Subgroups — C₃₁×#35064 #21491823

Order 7936.

2822 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#525	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃₁×#123	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#2854	C₂	1	4	yes	maximal, complemented
4	C₃₁×#2663	C₂	1	2	yes	maximal, complemented
5	C₃₁×#2661	C₂	1	2	yes	maximal, complemented
6	C₃₁×#2602	C₂	1	4	yes	maximal, complemented
7	C₃₁×#2591	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#2583	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#2561	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#2539	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#2498	C₂	1	2	yes	maximal, complemented
12	C₃₁×#2430	C₂	1	2	yes	maximal, complemented
13	C₃₁×#2412	C₂	1	2	yes	maximal, complemented
14	C₃₁×#2410	C₂	1	2	yes	maximal, complemented
15	C₃₁×#2322	C₂	1	2	yes	maximal, complemented
16	C₃₁×#2321	C₂	1	2	yes	maximal, complemented
17	C₂×C₄×C₂²⋊C₄×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×#41×C₃₁	C₂²	1	1	yes	characteristic, complemented
19	C₂³×D₄×C₃₁	C₂²	1	1	yes	characteristic
20	C₂⁴×C₄×C₃₁	C₂²	1	1	yes	characteristic
21	C₃₁×#525	—	2	8	no	—
22	C₂×C₃₁×#123	—	2	8	no	—
23	C₂×C₃₁×#123	C₂²	1	2	yes	—
24	C₂×C₃₁×#123	C₂²	1	2	yes	—
25	C₂×C₃₁×#123	C₂²	1	2	yes	—
26	C₂×C₃₁×#123	C₂²	1	2	yes	—
27	C₂×C₃₁×#123	C₂²	1	2	yes	—
28	C₂×C₃₁×#123	C₂²	1	2	yes	complemented
29	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
30	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
31	C₂×C₃₁×#121	C₂²	1	1	yes	characteristic
32	C₂×C₃₁×#121	C₂²	1	4	yes	—
33	C₂×C₃₁×#121	C₂²	1	1	yes	characteristic, complemented
34	C₂×C₃₁×#120	C₂²	1	2	yes	—
35	C₂×C₃₁×#120	C₂²	1	2	yes	—
36	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
37	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	complemented
38	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic, complemented
39	C₂²×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
40	C₂²×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
41	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
42	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
43	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
44	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
45	C₂²×C₄²×C₃₁	C₂²	1	2	yes	complemented
46	C₃₁×#400	C₂²	1	2	yes	complemented
47	C₃₁×#399	C₂²	1	2	yes	complemented
48	C₃₁×#398	C₂²	1	2	yes	complemented
49	C₃₁×#397	C₂²	1	4	yes	complemented
50	C₃₁×#397	C₂²	1	2	yes	complemented
51	C₃₁×#395	C₂²	1	2	yes	complemented
52	C₃₁×#394	C₂²	1	4	yes	—
53	C₃₁×#394	C₂²	1	2	yes	complemented
54	C₃₁×#394	C₂²	1	4	yes	complemented
55	C₃₁×#393	C₂²	1	2	yes	complemented
56	C₃₁×#392	C₂²	1	4	yes	—
57	C₃₁×#392	C₂²	1	2	yes	complemented
58	C₃₁×#390	C₂²	1	4	yes	complemented
59	C₃₁×#390	C₂²	1	4	yes	complemented
60	C₃₁×#389	C₂²	1	4	yes	complemented
61	C₃₁×#389	C₂²	1	4	yes	complemented
62	C₃₁×#388	C₂²	1	4	yes	complemented
63	C₃₁×#388	C₂²	1	4	yes	complemented
64	C₃₁×#388	C₂²	1	4	yes	complemented
65	C₃₁×#388	C₂²	1	4	yes	complemented
66	C₃₁×#388	C₂²	1	4	yes	complemented
67	C₃₁×#387	C₂²	1	4	yes	complemented
68	C₃₁×#386	C₂²	1	2	yes	—
69	C₃₁×#386	C₂²	1	2	yes	—
70	C₃₁×#386	C₂²	1	4	yes	—
71	C₃₁×#386	C₂²	1	4	yes	complemented
72	C₃₁×#386	C₂²	1	4	yes	complemented
73	C₃₁×#385	C₂²	1	2	yes	—
74	C₃₁×#385	C₂²	1	2	yes	—
75	C₃₁×#385	C₂²	1	4	yes	complemented
76	C₃₁×#381	C₂²	1	2	yes	—
77	C₃₁×#380	C₂²	1	4	yes	complemented
78	C₃₁×#379	C₂²	1	2	yes	—
79	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
80	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
81	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
82	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	complemented
83	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	complemented
84	C₂×C₃₁×#95	C₂²	1	2	yes	complemented
85	C₂⁵×C₃₁	C₂³	1	1	yes	characteristic
86	C₂⁵×C₃₁	C₂³	1	1	yes	characteristic
87	C₂×#41×C₃₁	—	2	4	no	—
88	C₂×#41×C₃₁	—	4	4	no	—
89	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
90	C₂²×D₄×C₃₁	—	2	4	no	—
91	C₂²×D₄×C₃₁	—	4	4	no	—
92	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
93	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
94	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
95	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
96	C₂²×D₄×C₃₁	C₂³	1	4	yes	—
97	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
98	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
99	C₂³×C₄×C₃₁	—	4	4	no	—
100	C₂³×C₄×C₃₁	D₄	1	8	yes	complemented
101	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
102	C₂³×C₄×C₃₁	C₂³	1	4	yes	—
103	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
104	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
105	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
106	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
107	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
108	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
109	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
110	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
111	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
112	C₃₁×#123	—	2	8	no	—
113	C₃₁×#123	—	2	8	no	—
114	C₃₁×#123	—	2	8	no	—
115	C₃₁×#123	—	2	8	no	—
116	C₃₁×#123	—	2	8	no	—
117	C₃₁×#123	—	2	8	no	—
118	C₃₁×C₂²⋊Q₈	—	2	4	no	—
119	C₃₁×C₂²⋊Q₈	—	2	4	no	—
120	C₃₁×#121	—	2	4	no	—
121	C₃₁×#121	—	2	4	no	—
122	C₃₁×#121	—	4	8	no	—
123	C₃₁×#120	—	2	8	no	—
124	C₃₁×#120	—	2	8	no	—
125	C₄×D₄×C₃₁	—	2	8	no	—
126	C₄×D₄×C₃₁	—	2	8	no	—
127	C₃₁×#117	—	2	4	no	—
128	C₂×C₄⋊C₄×C₃₁	—	2	4	no	—
129	C₂×C₄⋊C₄×C₃₁	—	2	4	no	—
130	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
131	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
132	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
133	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
134	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
135	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
136	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
137	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
138	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
139	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
140	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
141	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
142	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
143	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
144	C₂×C₂²⋊C₄×C₃₁	—	2	8	no	—
145	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
146	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
147	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
148	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
149	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
150	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
151	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
152	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
153	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
154	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
155	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
156	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
157	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
158	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
159	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
160	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
161	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
162	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
163	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
164	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
165	C₂×C₄²×C₃₁	—	4	4	no	—
166	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
167	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
168	C₂×C₄²×C₃₁	C₂³	1	4	yes	—
169	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
170	C₃₁×#95	C₂³	1	4	yes	—
171	C₃₁×#95	C₂³	1	2	yes	—
172	C₃₁×#95	C₂³	1	2	yes	—
173	C₃₁×#95	C₂³	1	4	yes	—
174	C₃₁×#95	C₂³	1	4	yes	—
175	C₃₁×#95	C₂³	1	4	yes	—
176	C₃₁×#95	C₂³	1	4	yes	—
177	C₃₁×#95	C₂³	1	4	yes	—
178	C₃₁×#95	C₂³	1	4	yes	—
179	C₂⁴×C₃₁	—	2	4	no	—
180	C₂⁴×C₃₁	—	2	4	no	—
181	C₂⁴×C₃₁	—	2	2	no	—
182	C₂⁴×C₃₁	—	2	4	no	—
183	C₂⁴×C₃₁	—	4	2	no	—
184	C₂⁴×C₃₁	—	4	2	no	—
185	C₂⁴×C₃₁	—	4	2	no	—
186	C₂⁴×C₃₁	C₂×D₄	1	4	yes	—
187	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
188	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
189	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
190	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
191	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
192	#41×C₃₁	—	4	16	no	—
193	C₂×Q₈×C₃₁	—	2	2	no	—
194	C₂×Q₈×C₃₁	—	4	2	no	—
195	C₂×D₄×C₃₁	—	2	4	no	—
196	C₂×D₄×C₃₁	—	2	4	no	—
197	C₂×D₄×C₃₁	—	2	4	no	—
198	C₂×D₄×C₃₁	—	2	4	no	—
199	C₂×D₄×C₃₁	—	2	4	no	—
200	C₂×D₄×C₃₁	—	2	4	no	—
201	C₂×D₄×C₃₁	—	2	4	no	—
202	C₂×D₄×C₃₁	—	2	8	no	—
203	C₂×D₄×C₃₁	—	2	8	no	—
204	C₂×D₄×C₃₁	—	2	2	no	—
205	C₂×D₄×C₃₁	—	2	8	no	—
206	C₂×D₄×C₃₁	—	4	4	no	—
207	C₂×D₄×C₃₁	—	4	4	no	—
208	C₂×D₄×C₃₁	—	4	2	no	—
209	C₂×D₄×C₃₁	—	4	4	no	—
210	C₂×D₄×C₃₁	—	4	4	no	—
211	C₂×D₄×C₃₁	—	4	16	no	—
212	C₂²×C₄×C₃₁	—	2	4	no	—
213	C₂²×C₄×C₃₁	—	2	4	no	—
214	C₂²×C₄×C₃₁	—	2	2	no	—
215	C₂²×C₄×C₃₁	—	2	2	no	—
216	C₂²×C₄×C₃₁	—	2	2	no	—
217	C₂²×C₄×C₃₁	—	2	4	no	—
218	C₂²×C₄×C₃₁	—	2	8	no	—
219	C₂²×C₄×C₃₁	—	2	4	no	—
220	C₂²×C₄×C₃₁	—	2	8	no	—
221	C₂²×C₄×C₃₁	—	4	16	no	—
222	C₂²×C₄×C₃₁	—	4	2	no	—
223	C₂²×C₄×C₃₁	—	4	2	no	—
224	C₂²×C₄×C₃₁	—	4	2	no	—
225	C₂²×C₄×C₃₁	—	4	2	no	—
226	C₂²×C₄×C₃₁	—	4	4	no	—
227	C₂²×C₄×C₃₁	—	4	2	no	—
228	C₂²×C₄×C₃₁	—	4	2	no	—
229	C₂²×C₄×C₃₁	—	4	4	no	—
230	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
231	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
232	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
233	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
234	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
235	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
236	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
237	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
238	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
239	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
240	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
241	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
242	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
243	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
244	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
245	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
246	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
247	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
248	C₄⋊C₄×C₃₁	—	2	4	no	—
249	C₄⋊C₄×C₃₁	—	2	4	no	—
250	C₄⋊C₄×C₃₁	—	2	4	no	—
251	C₄⋊C₄×C₃₁	—	2	4	no	—
252	C₄⋊C₄×C₃₁	—	2	2	no	—
253	C₄⋊C₄×C₃₁	—	2	2	no	—
254	C₄⋊C₄×C₃₁	—	2	4	no	—
255	C₄⋊C₄×C₃₁	—	2	4	no	—
256	C₄⋊C₄×C₃₁	—	2	8	no	—
257	C₄⋊C₄×C₃₁	—	4	4	no	—
258	C₄⋊C₄×C₃₁	—	4	4	no	—
259	C₂²⋊C₄×C₃₁	—	2	4	no	—
260	C₂²⋊C₄×C₃₁	—	2	4	no	—
261	C₂²⋊C₄×C₃₁	—	2	4	no	—
262	C₂²⋊C₄×C₃₁	—	2	4	no	—
263	C₂²⋊C₄×C₃₁	—	2	4	no	—
264	C₂²⋊C₄×C₃₁	—	2	4	no	—
265	C₂²⋊C₄×C₃₁	—	2	4	no	—
266	C₂²⋊C₄×C₃₁	—	2	4	no	—
267	C₂²⋊C₄×C₃₁	—	2	4	no	—
268	C₂²⋊C₄×C₃₁	—	2	4	no	—
269	C₂²⋊C₄×C₃₁	—	2	4	no	—
270	C₂²⋊C₄×C₃₁	—	2	4	no	—
271	C₂²⋊C₄×C₃₁	—	2	8	no	—
272	C₂²⋊C₄×C₃₁	—	2	8	no	—
273	C₂²⋊C₄×C₃₁	—	2	8	no	—
274	C₂²⋊C₄×C₃₁	—	4	4	no	—
275	C₂²⋊C₄×C₃₁	—	4	4	no	—
276	C₂²⋊C₄×C₃₁	—	4	4	no	—
277	C₂²⋊C₄×C₃₁	—	4	4	no	—
278	C₂²⋊C₄×C₃₁	#41	1	8	yes	complemented
279	C₄²×C₃₁	—	2	4	no	—
280	C₄²×C₃₁	—	4	2	no	—
281	C₄²×C₃₁	—	4	4	no	—
282	C₄²×C₃₁	—	4	2	no	—
283	#35064	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
284	C₂³×C₃₁	—	2	2	no	—
285	C₂³×C₃₁	—	2	2	no	—
286	C₂³×C₃₁	—	2	2	no	—
287	C₂³×C₃₁	—	2	2	no	—
288	C₂³×C₃₁	—	2	8	no	—
289	C₂³×C₃₁	—	2	8	no	—
290	C₂³×C₃₁	—	2	2	no	—
291	C₂³×C₃₁	—	2	2	no	—
292	C₂³×C₃₁	—	2	2	no	—
293	C₂³×C₃₁	—	2	2	no	—
294	C₂³×C₃₁	—	2	2	no	—
295	C₂³×C₃₁	—	2	2	no	—
296	C₂³×C₃₁	—	2	4	no	—
297	C₂³×C₃₁	—	2	2	no	—
298	C₂³×C₃₁	—	2	4	no	—
299	C₂³×C₃₁	—	2	4	no	—
300	C₂³×C₃₁	—	2	2	no	—
301	C₂³×C₃₁	—	2	4	no	—
302	C₂³×C₃₁	—	2	2	no	—
303	C₂³×C₃₁	—	4	4	no	—
304	C₂³×C₃₁	—	4	16	no	—
305	C₂³×C₃₁	—	4	4	no	—
306	C₂³×C₃₁	—	4	4	no	—
307	C₂³×C₃₁	—	4	4	no	—
308	C₂³×C₃₁	—	8	8	no	—
309	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
310	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
311	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
312	C₂³×C₃₁	C₂×#41	1	4	yes	—
313	C₂³×C₃₁	H(5,𝔽₂)	1	4	yes	—
314	C₂³×C₃₁	C₂⁵	1	1	yes	characteristic
315	Q₈×C₃₁	—	4	4	no	—
316	D₄×C₃₁	—	4	4	no	—
317	D₄×C₃₁	—	4	8	no	—
318	D₄×C₃₁	—	4	8	no	—
319	D₄×C₃₁	—	4	8	no	—
320	D₄×C₃₁	—	4	8	no	—
321	D₄×C₃₁	—	4	8	no	—
322	D₄×C₃₁	—	8	8	no	—
323	C₂×C₄×C₃₁	—	2	8	no	—
324	C₂×C₄×C₃₁	—	2	8	no	—
325	C₂×C₄×C₃₁	—	2	4	no	—
326	C₂×C₄×C₃₁	—	2	2	no	—
327	C₂×C₄×C₃₁	—	2	2	no	—
328	C₂×C₄×C₃₁	—	2	2	no	—
329	C₂×C₄×C₃₁	—	2	2	no	—
330	C₂×C₄×C₃₁	—	2	4	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	2	no	—
336	C₂×C₄×C₃₁	—	2	2	no	—
337	C₂×C₄×C₃₁	—	2	4	no	—
338	C₂×C₄×C₃₁	—	2	2	no	—
339	C₂×C₄×C₃₁	—	2	4	no	—
340	C₂×C₄×C₃₁	—	2	2	no	—
341	C₂×C₄×C₃₁	—	2	4	no	—
342	C₂×C₄×C₃₁	—	2	4	no	—
343	C₂×C₄×C₃₁	—	2	4	no	—
344	C₂×C₄×C₃₁	—	2	2	no	—
345	C₂×C₄×C₃₁	—	2	4	no	—
346	C₂×C₄×C₃₁	—	2	4	no	—
347	C₂×C₄×C₃₁	—	2	2	no	—
348	C₂×C₄×C₃₁	—	4	4	no	—
349	C₂×C₄×C₃₁	—	4	4	no	—
350	C₂×C₄×C₃₁	—	4	4	no	—
351	C₂×C₄×C₃₁	—	4	4	no	—
352	C₂×C₄×C₃₁	—	4	16	no	—
353	C₂×C₄×C₃₁	—	4	8	no	—
354	C₂×C₄×C₃₁	—	4	4	no	—
355	C₂×C₄×C₃₁	—	4	4	no	—
356	C₂×C₄×C₃₁	—	4	4	no	—
357	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
358	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
359	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
360	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
361	C₂×C₄×C₃₁	C₂×#41	1	8	yes	—
362	C₂×#525	C₂×C₃₁	1	1	yes	characteristic, complemented
363	C₂²×#123	C₂×C₃₁	1	1	yes	characteristic, complemented
364	#2854	C₂×C₃₁	1	4	yes	complemented
365	#2663	C₂×C₃₁	1	2	yes	complemented
366	#2661	C₂×C₃₁	1	2	yes	complemented
367	#2602	C₂×C₃₁	1	4	yes	complemented
368	#2591	C₂×C₃₁	1	1	yes	characteristic, complemented
369	#2583	C₂×C₃₁	1	1	yes	characteristic, complemented
370	#2561	C₂×C₃₁	1	1	yes	characteristic, complemented
371	#2539	C₂×C₃₁	1	1	yes	characteristic, complemented
372	#2498	C₂×C₃₁	1	2	yes	complemented
373	#2430	C₂×C₃₁	1	2	yes	complemented
374	#2412	C₂×C₃₁	1	2	yes	complemented
375	#2410	C₂×C₃₁	1	2	yes	complemented
376	#2322	C₂×C₃₁	1	2	yes	complemented
377	#2321	C₂×C₃₁	1	2	yes	complemented
378	C₂×C₄×C₂²⋊C₄	C₂×C₃₁	1	1	yes	characteristic, complemented
379	C₂²×C₃₁	—	2	2	no	—
380	C₂²×C₃₁	—	2	2	no	—
381	C₂²×C₃₁	—	2	2	no	—
382	C₂²×C₃₁	—	2	2	no	—
383	C₂²×C₃₁	—	2	8	no	—
384	C₂²×C₃₁	—	2	8	no	—
385	C₂²×C₃₁	—	2	2	no	—
386	C₂²×C₃₁	—	2	2	no	—
387	C₂²×C₃₁	—	2	2	no	—
388	C₂²×C₃₁	—	4	16	no	—
389	C₂²×C₃₁	—	4	4	no	—
390	C₂²×C₃₁	—	4	2	no	—
391	C₂²×C₃₁	—	4	2	no	—
392	C₂²×C₃₁	—	4	2	no	—
393	C₂²×C₃₁	—	4	2	no	—
394	C₂²×C₃₁	—	4	2	no	—
395	C₂²×C₃₁	—	4	2	no	—
396	C₂²×C₃₁	—	4	4	no	—
397	C₂²×C₃₁	—	4	4	no	—
398	C₂²×C₃₁	—	4	4	no	—
399	C₂²×C₃₁	—	4	4	no	—
400	C₂²×C₃₁	—	8	8	no	—
401	C₂²×C₃₁	#532	1	4	yes	—
402	C₂²×C₃₁	#534	1	4	yes	—
403	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
404	C₂²×C₃₁	C₂²×#41	1	2	yes	—
405	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	2	yes	—
406	C₂²×C₃₁	#585	1	2	yes	—
407	C₄×C₃₁	—	2	2	no	—
408	C₄×C₃₁	—	2	2	no	—
409	C₄×C₃₁	—	2	2	no	—
410	C₄×C₃₁	—	2	2	no	—
411	C₄×C₃₁	—	2	8	no	—
412	C₄×C₃₁	—	4	2	no	—
413	C₄×C₃₁	—	4	2	no	—
414	C₄×C₃₁	—	4	2	no	—
415	C₄×C₃₁	—	4	2	no	—
416	C₄×C₃₁	—	4	2	no	—
417	C₄×C₃₁	—	4	2	no	—
418	C₄×C₃₁	—	4	4	no	—
419	C₂²×#41	C₂²×C₃₁	1	1	yes	characteristic, complemented
420	C₂³×D₄	C₂²×C₃₁	1	1	yes	characteristic
421	C₂⁴×C₄	C₂²×C₃₁	1	1	yes	characteristic
422	#525	—	2	8	no	—
423	C₂×#123	—	2	8	no	—
424	C₂×#123	C₂²×C₃₁	1	2	yes	—
425	C₂×#123	C₂²×C₃₁	1	2	yes	—
426	C₂×#123	C₂²×C₃₁	1	2	yes	—
427	C₂×#123	C₂²×C₃₁	1	2	yes	—
428	C₂×#123	C₂²×C₃₁	1	2	yes	—
429	C₂×#123	C₂²×C₃₁	1	2	yes	complemented
430	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
431	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
432	C₂×#121	C₂²×C₃₁	1	1	yes	characteristic
433	C₂×#121	C₂²×C₃₁	1	4	yes	—
434	C₂×#121	C₂²×C₃₁	1	1	yes	characteristic, complemented
435	C₂×#120	C₂²×C₃₁	1	2	yes	—
436	C₂×#120	C₂²×C₃₁	1	2	yes	—
437	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
438	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	complemented
439	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic, complemented
440	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
441	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
442	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
443	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
444	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
445	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
446	C₂²×C₄²	C₂²×C₃₁	1	2	yes	complemented
447	#400	C₂²×C₃₁	1	2	yes	complemented
448	#399	C₂²×C₃₁	1	2	yes	complemented
449	#398	C₂²×C₃₁	1	2	yes	complemented
450	#397	C₂²×C₃₁	1	2	yes	complemented
451	#397	C₂²×C₃₁	1	4	yes	complemented
452	#395	C₂²×C₃₁	1	2	yes	complemented
453	#394	C₂²×C₃₁	1	4	yes	—
454	#394	C₂²×C₃₁	1	2	yes	complemented
455	#394	C₂²×C₃₁	1	4	yes	complemented
456	#393	C₂²×C₃₁	1	2	yes	complemented
457	#392	C₂²×C₃₁	1	4	yes	—
458	#392	C₂²×C₃₁	1	2	yes	complemented
459	#390	C₂²×C₃₁	1	4	yes	complemented
460	#390	C₂²×C₃₁	1	4	yes	complemented
461	#389	C₂²×C₃₁	1	4	yes	complemented
462	#389	C₂²×C₃₁	1	4	yes	complemented
463	#388	C₂²×C₃₁	1	4	yes	complemented
464	#388	C₂²×C₃₁	1	4	yes	complemented
465	#388	C₂²×C₃₁	1	4	yes	complemented
466	#388	C₂²×C₃₁	1	4	yes	complemented
467	#388	C₂²×C₃₁	1	4	yes	complemented
468	#387	C₂²×C₃₁	1	4	yes	complemented
469	#386	C₂²×C₃₁	1	2	yes	—
470	#386	C₂²×C₃₁	1	2	yes	—
471	#386	C₂²×C₃₁	1	4	yes	—
472	#386	C₂²×C₃₁	1	4	yes	complemented
473	#386	C₂²×C₃₁	1	4	yes	complemented
474	#385	C₂²×C₃₁	1	2	yes	—
475	#385	C₂²×C₃₁	1	2	yes	—
476	#385	C₂²×C₃₁	1	4	yes	complemented
477	#381	C₂²×C₃₁	1	2	yes	—
478	#380	C₂²×C₃₁	1	4	yes	complemented
479	#379	C₂²×C₃₁	1	2	yes	—
480	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
481	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
482	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
483	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	complemented
484	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	complemented
485	C₂×#95	C₂²×C₃₁	1	2	yes	complemented
486	C₂×C₃₁	—	2	4	no	—
487	C₂×C₃₁	—	2	4	no	—
488	C₂×C₃₁	—	4	2	no	—
489	C₂×C₃₁	—	8	2	no	—
490	C₂×C₃₁	—	8	2	no	—
491	C₂×C₃₁	C₂×#532	1	1	yes	characteristic
492	C₂×C₃₁	C₂×#534	1	1	yes	characteristic
493	C₂×C₃₁	#3449	1	1	yes	characteristic
494	C₂×C₃₁	#3513	1	4	yes	—
495	C₂⁵	C₂³×C₃₁	1	1	yes	characteristic
496	C₂⁵	C₂³×C₃₁	1	1	yes	characteristic
497	C₂×#41	—	2	4	no	—
498	C₂×#41	—	4	4	no	—
499	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
500	C₂²×D₄	—	2	4	no	—
501	C₂²×D₄	—	4	4	no	—
502	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
503	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
504	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
505	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
506	C₂²×D₄	C₂³×C₃₁	1	4	yes	—
507	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
508	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
509	C₂³×C₄	—	4	4	no	—
510	C₂³×C₄	D₄×C₃₁	1	8	yes	complemented
511	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
512	C₂³×C₄	C₂³×C₃₁	1	4	yes	—
513	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
514	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
515	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
516	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
517	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
518	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
519	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
520	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
521	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
522	#123	—	2	8	no	—
523	#123	—	2	8	no	—
524	#123	—	2	8	no	—
525	#123	—	2	8	no	—
526	#123	—	2	8	no	—
527	#123	—	2	8	no	—
528	C₂²⋊Q₈	—	2	4	no	—
529	C₂²⋊Q₈	—	2	4	no	—
530	#121	—	2	4	no	—
531	#121	—	2	4	no	—
532	#121	—	4	8	no	—
533	#120	—	2	8	no	—
534	#120	—	2	8	no	—
535	C₄×D₄	—	2	8	no	—
536	C₄×D₄	—	2	8	no	—
537	#117	—	2	4	no	—
538	C₂×C₄⋊C₄	—	2	4	no	—
539	C₂×C₄⋊C₄	—	2	4	no	—
540	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
541	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
542	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
543	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
544	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
545	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
546	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
547	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
548	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
549	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
550	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
551	C₂×C₂²⋊C₄	—	2	4	no	—
552	C₂×C₂²⋊C₄	—	2	4	no	—
553	C₂×C₂²⋊C₄	—	2	4	no	—
554	C₂×C₂²⋊C₄	—	2	8	no	—
555	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
556	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
557	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
558	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
559	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
560	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
561	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
562	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
563	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
564	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
565	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
566	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
567	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
568	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
569	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
570	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
571	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
572	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
573	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
574	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
575	C₂×C₄²	—	4	4	no	—
576	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
577	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
578	C₂×C₄²	C₂³×C₃₁	1	4	yes	—
579	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
580	#95	C₂³×C₃₁	1	4	yes	—
581	#95	C₂³×C₃₁	1	2	yes	—
582	#95	C₂³×C₃₁	1	2	yes	—
583	#95	C₂³×C₃₁	1	4	yes	—
584	#95	C₂³×C₃₁	1	4	yes	—
585	#95	C₂³×C₃₁	1	4	yes	—
586	#95	C₂³×C₃₁	1	4	yes	—
587	#95	C₂³×C₃₁	1	4	yes	—
588	#95	C₂³×C₃₁	1	4	yes	—
589	C₃₁	#35064	1	1	yes	characteristic, direct product factor, Sylow
590	C₂⁴	—	2	4	no	—
591	C₂⁴	—	2	4	no	—
592	C₂⁴	—	2	2	no	—
593	C₂⁴	—	2	4	no	—
594	C₂⁴	—	4	2	no	—
595	C₂⁴	—	4	2	no	—
596	C₂⁴	—	4	2	no	—
597	C₂⁴	C₂×D₄×C₃₁	1	4	yes	—
598	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
599	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
600	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
601	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
602	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
603	#41	—	4	16	no	—
604	C₂×Q₈	—	2	2	no	—
605	C₂×Q₈	—	4	2	no	—
606	C₂×D₄	—	2	4	no	—
607	C₂×D₄	—	2	4	no	—
608	C₂×D₄	—	2	4	no	—
609	C₂×D₄	—	2	4	no	—
610	C₂×D₄	—	2	4	no	—
611	C₂×D₄	—	2	4	no	—
612	C₂×D₄	—	2	4	no	—
613	C₂×D₄	—	2	8	no	—
614	C₂×D₄	—	2	8	no	—
615	C₂×D₄	—	2	2	no	—
616	C₂×D₄	—	2	8	no	—
617	C₂×D₄	—	4	4	no	—
618	C₂×D₄	—	4	4	no	—
619	C₂×D₄	—	4	2	no	—
620	C₂×D₄	—	4	4	no	—
621	C₂×D₄	—	4	4	no	—
622	C₂×D₄	—	4	16	no	—
623	C₂²×C₄	—	2	4	no	—
624	C₂²×C₄	—	2	4	no	—
625	C₂²×C₄	—	2	2	no	—
626	C₂²×C₄	—	2	2	no	—
627	C₂²×C₄	—	2	2	no	—
628	C₂²×C₄	—	2	4	no	—
629	C₂²×C₄	—	2	8	no	—
630	C₂²×C₄	—	2	4	no	—
631	C₂²×C₄	—	2	8	no	—
632	C₂²×C₄	—	4	16	no	—
633	C₂²×C₄	—	4	2	no	—
634	C₂²×C₄	—	4	2	no	—
635	C₂²×C₄	—	4	2	no	—
636	C₂²×C₄	—	4	2	no	—
637	C₂²×C₄	—	4	4	no	—
638	C₂²×C₄	—	4	2	no	—
639	C₂²×C₄	—	4	2	no	—
640	C₂²×C₄	—	4	4	no	—
641	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
642	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
643	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
644	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
645	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
646	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
647	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
648	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
649	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
650	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
651	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
652	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
653	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
654	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
655	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
656	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
657	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
658	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
659	C₄⋊C₄	—	2	4	no	—
660	C₄⋊C₄	—	2	4	no	—
661	C₄⋊C₄	—	2	4	no	—
662	C₄⋊C₄	—	2	4	no	—
663	C₄⋊C₄	—	2	2	no	—
664	C₄⋊C₄	—	2	2	no	—
665	C₄⋊C₄	—	2	4	no	—
666	C₄⋊C₄	—	2	4	no	—
667	C₄⋊C₄	—	2	8	no	—
668	C₄⋊C₄	—	4	4	no	—
669	C₄⋊C₄	—	4	4	no	—
670	C₂²⋊C₄	—	2	4	no	—
671	C₂²⋊C₄	—	2	4	no	—
672	C₂²⋊C₄	—	2	4	no	—
673	C₂²⋊C₄	—	2	4	no	—
674	C₂²⋊C₄	—	2	4	no	—
675	C₂²⋊C₄	—	2	4	no	—
676	C₂²⋊C₄	—	2	4	no	—
677	C₂²⋊C₄	—	2	4	no	—
678	C₂²⋊C₄	—	2	4	no	—
679	C₂²⋊C₄	—	2	4	no	—
680	C₂²⋊C₄	—	2	4	no	—
681	C₂²⋊C₄	—	2	4	no	—
682	C₂²⋊C₄	—	2	8	no	—
683	C₂²⋊C₄	—	2	8	no	—
684	C₂²⋊C₄	—	2	8	no	—
685	C₂²⋊C₄	—	4	4	no	—
686	C₂²⋊C₄	—	4	4	no	—
687	C₂²⋊C₄	—	4	4	no	—
688	C₂²⋊C₄	—	4	4	no	—
689	C₂²⋊C₄	#41×C₃₁	1	8	yes	complemented
690	C₄²	—	2	4	no	—
691	C₄²	—	4	2	no	—
692	C₄²	—	4	4	no	—
693	C₄²	—	4	2	no	—
694	C₂³	—	2	2	no	—
695	C₂³	—	2	2	no	—
696	C₂³	—	2	2	no	—
697	C₂³	—	2	2	no	—
698	C₂³	—	2	8	no	—
699	C₂³	—	2	8	no	—
700	C₂³	—	2	2	no	—
701	C₂³	—	2	2	no	—
702	C₂³	—	2	2	no	—
703	C₂³	—	2	2	no	—
704	C₂³	—	2	2	no	—
705	C₂³	—	2	2	no	—
706	C₂³	—	2	4	no	—
707	C₂³	—	2	2	no	—
708	C₂³	—	2	4	no	—
709	C₂³	—	2	4	no	—
710	C₂³	—	2	2	no	—
711	C₂³	—	2	4	no	—
712	C₂³	—	2	2	no	—
713	C₂³	—	4	4	no	—
714	C₂³	—	4	16	no	—
715	C₂³	—	4	4	no	—
716	C₂³	—	4	4	no	—
717	C₂³	—	4	4	no	—
718	C₂³	—	8	8	no	—
719	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
720	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
721	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
722	C₂³	C₂×#41×C₃₁	1	4	yes	—
723	C₂³	C₃₁×H(5,𝔽₂)	1	4	yes	—
724	C₂³	C₂⁵×C₃₁	1	1	yes	characteristic
725	Q₈	—	4	4	no	—
726	D₄	—	4	4	no	—
727	D₄	—	4	8	no	—
728	D₄	—	4	8	no	—
729	D₄	—	4	8	no	—
730	D₄	—	4	8	no	—
731	D₄	—	4	8	no	—
732	D₄	—	8	8	no	—
733	C₂×C₄	—	2	8	no	—
734	C₂×C₄	—	2	8	no	—
735	C₂×C₄	—	2	4	no	—
736	C₂×C₄	—	2	2	no	—
737	C₂×C₄	—	2	2	no	—
738	C₂×C₄	—	2	2	no	—
739	C₂×C₄	—	2	2	no	—
740	C₂×C₄	—	2	4	no	—
741	C₂×C₄	—	2	2	no	—
742	C₂×C₄	—	2	2	no	—
743	C₂×C₄	—	2	2	no	—
744	C₂×C₄	—	2	2	no	—
745	C₂×C₄	—	2	2	no	—
746	C₂×C₄	—	2	2	no	—
747	C₂×C₄	—	2	4	no	—
748	C₂×C₄	—	2	2	no	—
749	C₂×C₄	—	2	4	no	—
750	C₂×C₄	—	2	2	no	—
751	C₂×C₄	—	2	4	no	—
752	C₂×C₄	—	2	4	no	—
753	C₂×C₄	—	2	4	no	—
754	C₂×C₄	—	2	2	no	—
755	C₂×C₄	—	2	4	no	—
756	C₂×C₄	—	2	4	no	—
757	C₂×C₄	—	2	2	no	—
758	C₂×C₄	—	4	4	no	—
759	C₂×C₄	—	4	4	no	—
760	C₂×C₄	—	4	4	no	—
761	C₂×C₄	—	4	4	no	—
762	C₂×C₄	—	4	16	no	—
763	C₂×C₄	—	4	8	no	—
764	C₂×C₄	—	4	4	no	—
765	C₂×C₄	—	4	4	no	—
766	C₂×C₄	—	4	4	no	—
767	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
768	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
769	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
770	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
771	C₂×C₄	C₂×#41×C₃₁	1	8	yes	—
772	C₂²	—	2	2	no	—
773	C₂²	—	2	2	no	—
774	C₂²	—	2	2	no	—
775	C₂²	—	2	2	no	—
776	C₂²	—	2	8	no	—
777	C₂²	—	2	8	no	—
778	C₂²	—	2	2	no	—
779	C₂²	—	2	2	no	—
780	C₂²	—	2	2	no	—
781	C₂²	—	4	16	no	—
782	C₂²	—	4	4	no	—
783	C₂²	—	4	2	no	—
784	C₂²	—	4	2	no	—
785	C₂²	—	4	2	no	—
786	C₂²	—	4	2	no	—
787	C₂²	—	4	2	no	—
788	C₂²	—	4	2	no	—
789	C₂²	—	4	4	no	—
790	C₂²	—	4	4	no	—
791	C₂²	—	4	4	no	—
792	C₂²	—	4	4	no	—
793	C₂²	—	8	8	no	—
794	C₂²	C₃₁×#532	1	4	yes	—
795	C₂²	C₃₁×#534	1	4	yes	—
796	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
797	C₂²	C₂²×#41×C₃₁	1	2	yes	—
798	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	2	yes	—
799	C₂²	C₃₁×#585	1	2	yes	—
800	C₄	—	2	2	no	—
801	C₄	—	2	2	no	—
802	C₄	—	2	2	no	—
803	C₄	—	2	2	no	—
804	C₄	—	2	8	no	—
805	C₄	—	4	2	no	—
806	C₄	—	4	2	no	—
807	C₄	—	4	2	no	—
808	C₄	—	4	2	no	—
809	C₄	—	4	2	no	—
810	C₄	—	4	2	no	—
811	C₄	—	4	4	no	—
812	C₂	—	2	4	no	—
813	C₂	—	2	4	no	—
814	C₂	—	4	2	no	—
815	C₂	—	8	2	no	—
816	C₂	—	8	2	no	—
817	C₂	C₂×C₃₁×#532	1	1	yes	characteristic
818	C₂	C₂×C₃₁×#534	1	1	yes	characteristic
819	C₂	C₃₁×#3449	1	1	yes	characteristic
820	C₂	C₃₁×#3513	1	4	yes	—

	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×#525	C₂	semidirect
2. C₂²×C₃₁×#123	C₂	semidirect
3. C₃₁×#2854	C₂	semidirect
4. C₃₁×#2663	C₂	semidirect
5. C₃₁×#2661	C₂	semidirect
6. C₃₁×#2602	C₂	semidirect
7. C₃₁×#2591	C₂	semidirect
8. C₃₁×#2583	C₂	semidirect
9. C₃₁×#2561	C₂	semidirect
10. C₃₁×#2539	C₂	semidirect
11. C₃₁×#2498	C₂	semidirect
12. C₃₁×#2430	C₂	semidirect
13. C₃₁×#2412	C₂	semidirect
14. C₃₁×#2410	C₂	semidirect
15. C₃₁×#2322	C₂	semidirect
16. C₃₁×#2321	C₂	semidirect
17. C₂×C₄×C₂²⋊C₄×C₃₁	C₂	semidirect
18. C₂²×#41×C₃₁	C₂²	semidirect
28. C₂×C₃₁×#123	C₂²	semidirect
30. C₂×C₃₁×C₂²⋊Q₈	C₂²	semidirect
33. C₂×C₃₁×#121	C₂²	semidirect
37. C₂×C₄×D₄×C₃₁	C₂²	semidirect
38. C₂×C₃₁×#117	C₂²	semidirect
45. C₂²×C₄²×C₃₁	C₂²	semidirect
46. C₃₁×#400	C₂²	semidirect
47. C₃₁×#399	C₂²	semidirect
48. C₃₁×#398	C₂²	semidirect
49. C₃₁×#397	C₂²	semidirect
50. C₃₁×#397	C₂²	semidirect
51. C₃₁×#395	C₂²	semidirect
53. C₃₁×#394	C₂²	semidirect
54. C₃₁×#394	C₂²	semidirect
55. C₃₁×#393	C₂²	semidirect
57. C₃₁×#392	C₂²	semidirect
58. C₃₁×#390	C₂²	semidirect
59. C₃₁×#390	C₂²	semidirect
60. C₃₁×#389	C₂²	semidirect
61. C₃₁×#389	C₂²	semidirect
62. C₃₁×#388	C₂²	semidirect
63. C₃₁×#388	C₂²	semidirect
64. C₃₁×#388	C₂²	semidirect
65. C₃₁×#388	C₂²	semidirect
66. C₃₁×#388	C₂²	semidirect
67. C₃₁×#387	C₂²	semidirect
71. C₃₁×#386	C₂²	semidirect
72. C₃₁×#386	C₂²	semidirect
75. C₃₁×#385	C₂²	semidirect
77. C₃₁×#380	C₂²	semidirect
82. C₄×C₂²⋊C₄×C₃₁	C₂²	semidirect
83. C₄×C₂²⋊C₄×C₃₁	C₂²	semidirect
84. C₂×C₃₁×#95	C₂²	semidirect
100. C₂³×C₄×C₃₁	D₄	semidirect
278. C₂²⋊C₄×C₃₁	#41	semidirect
283. #35064	C₃₁	direct (N × H)
362. C₂×#525	C₂×C₃₁	semidirect
363. C₂²×#123	C₂×C₃₁	semidirect
364. #2854	C₂×C₃₁	semidirect
365. #2663	C₂×C₃₁	semidirect
366. #2661	C₂×C₃₁	semidirect
367. #2602	C₂×C₃₁	semidirect
368. #2591	C₂×C₃₁	semidirect
369. #2583	C₂×C₃₁	semidirect
370. #2561	C₂×C₃₁	semidirect
371. #2539	C₂×C₃₁	semidirect
372. #2498	C₂×C₃₁	semidirect
373. #2430	C₂×C₃₁	semidirect
374. #2412	C₂×C₃₁	semidirect
375. #2410	C₂×C₃₁	semidirect
376. #2322	C₂×C₃₁	semidirect
377. #2321	C₂×C₃₁	semidirect
378. C₂×C₄×C₂²⋊C₄	C₂×C₃₁	semidirect
419. C₂²×#41	C₂²×C₃₁	semidirect
429. C₂×#123	C₂²×C₃₁	semidirect
431. C₂×C₂²⋊Q₈	C₂²×C₃₁	semidirect
434. C₂×#121	C₂²×C₃₁	semidirect
438. C₂×C₄×D₄	C₂²×C₃₁	semidirect
439. C₂×#117	C₂²×C₃₁	semidirect
446. C₂²×C₄²	C₂²×C₃₁	semidirect
447. #400	C₂²×C₃₁	semidirect
448. #399	C₂²×C₃₁	semidirect
449. #398	C₂²×C₃₁	semidirect
450. #397	C₂²×C₃₁	semidirect
451. #397	C₂²×C₃₁	semidirect
452. #395	C₂²×C₃₁	semidirect
454. #394	C₂²×C₃₁	semidirect
455. #394	C₂²×C₃₁	semidirect
456. #393	C₂²×C₃₁	semidirect
458. #392	C₂²×C₃₁	semidirect
459. #390	C₂²×C₃₁	semidirect
460. #390	C₂²×C₃₁	semidirect
461. #389	C₂²×C₃₁	semidirect
462. #389	C₂²×C₃₁	semidirect
463. #388	C₂²×C₃₁	semidirect
464. #388	C₂²×C₃₁	semidirect
465. #388	C₂²×C₃₁	semidirect
466. #388	C₂²×C₃₁	semidirect
467. #388	C₂²×C₃₁	semidirect
468. #387	C₂²×C₃₁	semidirect
472. #386	C₂²×C₃₁	semidirect
473. #386	C₂²×C₃₁	semidirect
476. #385	C₂²×C₃₁	semidirect
478. #380	C₂²×C₃₁	semidirect
483. C₄×C₂²⋊C₄	C₂²×C₃₁	semidirect
484. C₄×C₂²⋊C₄	C₂²×C₃₁	semidirect
485. C₂×#95	C₂²×C₃₁	semidirect
510. C₂³×C₄	D₄×C₃₁	semidirect
589. C₃₁	#35064	direct (N × H)
689. C₂²⋊C₄	#41×C₃₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃₁×#525	2
C₂²×C₃₁×#123	2
C₃₁×#2854	2
C₃₁×#2663	2
C₃₁×#2661	2
C₃₁×#2602	2
C₃₁×#2591	2
C₃₁×#2583	2
C₃₁×#2561	2
C₃₁×#2539	2
C₃₁×#2498	2
C₃₁×#2430	2
C₃₁×#2412	2
C₃₁×#2410	2
C₃₁×#2322	2
C₃₁×#2321	2
C₂×C₄×C₂²⋊C₄×C₃₁	2
#35064	31

Subgroups — C31×#35064 #21491823

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#35064 #21491823