×C₃₁	1	4	yes	—
466	C₂²×D₄	C₂³×C₃₁	1	4	yes	—
467	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
468	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
469	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
470	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
471	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
472	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
473	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
474	C₂³×C₄	C₂³×C₃₁	1	4	yes	—
475	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
476	C₂³×C₄	C₂³×C₃₁	1	4	yes	—
477	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
478	#127	C₂×C₄×C₃₁	1	16	yes	complemented
479	#124	C₂×C₄×C₃₁	1	16	yes	complemented
480	#121	C₂×C₄×C₃₁	1	16	yes	complemented
481	#121	C₂×C₄×C₃₁	1	16	yes	complemented
482	#120	C₂×C₄×C₃₁	1	16	yes	complemented
483	#120	C₂×C₄×C₃₁	1	16	yes	complemented
484	C₄×D₄	—	4	8	no	—
485	C₄×D₄	—	4	4	no	—
486	C₄×D₄	—	4	4	no	—
487	C₄×D₄	—	4	8	no	—
488	#117	—	4	2	no	—
489	#117	—	4	2	no	—
490	#117	C₂×C₄×C₃₁	1	8	yes	complemented
491	C₂×C₄⋊C₄	—	4	2	no	—
492	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
493	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
494	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
495	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
496	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
497	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
498	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
499	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
500	C₂×C₂²⋊C₄	—	4	8	no	—
501	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
502	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
503	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
504	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
505	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
506	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
507	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
508	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
509	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
510	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
511	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
512	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
513	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
514	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
515	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
516	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
517	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
518	C₂×C₄²	—	4	2	no	—
519	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
520	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
521	C₂×C₄²	C₂³×C₃₁	1	4	yes	—
522	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
523	C₂×C₄²	C₂³×C₃₁	1	4	yes	—
524	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
525	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
526	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
527	#95	C₂³×C₃₁	1	2	yes	—
528	#95	C₂³×C₃₁	1	4	yes	—
529	#95	C₂³×C₃₁	1	4	yes	—
530	#95	C₂³×C₃₁	1	4	yes	—
531	#95	C₂³×C₃₁	1	2	yes	—
532	#95	C₂³×C₃₁	1	2	yes	—
533	#95	C₂³×C₃₁	1	4	yes	—
534	#95	C₂³×C₃₁	1	2	yes	—
535	#95	C₂³×C₃₁	1	4	yes	—
536	#95	C₂³×C₃₁	1	4	yes	—
537	C₃₁	#34415	1	1	yes	characteristic, direct product factor, Sylow
538	C₂⁴	—	4	4	no	—
539	C₂⁴	—	4	2	no	—
540	C₂⁴	—	4	2	no	—
541	C₂⁴	—	4	4	no	—
542	C₂⁴	C₂²×C₄×C₃₁	1	8	yes	—
543	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
544	C₂⁴	C₂⁴×C₃₁	1	4	yes	—
545	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
546	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
547	#41	—	4	16	no	—
548	C₂×Q₈	—	4	1	no	—
549	C₂×Q₈	—	4	1	no	—
550	C₂×Q₈	C₂²×C₄×C₃₁	1	4	yes	—
551	C₂×D₄	—	2	4	no	—
552	C₂×D₄	—	2	4	no	—
553	C₂×D₄	—	4	16	no	—
554	C₂×D₄	—	4	4	no	—
555	C₂×D₄	—	4	4	no	—
556	C₂×D₄	—	4	2	no	—
557	C₂×D₄	—	4	2	no	—
558	C₂×D₄	—	4	4	no	—
559	C₂×D₄	—	4	4	no	—
560	C₂×D₄	—	4	1	no	—
561	C₂×D₄	—	4	1	no	—
562	C₂×D₄	—	4	1	no	—
563	C₂×D₄	—	4	1	no	—
564	C₂×D₄	—	4	1	no	—
565	C₂×D₄	—	4	1	no	—
566	C₂×D₄	C₂²×C₄×C₃₁	1	8	yes	—
567	C₂×D₄	C₂²×C₄×C₃₁	1	4	yes	—
568	C₂×D₄	C₂²×C₄×C₃₁	1	4	yes	—
569	C₂×D₄	C₂²×C₄×C₃₁	1	16	yes	—
570	C₂×D₄	C₂²×C₄×C₃₁	1	16	yes	—
571	C₂×D₄	C₂²×C₄×C₃₁	1	8	yes	—
572	C₂×D₄	C₂²×C₄×C₃₁	1	4	yes	—
573	C₂²×C₄	—	2	2	no	—
574	C₂²×C₄	—	2	2	no	—
575	C₂²×C₄	—	2	2	no	—
576	C₂²×C₄	—	2	2	no	—
577	C₂²×C₄	—	2	2	no	—
578	C₂²×C₄	—	2	2	no	—
579	C₂²×C₄	—	2	4	no	—
580	C₂²×C₄	—	2	8	no	—
581	C₂²×C₄	—	4	2	no	—
582	C₂²×C₄	—	4	2	no	—
583	C₂²×C₄	—	4	4	no	—
584	C₂²×C₄	—	4	2	no	—
585	C₂²×C₄	—	4	4	no	—
586	C₂²×C₄	—	4	4	no	—
587	C₂²×C₄	—	4	4	no	—
588	C₂²×C₄	—	4	4	no	—
589	C₂²×C₄	—	4	4	no	—
590	C₂²×C₄	C₂²×C₄×C₃₁	1	4	yes	—
591	C₂²×C₄	C₂²×C₄×C₃₁	1	4	yes	—
592	C₂²×C₄	C₂²×C₄×C₃₁	1	4	yes	—
593	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
594	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
595	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
596	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
597	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
598	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
599	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
600	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
601	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
602	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
603	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
604	C₄⋊C₄	—	2	4	no	—
605	C₄⋊C₄	—	2	4	no	—
606	C₄⋊C₄	—	4	2	no	—
607	C₄⋊C₄	—	4	1	no	—
608	C₄⋊C₄	—	4	1	no	—
609	C₄⋊C₄	—	4	4	no	—
610	C₄⋊C₄	—	4	4	no	—
611	C₄⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
612	C₂²⋊C₄	—	2	4	no	—
613	C₂²⋊C₄	—	2	8	no	—
614	C₂²⋊C₄	—	2	4	no	—
615	C₂²⋊C₄	—	4	4	no	—
616	C₂²⋊C₄	—	4	4	no	—
617	C₂²⋊C₄	—	4	2	no	—
618	C₂²⋊C₄	—	4	4	no	—
619	C₂²⋊C₄	—	4	2	no	—
620	C₂²⋊C₄	—	4	2	no	—
621	C₂²⋊C₄	—	4	2	no	—
622	C₂²⋊C₄	—	4	4	no	—
623	C₂²⋊C₄	—	4	4	no	—
624	C₂²⋊C₄	—	4	4	no	—
625	C₂²⋊C₄	—	4	4	no	—
626	C₂²⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
627	C₂²⋊C₄	C₂²×C₄×C₃₁	1	16	yes	—
628	C₂²⋊C₄	C₂²×C₄×C₃₁	1	16	yes	—
629	C₄²	—	2	4	no	—
630	C₄²	—	2	4	no	—
631	C₄²	—	2	8	no	—
632	C₄²	—	4	1	no	—
633	C₄²	—	4	1	no	—
634	C₄²	—	4	4	no	—
635	C₄²	—	4	2	no	—
636	C₄²	C₂²×C₄×C₃₁	1	8	yes	—
637	C₂³	—	2	2	no	—
638	C₂³	—	2	4	no	—
639	C₂³	—	2	2	no	—
640	C₂³	—	2	1	no	—
641	C₂³	—	2	1	no	—
642	C₂³	—	2	2	no	—
643	C₂³	—	2	4	no	—
644	C₂³	—	2	4	no	—
645	C₂³	—	2	4	no	—
646	C₂³	—	2	1	no	—
647	C₂³	—	2	1	no	—
648	C₂³	—	2	1	no	—
649	C₂³	—	2	1	no	—
650	C₂³	—	2	2	no	—
651	C₂³	—	2	4	no	—
652	C₂³	—	2	2	no	—
653	C₂³	—	2	2	no	—
654	C₂³	—	2	4	no	—
655	C₂³	—	4	8	no	—
656	C₂³	—	4	16	no	—
657	C₂³	—	8	8	no	—
658	C₂³	—	8	4	no	—
659	C₂³	—	8	4	no	—
660	C₂³	C₂³×C₄×C₃₁	1	2	yes	—
661	C₂³	C₂³×C₄×C₃₁	1	8	yes	—
662	C₂³	C₂³×C₄×C₃₁	1	2	yes	—
663	C₂³	C₂³×C₄×C₃₁	1	2	yes	—
664	C₂³	C₂⁵×C₃₁	1	1	yes	characteristic
665	Q₈	—	4	4	no	—
666	D₄	—	2	16	no	—
667	D₄	—	4	8	no	—
668	D₄	—	4	16	no	—
669	D₄	—	4	16	no	—
670	D₄	—	4	4	no	—
671	D₄	—	4	4	no	—
672	D₄	—	4	4	no	—
673	C₂×C₄	—	2	2	no	—
674	C₂×C₄	—	2	4	no	—
675	C₂×C₄	—	2	1	no	—
676	C₂×C₄	—	2	1	no	—
677	C₂×C₄	—	2	1	no	—
678	C₂×C₄	—	2	1	no	—
679	C₂×C₄	—	2	1	no	—
680	C₂×C₄	—	2	1	no	—
681	C₂×C₄	—	2	4	no	—
682	C₂×C₄	—	2	2	no	—
683	C₂×C₄	—	2	8	no	—
684	C₂×C₄	—	2	8	no	—
685	C₂×C₄	—	2	8	no	—
686	C₂×C₄	—	2	2	no	—
687	C₂×C₄	—	2	2	no	—
688	C₂×C₄	—	2	4	no	—
689	C₂×C₄	—	2	2	no	—
690	C₂×C₄	—	2	4	no	—
691	C₂×C₄	—	2	2	no	—
692	C₂×C₄	—	2	4	no	—
693	C₂×C₄	—	2	2	no	—
694	C₂×C₄	—	2	4	no	—
695	C₂×C₄	—	2	2	no	—
696	C₂×C₄	—	2	4	no	—
697	C₂×C₄	—	2	2	no	—
698	C₂×C₄	—	2	4	no	—
699	C₂×C₄	—	2	2	no	—
700	C₂×C₄	—	2	2	no	—
701	C₂×C₄	—	4	8	no	—
702	C₂×C₄	—	8	8	no	—
703	C₂×C₄	—	8	4	no	—
704	C₂×C₄	—	8	8	no	—
705	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
706	C₂×C₄	C₂³×C₄×C₃₁	1	8	yes	—
707	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
708	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
709	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
710	C₂×C₄	C₃₁×H(5,𝔽₂)	1	4	yes	—
711	C₂×C₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
712	C₂×C₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
713	C₂²	—	2	2	no	—
714	C₂²	—	2	2	no	—
715	C₂²	—	2	2	no	—
716	C₂²	—	2	8	no	—
717	C₂²	—	2	4	no	—
718	C₂²	—	2	4	no	—
719	C₂²	—	2	8	no	—
720	C₂²	—	2	8	no	—
721	C₂²	—	2	4	no	—
722	C₂²	—	4	2	no	—
723	C₂²	—	4	4	no	—
724	C₂²	—	4	2	no	—
725	C₂²	—	4	4	no	—
726	C₂²	—	4	2	no	—
727	C₂²	—	4	1	no	—
728	C₂²	—	4	4	no	—
729	C₂²	—	4	1	no	—
730	C₂²	—	4	1	no	—
731	C₂²	—	4	1	no	—
732	C₂²	—	4	4	no	—
733	C₂²	—	4	1	no	—
734	C₂²	—	4	1	no	—
735	C₂²	—	8	16	no	—
736	C₂²	C₂⁴×C₄×C₃₁	1	1	yes	characteristic
737	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
738	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
739	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	2	yes	—
740	C₂²	C₃₁×#585	1	2	yes	—
741	C₄	—	2	2	no	—
742	C₄	—	2	2	no	—
743	C₄	—	2	2	no	—
744	C₄	—	2	8	no	—
745	C₄	—	2	4	no	—
746	C₄	—	4	2	no	—
747	C₄	—	4	4	no	—
748	C₄	—	4	4	no	—
749	C₄	—	4	2	no	—
750	C₄	—	4	2	no	—
751	C₄	C₃₁×#518	1	4	yes	—
752	C₂	—	4	2	no	—
753	C₂	—	4	8	no	—
754	C₂	—	4	2	no	—
755	C₂	—	4	2	no	—
756	C₂	C₂×C₃₁×#518	1	1	yes	characteristic
757	C₂	C₄×C₃₁×H(5,𝔽₂)	1	2	yes	—
758	C₂	C₃₁×#3542	1	2	yes	—
759	C₂	C₃₁×#3549	1	1	yes	characteristic
760	C₂	C₃₁×#3551	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃₁	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₃₁
Frattini, cosocle	C₂³	C₂⁵×C₃₁
prime radical	C₂×C₃₁×#535	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃₁×#2379	C₂	semidirect
3. C₃₁×#2375	C₂	semidirect
4. C₃₁×#2372	C₂	semidirect
5. C₃₁×#2363	C₂	semidirect
6. C₃₁×#2361	C₂	semidirect
7. C₃₁×#2358	C₂	semidirect
8. C₃₁×#2346	C₂	semidirect
9. D₄×C₂²⋊C₄×C₃₁	C₂	semidirect
10. C₃₁×#2328	C₂	semidirect
11. C₃₁×#2324	C₂	semidirect
12. C₃₁×#2321	C₂	semidirect
13. C₃₁×#2311	C₂	semidirect
14. C₄×C₃₁×#121	C₂	semidirect
15. C₃₁×#2297	C₂	semidirect
18. C₃₁×#535	C₄	semidirect
27. C₂×C₄×D₄×C₃₁	C₂²	semidirect
28. C₂×C₄×D₄×C₃₁	C₂²	semidirect
30. C₂×C₃₁×#117	C₂²	semidirect
31. C₂×C₃₁×#117	C₂²	semidirect
32. C₂²×C₄⋊C₄×C₃₁	C₂²	semidirect
34. C₂²×C₄²×C₃₁	C₂²	semidirect
35. C₃₁×#391	C₂²	semidirect
36. C₃₁×#391	C₂²	semidirect
37. C₃₁×#391	C₂²	semidirect
43. C₃₁×#390	C₂²	semidirect
44. C₃₁×#390	C₂²	semidirect
45. C₃₁×#389	C₂²	semidirect
46. C₃₁×#389	C₂²	semidirect
49. C₃₁×#388	C₂²	semidirect
50. C₃₁×#388	C₂²	semidirect
51. C₃₁×#388	C₂²	semidirect
52. C₃₁×#388	C₂²	semidirect
57. C₃₁×#386	C₂²	semidirect
58. C₃₁×#386	C₂²	semidirect
59. C₃₁×#386	C₂²	semidirect
60. C₃₁×#386	C₂²	semidirect
61. C₃₁×#386	C₂²	semidirect
62. C₃₁×#386	C₂²	semidirect
63. C₃₁×#385	C₂²	semidirect
64. C₃₁×#385	C₂²	semidirect
65. C₃₁×#382	C₂²	semidirect
67. C₃₁×#380	C₂²	semidirect
69. C₄×C₄⋊C₄×C₃₁	C₂²	semidirect
70. C₄×C₄⋊C₄×C₃₁	C₂²	semidirect
72. C₄×C₂²⋊C₄×C₃₁	C₂²	semidirect
73. C₄×C₂²⋊C₄×C₃₁	C₂²	semidirect
74. C₄×C₂²⋊C₄×C₃₁	C₂²	semidirect
75. C₃₁×#376	C₂²	semidirect
79. C₂×#41×C₃₁	C₂×C₄	semidirect
83. C₂²×D₄×C₃₁	C₂×C₄	semidirect
98. C₃₁×#127	C₂×C₄	semidirect
99. C₃₁×#124	C₂×C₄	semidirect
100. C₃₁×#121	C₂×C₄	semidirect
101. C₃₁×#121	C₂×C₄	semidirect
102. C₃₁×#120	C₂×C₄	semidirect
103. C₃₁×#120	C₂×C₄	semidirect
110. C₃₁×#117	C₂×C₄	semidirect
256. #34415	C₃₁	direct (N × H)
334. #2379	C₂×C₃₁	semidirect
335. #2375	C₂×C₃₁	semidirect
336. #2372	C₂×C₃₁	semidirect
337. #2363	C₂×C₃₁	semidirect
338. #2361	C₂×C₃₁	semidirect
339. #2358	C₂×C₃₁	semidirect
340. #2346	C₂×C₃₁	semidirect
341. D₄×C₂²⋊C₄	C₂×C₃₁	semidirect
342. #2328	C₂×C₃₁	semidirect
343. #2324	C₂×C₃₁	semidirect
344. #2321	C₂×C₃₁	semidirect
345. #2311	C₂×C₃₁	semidirect
346. C₄×#121	C₂×C₃₁	semidirect
347. #2297	C₂×C₃₁	semidirect
389. #535	C₄×C₃₁	semidirect
398. C₂×C₄×D₄	C₂²×C₃₁	semidirect
399. C₂×C₄×D₄	C₂²×C₃₁	semidirect
401. C₂×#117	C₂²×C₃₁	semidirect
402. C₂×#117	C₂²×C₃₁	semidirect
403. C₂²×C₄⋊C₄	C₂²×C₃₁	semidirect
405. C₂²×C₄²	C₂²×C₃₁	semidirect
406. #391	C₂²×C₃₁	semidirect
407. #391	C₂²×C₃₁	semidirect
408. #391	C₂²×C₃₁	semidirect
414. #390	C₂²×C₃₁	semidirect
415. #390	C₂²×C₃₁	semidirect
416. #389	C₂²×C₃₁	semidirect
417. #389	C₂²×C₃₁	semidirect
420. #388	C₂²×C₃₁	semidirect
421. #388	C₂²×C₃₁	semidirect
422. #388	C₂²×C₃₁	semidirect
423. #388	C₂²×C₃₁	semidirect
428. #386	C₂²×C₃₁	semidirect
429. #386	C₂²×C₃₁	semidirect
430. #386	C₂²×C₃₁	semidirect
431. #386	C₂²×C₃₁	semidirect
432. #386	C₂²×C₃₁	semidirect
433. #386	C₂²×C₃₁	semidirect
434. #385	C₂²×C₃₁	semidirect
435. #385	C₂²×C₃₁	semidirect
436. #382	C₂²×C₃₁	semidirect
438. #380	C₂²×C₃₁	semidirect
440. C₄×C₄⋊C₄	C₂²×C₃₁	semidirect
441. C₄×C₄⋊C₄	C₂²×C₃₁	semidirect
443. C₄×C₂²⋊C₄	C₂²×C₃₁	semidirect
444. C₄×C₂²⋊C₄	C₂²×C₃₁	semidirect
445. C₄×C₂²⋊C₄	C₂²×C₃₁	semidirect
446. #376	C₂²×C₃₁	semidirect
459. C₂×#41	C₂×C₄×C₃₁	semidirect
463. C₂²×D₄	C₂×C₄×C₃₁	semidirect
478. #127	C₂×C₄×C₃₁	semidirect
479. #124	C₂×C₄×C₃₁	semidirect
480. #121	C₂×C₄×C₃₁	semidirect
481. #121	C₂×C₄×C₃₁	semidirect
482. #120	C₂×C₄×C₃₁	semidirect
483. #120	C₂×C₄×C₃₁	semidirect
490. #117	C₂×C₄×C₃₁	semidirect
537. C₃₁	#34415	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃₁×#535	2
C₃₁×#2379	2
C₃₁×#2375	2
C₃₁×#2372	2
C₃₁×#2363	2
C₃₁×#2361	2
C₃₁×#2358	2
C₃₁×#2346	2
D₄×C₂²⋊C₄×C₃₁	2
C₃₁×#2328	2
C₃₁×#2324	2
C₃₁×#2321	2
C₃₁×#2311	2
C₄×C₃₁×#121	2
C₃₁×#2297	2
#34415	31

Subgroups — C31×#34415 #21491174

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#34415 #21491174