Subgroups — C₃₁×#34957 #21491716

Order 7936.

3206 conjugacy classes of subgroups.

The subgroup lattice has 840 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×C₄×D₄×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#2602	C₂	1	4	yes	maximal, complemented
4	C₃₁×#2591	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#2583	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#2564	C₂	1	2	yes	maximal, complemented
7	C₃₁×#2561	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#2543	C₂	1	2	yes	maximal, complemented
9	C₃₁×#2539	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#2412	C₂	1	2	yes	maximal, complemented
11	C₃₁×#2410	C₂	1	2	yes	maximal, complemented
12	C₃₁×#2395	C₂	1	2	yes	maximal, complemented
13	C₃₁×#2388	C₂	1	2	yes	maximal, complemented
14	C₄×C₃₁×#123	C₂	1	2	yes	maximal, complemented
15	C₄×C₃₁×#121	C₂	1	4	yes	maximal, complemented
16	C₄×C₃₁×#120	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	C₂⁴×C₄×C₃₁	C₂²	1	1	yes	characteristic
22	C₃₁×#525	—	2	8	no	—
23	C₂×C₃₁×#123	C₂²	1	2	yes	—
24	C₂×C₃₁×#123	C₂²	1	2	yes	complemented
25	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
26	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₃₁×#121	C₂²	1	1	yes	characteristic
28	C₂×C₃₁×#121	C₂²	1	4	yes	—
29	C₂×C₃₁×#121	C₂²	1	1	yes	characteristic, complemented
30	C₂×C₃₁×#120	C₂²	1	2	yes	—
31	C₂×C₃₁×#120	C₂²	1	2	yes	—
32	C₂×C₄×D₄×C₃₁	—	2	8	no	—
33	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
34	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
35	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
36	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
37	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
38	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	complemented
39	C₂×C₄×D₄×C₃₁	C₂²	1	4	yes	complemented
40	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic, complemented
41	C₂²×C₄⋊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	1	yes	characteristic
46	C₂²×C₄²×C₃₁	C₂²	1	2	yes	complemented
47	C₃₁×#400	C₂²	1	2	yes	complemented
48	C₃₁×#399	C₂²	1	2	yes	complemented
49	C₃₁×#398	C₂²	1	2	yes	complemented
50	C₃₁×#397	C₂²	1	4	yes	complemented
51	C₃₁×#397	C₂²	1	2	yes	complemented
52	C₃₁×#395	C₂²	1	2	yes	complemented
53	C₃₁×#394	C₂²	1	4	yes	—
54	C₃₁×#394	C₂²	1	2	yes	complemented
55	C₃₁×#394	C₂²	1	4	yes	complemented
56	C₃₁×#393	C₂²	1	2	yes	complemented
57	C₃₁×#392	C₂²	1	4	yes	—
58	C₃₁×#392	C₂²	1	2	yes	complemented
59	C₃₁×#390	C₂²	1	4	yes	complemented
60	C₃₁×#389	C₂²	1	4	yes	complemented
61	C₃₁×#388	C₂²	1	4	yes	complemented
62	C₃₁×#388	C₂²	1	4	yes	complemented
63	C₃₁×#388	C₂²	1	4	yes	complemented
64	C₃₁×#387	C₂²	1	4	yes	complemented
65	C₃₁×#386	C₂²	1	4	yes	—
66	C₃₁×#386	C₂²	1	2	yes	—
67	C₃₁×#386	C₂²	1	2	yes	—
68	C₃₁×#386	C₂²	1	4	yes	complemented
69	C₃₁×#386	C₂²	1	4	yes	complemented
70	C₃₁×#385	C₂²	1	2	yes	—
71	C₃₁×#385	C₂²	1	2	yes	—
72	C₃₁×#385	C₂²	1	4	yes	complemented
73	C₃₁×#381	C₂²	1	2	yes	—
74	C₃₁×#380	C₂²	1	4	yes	complemented
75	C₃₁×#379	C₂²	1	2	yes	—
76	C₄×C₄⋊C₄×C₃₁	C₂²	1	4	yes	complemented
77	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
78	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
79	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
80	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	complemented
81	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	complemented
82	C₄×C₂²⋊C₄×C₃₁	C₂²	1	4	yes	complemented
83	C₄×C₂²⋊C₄×C₃₁	C₂²	1	4	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	—	2	8	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	4	yes	—
96	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
97	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
98	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
99	C₂³×C₄×C₃₁	—	2	4	no	—
100	C₂³×C₄×C₃₁	—	4	4	no	—
101	C₂³×C₄×C₃₁	—	4	4	no	—
102	C₂³×C₄×C₃₁	D₄	1	8	yes	complemented
103	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
104	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
105	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
106	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
107	C₂³×C₄×C₃₁	C₂³	1	4	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	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
113	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
114	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
115	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
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	16	no	—
121	C₃₁×#121	—	2	4	no	—
122	C₃₁×#121	—	2	4	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	C₄×D₄×C₃₁	—	2	8	no	—
128	C₄×D₄×C₃₁	—	2	8	no	—
129	C₄×D₄×C₃₁	—	2	8	no	—
130	C₄×D₄×C₃₁	—	2	8	no	—
131	C₄×D₄×C₃₁	—	4	8	no	—
132	C₃₁×#117	—	2	4	no	—
133	C₂×C₄⋊C₄×C₃₁	—	2	4	no	—
134	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
135	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
136	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
137	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
138	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
139	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
140	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
141	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
142	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
143	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
144	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
145	C₂×C₂²⋊C₄×C₃₁	—	2	8	no	—
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	2	yes	—
149	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
150	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
151	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	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	2	yes	—
164	C₂×C₄²×C₃₁	—	2	4	no	—
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	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
171	C₂×C₄²×C₃₁	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	2	yes	—
177	C₃₁×#95	C₂³	1	4	yes	—
178	C₃₁×#95	C₂³	1	4	yes	—
179	C₃₁×#95	C₂³	1	4	yes	—
180	C₃₁×#95	C₂³	1	4	yes	—
181	C₂⁴×C₃₁	—	2	2	no	—
182	C₂⁴×C₃₁	—	2	4	no	—
183	C₂⁴×C₃₁	—	2	4	no	—
184	C₂⁴×C₃₁	—	2	4	no	—
185	C₂⁴×C₃₁	—	2	4	no	—
186	C₂⁴×C₃₁	—	4	2	no	—
187	C₂⁴×C₃₁	—	4	2	no	—
188	C₂⁴×C₃₁	C₂×D₄	1	4	yes	—
189	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
190	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
191	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
192	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
193	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
194	#41×C₃₁	—	4	16	no	—
195	C₂×Q₈×C₃₁	—	2	2	no	—
196	C₂×Q₈×C₃₁	—	4	2	no	—
197	C₂×D₄×C₃₁	—	2	32	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	4	no	—
203	C₂×D₄×C₃₁	—	2	4	no	—
204	C₂×D₄×C₃₁	—	2	4	no	—
205	C₂×D₄×C₃₁	—	2	4	no	—
206	C₂×D₄×C₃₁	—	2	8	no	—
207	C₂×D₄×C₃₁	—	2	8	no	—
208	C₂×D₄×C₃₁	—	2	4	no	—
209	C₂×D₄×C₃₁	—	2	2	no	—
210	C₂×D₄×C₃₁	—	2	4	no	—
211	C₂×D₄×C₃₁	—	2	8	no	—
212	C₂×D₄×C₃₁	—	4	4	no	—
213	C₂×D₄×C₃₁	—	4	2	no	—
214	C₂×D₄×C₃₁	—	4	4	no	—
215	C₂×D₄×C₃₁	#41	1	8	yes	complemented
216	C₂²×C₄×C₃₁	—	2	2	no	—
217	C₂²×C₄×C₃₁	—	2	4	no	—
218	C₂²×C₄×C₃₁	—	2	4	no	—
219	C₂²×C₄×C₃₁	—	2	4	no	—
220	C₂²×C₄×C₃₁	—	2	4	no	—
221	C₂²×C₄×C₃₁	—	2	2	no	—
222	C₂²×C₄×C₃₁	—	2	2	no	—
223	C₂²×C₄×C₃₁	—	2	8	no	—
224	C₂²×C₄×C₃₁	—	2	4	no	—
225	C₂²×C₄×C₃₁	—	2	4	no	—
226	C₂²×C₄×C₃₁	—	2	4	no	—
227	C₂²×C₄×C₃₁	—	2	4	no	—
228	C₂²×C₄×C₃₁	—	2	8	no	—
229	C₂²×C₄×C₃₁	—	2	8	no	—
230	C₂²×C₄×C₃₁	—	2	8	no	—
231	C₂²×C₄×C₃₁	—	4	16	no	—
232	C₂²×C₄×C₃₁	—	4	4	no	—
233	C₂²×C₄×C₃₁	—	4	2	no	—
234	C₂²×C₄×C₃₁	—	4	2	no	—
235	C₂²×C₄×C₃₁	—	4	2	no	—
236	C₂²×C₄×C₃₁	—	4	4	no	—
237	C₂²×C₄×C₃₁	—	4	2	no	—
238	C₂²×C₄×C₃₁	—	4	16	no	—
239	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
240	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
241	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
242	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
243	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
244	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
245	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
246	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
247	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
248	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
249	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
250	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
251	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
252	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
253	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
254	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
255	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
256	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
257	C₄⋊C₄×C₃₁	—	2	4	no	—
258	C₄⋊C₄×C₃₁	—	2	4	no	—
259	C₄⋊C₄×C₃₁	—	2	2	no	—
260	C₄⋊C₄×C₃₁	—	2	2	no	—
261	C₄⋊C₄×C₃₁	—	2	4	no	—
262	C₄⋊C₄×C₃₁	—	2	4	no	—
263	C₄⋊C₄×C₃₁	—	2	8	no	—
264	C₄⋊C₄×C₃₁	—	2	8	no	—
265	C₄⋊C₄×C₃₁	—	4	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	4	no	—
272	C₂²⋊C₄×C₃₁	—	2	8	no	—
273	C₂²⋊C₄×C₃₁	—	2	4	no	—
274	C₂²⋊C₄×C₃₁	—	2	4	no	—
275	C₂²⋊C₄×C₃₁	—	2	4	no	—
276	C₂²⋊C₄×C₃₁	—	2	4	no	—
277	C₂²⋊C₄×C₃₁	—	2	8	no	—
278	C₂²⋊C₄×C₃₁	—	2	8	no	—
279	C₂²⋊C₄×C₃₁	—	2	8	no	—
280	C₂²⋊C₄×C₃₁	—	2	8	no	—
281	C₂²⋊C₄×C₃₁	—	4	4	no	—
282	C₂²⋊C₄×C₃₁	—	4	4	no	—
283	C₂²⋊C₄×C₃₁	#41	1	8	yes	complemented
284	C₄²×C₃₁	—	2	4	no	—
285	C₄²×C₃₁	—	2	4	no	—
286	C₄²×C₃₁	—	2	4	no	—
287	C₄²×C₃₁	—	2	8	no	—
288	C₄²×C₃₁	—	4	2	no	—
289	C₄²×C₃₁	—	4	2	no	—
290	#34957	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
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	8	no	—
296	C₂³×C₃₁	—	2	8	no	—
297	C₂³×C₃₁	—	2	8	no	—
298	C₂³×C₃₁	—	2	2	no	—
299	C₂³×C₃₁	—	2	2	no	—
300	C₂³×C₃₁	—	2	4	no	—
301	C₂³×C₃₁	—	2	2	no	—
302	C₂³×C₃₁	—	2	2	no	—
303	C₂³×C₃₁	—	2	4	no	—
304	C₂³×C₃₁	—	2	2	no	—
305	C₂³×C₃₁	—	2	2	no	—
306	C₂³×C₃₁	—	2	2	no	—
307	C₂³×C₃₁	—	2	4	no	—
308	C₂³×C₃₁	—	2	2	no	—
309	C₂³×C₃₁	—	2	4	no	—
310	C₂³×C₃₁	—	4	4	no	—
311	C₂³×C₃₁	—	4	16	no	—
312	C₂³×C₃₁	—	4	16	no	—
313	C₂³×C₃₁	—	4	4	no	—
314	C₂³×C₃₁	—	4	4	no	—
315	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
316	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
317	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
318	C₂³×C₃₁	C₂×#41	1	4	yes	—
319	C₂³×C₃₁	C₂×#41	1	4	yes	—
320	C₂³×C₃₁	C₂×#41	1	4	yes	—
321	C₂³×C₃₁	C₂⁵	1	1	yes	characteristic
322	Q₈×C₃₁	—	4	4	no	—
323	D₄×C₃₁	—	2	16	no	—
324	D₄×C₃₁	—	2	16	no	—
325	D₄×C₃₁	—	4	16	no	—
326	D₄×C₃₁	—	4	4	no	—
327	D₄×C₃₁	—	4	8	no	—
328	D₄×C₃₁	—	4	8	no	—
329	D₄×C₃₁	—	4	8	no	—
330	C₂×C₄×C₃₁	—	2	8	no	—
331	C₂×C₄×C₃₁	—	2	2	no	—
332	C₂×C₄×C₃₁	—	2	4	no	—
333	C₂×C₄×C₃₁	—	2	2	no	—
334	C₂×C₄×C₃₁	—	2	4	no	—
335	C₂×C₄×C₃₁	—	2	2	no	—
336	C₂×C₄×C₃₁	—	2	2	no	—
337	C₂×C₄×C₃₁	—	2	2	no	—
338	C₂×C₄×C₃₁	—	2	8	no	—
339	C₂×C₄×C₃₁	—	2	8	no	—
340	C₂×C₄×C₃₁	—	2	8	no	—
341	C₂×C₄×C₃₁	—	2	2	no	—
342	C₂×C₄×C₃₁	—	2	2	no	—
343	C₂×C₄×C₃₁	—	2	2	no	—
344	C₂×C₄×C₃₁	—	2	2	no	—
345	C₂×C₄×C₃₁	—	2	2	no	—
346	C₂×C₄×C₃₁	—	2	4	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	4	no	—
353	C₂×C₄×C₃₁	—	2	4	no	—
354	C₂×C₄×C₃₁	—	2	4	no	—
355	C₂×C₄×C₃₁	—	4	4	no	—
356	C₂×C₄×C₃₁	—	4	4	no	—
357	C₂×C₄×C₃₁	—	4	4	no	—
358	C₂×C₄×C₃₁	—	4	16	no	—
359	C₂×C₄×C₃₁	—	4	8	no	—
360	C₂×C₄×C₃₁	—	4	4	no	—
361	C₂×C₄×C₃₁	—	4	4	no	—
362	C₂×C₄×C₃₁	—	4	8	no	—
363	C₂×C₄×C₃₁	—	4	8	no	—
364	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
365	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
366	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
367	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
368	C₂×C₄×C₃₁	C₂×#41	1	8	yes	—
369	C₂×C₄×C₃₁	C₂×#41	1	4	yes	—
370	C₂×C₄×C₃₁	H(5,𝔽₂)	1	4	yes	—
371	C₂×#525	C₂×C₃₁	1	1	yes	characteristic, complemented
372	C₂²×C₄×D₄	C₂×C₃₁	1	1	yes	characteristic, complemented
373	#2602	C₂×C₃₁	1	4	yes	complemented
374	#2591	C₂×C₃₁	1	1	yes	characteristic, complemented
375	#2583	C₂×C₃₁	1	1	yes	characteristic, complemented
376	#2564	C₂×C₃₁	1	2	yes	complemented
377	#2561	C₂×C₃₁	1	1	yes	characteristic, complemented
378	#2543	C₂×C₃₁	1	2	yes	complemented
379	#2539	C₂×C₃₁	1	1	yes	characteristic, complemented
380	#2412	C₂×C₃₁	1	2	yes	complemented
381	#2410	C₂×C₃₁	1	2	yes	complemented
382	#2395	C₂×C₃₁	1	2	yes	complemented
383	#2388	C₂×C₃₁	1	2	yes	complemented
384	C₄×#123	C₂×C₃₁	1	2	yes	complemented
385	C₄×#121	C₂×C₃₁	1	4	yes	complemented
386	C₄×#120	C₂×C₃₁	1	2	yes	complemented
387	C₂×C₄×C₂²⋊C₄	C₂×C₃₁	1	1	yes	characteristic, complemented
388	C₂²×C₃₁	—	2	2	no	—
389	C₂²×C₃₁	—	2	2	no	—
390	C₂²×C₃₁	—	2	2	no	—
391	C₂²×C₃₁	—	2	2	no	—
392	C₂²×C₃₁	—	2	8	no	—
393	C₂²×C₃₁	—	2	8	no	—
394	C₂²×C₃₁	—	2	2	no	—
395	C₂²×C₃₁	—	2	4	no	—
396	C₂²×C₃₁	—	2	2	no	—
397	C₂²×C₃₁	—	2	2	no	—
398	C₂²×C₃₁	—	2	8	no	—
399	C₂²×C₃₁	—	4	16	no	—
400	C₂²×C₃₁	—	4	16	no	—
401	C₂²×C₃₁	—	4	2	no	—
402	C₂²×C₃₁	—	4	2	no	—
403	C₂²×C₃₁	—	4	4	no	—
404	C₂²×C₃₁	—	4	4	no	—
405	C₂²×C₃₁	—	4	2	no	—
406	C₂²×C₃₁	—	4	2	no	—
407	C₂²×C₃₁	—	4	2	no	—
408	C₂²×C₃₁	—	4	4	no	—
409	C₂²×C₃₁	—	4	4	no	—
410	C₂²×C₃₁	#525	1	4	yes	—
411	C₂²×C₃₁	#532	1	4	yes	—
412	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
413	C₂²×C₃₁	C₂²×#41	1	2	yes	—
414	C₂²×C₃₁	C₂²×#41	1	2	yes	—
415	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	2	yes	—
416	C₄×C₃₁	—	2	4	no	—
417	C₄×C₃₁	—	2	2	no	—
418	C₄×C₃₁	—	2	2	no	—
419	C₄×C₃₁	—	2	2	no	—
420	C₄×C₃₁	—	2	8	no	—
421	C₄×C₃₁	—	4	2	no	—
422	C₄×C₃₁	—	4	2	no	—
423	C₄×C₃₁	—	4	2	no	—
424	C₄×C₃₁	—	4	2	no	—
425	C₄×C₃₁	—	4	2	no	—
426	C₄×C₃₁	—	4	4	no	—
427	C₄×C₃₁	#534	1	4	yes	—
428	C₂²×#41	C₂²×C₃₁	1	1	yes	characteristic, complemented
429	C₂³×D₄	C₂²×C₃₁	1	1	yes	characteristic
430	C₂⁴×C₄	C₂²×C₃₁	1	1	yes	characteristic
431	C₂⁴×C₄	C₂²×C₃₁	1	1	yes	characteristic
432	#525	—	2	8	no	—
433	C₂×#123	C₂²×C₃₁	1	2	yes	—
434	C₂×#123	C₂²×C₃₁	1	2	yes	complemented
435	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
436	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
437	C₂×#121	C₂²×C₃₁	1	1	yes	characteristic
438	C₂×#121	C₂²×C₃₁	1	4	yes	—
439	C₂×#121	C₂²×C₃₁	1	1	yes	characteristic, complemented
440	C₂×#120	C₂²×C₃₁	1	2	yes	—
441	C₂×#120	C₂²×C₃₁	1	2	yes	—
442	C₂×C₄×D₄	—	2	8	no	—
443	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
444	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
445	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
446	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
447	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
448	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	complemented
449	C₂×C₄×D₄	C₂²×C₃₁	1	4	yes	complemented
450	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic, complemented
451	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
452	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
453	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
454	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
455	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
456	C₂²×C₄²	C₂²×C₃₁	1	2	yes	complemented
457	#400	C₂²×C₃₁	1	2	yes	complemented
458	#399	C₂²×C₃₁	1	2	yes	complemented
459	#398	C₂²×C₃₁	1	2	yes	complemented
460	#397	C₂²×C₃₁	1	2	yes	complemented
461	#397	C₂²×C₃₁	1	4	yes	complemented
462	#395	C₂²×C₃₁	1	2	yes	complemented
463	#394	C₂²×C₃₁	1	4	yes	—
464	#394	C₂²×C₃₁	1	2	yes	complemented
465	#394	C₂²×C₃₁	1	4	yes	complemented
466	#393	C₂²×C₃₁	1	2	yes	complemented
467	#392	C₂²×C₃₁	1	4	yes	—
468	#392	C₂²×C₃₁	1	2	yes	complemented
469	#390	C₂²×C₃₁	1	4	yes	complemented
470	#389	C₂²×C₃₁	1	4	yes	complemented
471	#388	C₂²×C₃₁	1	4	yes	complemented
472	#388	C₂²×C₃₁	1	4	yes	complemented
473	#388	C₂²×C₃₁	1	4	yes	complemented
474	#387	C₂²×C₃₁	1	4	yes	complemented
475	#386	C₂²×C₃₁	1	4	yes	—
476	#386	C₂²×C₃₁	1	2	yes	—
477	#386	C₂²×C₃₁	1	2	yes	—
478	#386	C₂²×C₃₁	1	4	yes	complemented
479	#386	C₂²×C₃₁	1	4	yes	complemented
480	#385	C₂²×C₃₁	1	2	yes	—
481	#385	C₂²×C₃₁	1	2	yes	—
482	#385	C₂²×C₃₁	1	4	yes	complemented
483	#381	C₂²×C₃₁	1	2	yes	—
484	#380	C₂²×C₃₁	1	4	yes	complemented
485	#379	C₂²×C₃₁	1	2	yes	—
486	C₄×C₄⋊C₄	C₂²×C₃₁	1	4	yes	complemented
487	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
488	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
489	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
490	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	complemented
491	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	complemented
492	C₄×C₂²⋊C₄	C₂²×C₃₁	1	4	yes	complemented
493	C₄×C₂²⋊C₄	C₂²×C₃₁	1	4	yes	complemented
494	C₂×#95	C₂²×C₃₁	1	2	yes	complemented
495	C₂×C₃₁	—	2	4	no	—
496	C₂×C₃₁	—	2	4	no	—
497	C₂×C₃₁	—	4	2	no	—
498	C₂×C₃₁	—	4	4	no	—
499	C₂×C₃₁	—	8	2	no	—
500	C₂×C₃₁	C₂×#525	1	1	yes	characteristic
501	C₂×C₃₁	C₂×#532	1	1	yes	characteristic
502	C₂×C₃₁	C₂×#534	1	1	yes	characteristic
503	C₂×C₃₁	#3481	1	4	yes	—
504	C₂⁵	C₂³×C₃₁	1	1	yes	characteristic
505	C₂⁵	C₂³×C₃₁	1	1	yes	characteristic
506	C₂×#41	—	2	4	no	—
507	C₂×#41	—	4	4	no	—
508	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
509	C₂²×D₄	—	2	4	no	—
510	C₂²×D₄	—	2	8	no	—
511	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
512	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
513	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
514	C₂²×D₄	C₂³×C₃₁	1	4	yes	—
515	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
516	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
517	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
518	C₂³×C₄	—	2	4	no	—
519	C₂³×C₄	—	4	4	no	—
520	C₂³×C₄	—	4	4	no	—
521	C₂³×C₄	D₄×C₃₁	1	8	yes	complemented
522	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
523	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
524	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
525	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
526	C₂³×C₄	C₂³×C₃₁	1	4	yes	—
527	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
528	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
529	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
530	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
531	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
532	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
533	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
534	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
535	#123	—	2	8	no	—
536	#123	—	2	8	no	—
537	C₂²⋊Q₈	—	2	4	no	—
538	C₂²⋊Q₈	—	2	4	no	—
539	#121	—	2	16	no	—
540	#121	—	2	4	no	—
541	#121	—	2	4	no	—
542	#120	—	2	8	no	—
543	#120	—	2	8	no	—
544	C₄×D₄	—	2	8	no	—
545	C₄×D₄	—	2	8	no	—
546	C₄×D₄	—	2	8	no	—
547	C₄×D₄	—	2	8	no	—
548	C₄×D₄	—	2	8	no	—
549	C₄×D₄	—	2	8	no	—
550	C₄×D₄	—	4	8	no	—
551	#117	—	2	4	no	—
552	C₂×C₄⋊C₄	—	2	4	no	—
553	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
554	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
555	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
556	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
557	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
558	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
559	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
560	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
561	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
562	C₂×C₂²⋊C₄	—	2	4	no	—
563	C₂×C₂²⋊C₄	—	2	4	no	—
564	C₂×C₂²⋊C₄	—	2	8	no	—
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	2	yes	—
569	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
570	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
571	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
572	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
573	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
574	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
575	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
576	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
577	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
578	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
579	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
580	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
581	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
582	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
583	C₂×C₄²	—	2	4	no	—
584	C₂×C₄²	—	4	4	no	—
585	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
586	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
587	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
588	C₂×C₄²	C₂³×C₃₁	1	4	yes	—
589	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
590	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
591	#95	C₂³×C₃₁	1	4	yes	—
592	#95	C₂³×C₃₁	1	2	yes	—
593	#95	C₂³×C₃₁	1	2	yes	—
594	#95	C₂³×C₃₁	1	4	yes	—
595	#95	C₂³×C₃₁	1	4	yes	—
596	#95	C₂³×C₃₁	1	4	yes	—
597	#95	C₂³×C₃₁	1	4	yes	—
598	#95	C₂³×C₃₁	1	4	yes	—
599	#95	C₂³×C₃₁	1	4	yes	—
600	C₃₁	#34957	1	1	yes	characteristic, direct product factor, Sylow
601	C₂⁴	—	2	2	no	—
602	C₂⁴	—	2	4	no	—
603	C₂⁴	—	2	4	no	—
604	C₂⁴	—	2	4	no	—
605	C₂⁴	—	2	4	no	—
606	C₂⁴	—	4	2	no	—
607	C₂⁴	—	4	2	no	—
608	C₂⁴	C₂×D₄×C₃₁	1	4	yes	—
609	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
610	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
611	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
612	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
613	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
614	#41	—	4	16	no	—
615	C₂×Q₈	—	2	2	no	—
616	C₂×Q₈	—	4	2	no	—
617	C₂×D₄	—	2	32	no	—
618	C₂×D₄	—	2	4	no	—
619	C₂×D₄	—	2	4	no	—
620	C₂×D₄	—	2	4	no	—
621	C₂×D₄	—	2	4	no	—
622	C₂×D₄	—	2	4	no	—
623	C₂×D₄	—	2	4	no	—
624	C₂×D₄	—	2	4	no	—
625	C₂×D₄	—	2	4	no	—
626	C₂×D₄	—	2	8	no	—
627	C₂×D₄	—	2	8	no	—
628	C₂×D₄	—	2	4	no	—
629	C₂×D₄	—	2	2	no	—
630	C₂×D₄	—	2	4	no	—
631	C₂×D₄	—	2	8	no	—
632	C₂×D₄	—	4	4	no	—
633	C₂×D₄	—	4	2	no	—
634	C₂×D₄	—	4	4	no	—
635	C₂×D₄	#41×C₃₁	1	8	yes	complemented
636	C₂²×C₄	—	2	2	no	—
637	C₂²×C₄	—	2	4	no	—
638	C₂²×C₄	—	2	4	no	—
639	C₂²×C₄	—	2	4	no	—
640	C₂²×C₄	—	2	4	no	—
641	C₂²×C₄	—	2	2	no	—
642	C₂²×C₄	—	2	2	no	—
643	C₂²×C₄	—	2	8	no	—
644	C₂²×C₄	—	2	4	no	—
645	C₂²×C₄	—	2	4	no	—
646	C₂²×C₄	—	2	4	no	—
647	C₂²×C₄	—	2	4	no	—
648	C₂²×C₄	—	2	8	no	—
649	C₂²×C₄	—	2	8	no	—
650	C₂²×C₄	—	2	8	no	—
651	C₂²×C₄	—	4	16	no	—
652	C₂²×C₄	—	4	4	no	—
653	C₂²×C₄	—	4	2	no	—
654	C₂²×C₄	—	4	2	no	—
655	C₂²×C₄	—	4	2	no	—
656	C₂²×C₄	—	4	4	no	—
657	C₂²×C₄	—	4	2	no	—
658	C₂²×C₄	—	4	16	no	—
659	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
660	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
661	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
662	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
663	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
664	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
665	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
666	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
667	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
668	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
669	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
670	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
671	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
672	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
673	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
674	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
675	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
676	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
677	C₄⋊C₄	—	2	4	no	—
678	C₄⋊C₄	—	2	4	no	—
679	C₄⋊C₄	—	2	2	no	—
680	C₄⋊C₄	—	2	2	no	—
681	C₄⋊C₄	—	2	4	no	—
682	C₄⋊C₄	—	2	4	no	—
683	C₄⋊C₄	—	2	8	no	—
684	C₄⋊C₄	—	2	8	no	—
685	C₄⋊C₄	—	4	4	no	—
686	C₂²⋊C₄	—	2	4	no	—
687	C₂²⋊C₄	—	2	4	no	—
688	C₂²⋊C₄	—	2	4	no	—
689	C₂²⋊C₄	—	2	4	no	—
690	C₂²⋊C₄	—	2	4	no	—
691	C₂²⋊C₄	—	2	4	no	—
692	C₂²⋊C₄	—	2	8	no	—
693	C₂²⋊C₄	—	2	4	no	—
694	C₂²⋊C₄	—	2	4	no	—
695	C₂²⋊C₄	—	2	4	no	—
696	C₂²⋊C₄	—	2	4	no	—
697	C₂²⋊C₄	—	2	8	no	—
698	C₂²⋊C₄	—	2	8	no	—
699	C₂²⋊C₄	—	2	8	no	—
700	C₂²⋊C₄	—	2	8	no	—
701	C₂²⋊C₄	—	4	4	no	—
702	C₂²⋊C₄	—	4	4	no	—
703	C₂²⋊C₄	#41×C₃₁	1	8	yes	complemented
704	C₄²	—	2	4	no	—
705	C₄²	—	2	4	no	—
706	C₄²	—	2	4	no	—
707	C₄²	—	2	8	no	—
708	C₄²	—	4	2	no	—
709	C₄²	—	4	2	no	—
710	C₂³	—	2	2	no	—
711	C₂³	—	2	2	no	—
712	C₂³	—	2	2	no	—
713	C₂³	—	2	2	no	—
714	C₂³	—	2	8	no	—
715	C₂³	—	2	8	no	—
716	C₂³	—	2	8	no	—
717	C₂³	—	2	2	no	—
718	C₂³	—	2	2	no	—
719	C₂³	—	2	4	no	—
720	C₂³	—	2	2	no	—
721	C₂³	—	2	2	no	—
722	C₂³	—	2	4	no	—
723	C₂³	—	2	2	no	—
724	C₂³	—	2	2	no	—
725	C₂³	—	2	2	no	—
726	C₂³	—	2	4	no	—
727	C₂³	—	2	2	no	—
728	C₂³	—	2	4	no	—
729	C₂³	—	4	4	no	—
730	C₂³	—	4	16	no	—
731	C₂³	—	4	16	no	—
732	C₂³	—	4	4	no	—
733	C₂³	—	4	4	no	—
734	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
735	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
736	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
737	C₂³	C₂×#41×C₃₁	1	4	yes	—
738	C₂³	C₂×#41×C₃₁	1	4	yes	—
739	C₂³	C₂×#41×C₃₁	1	4	yes	—
740	C₂³	C₂⁵×C₃₁	1	1	yes	characteristic
741	Q₈	—	4	4	no	—
742	D₄	—	2	16	no	—
743	D₄	—	2	16	no	—
744	D₄	—	4	16	no	—
745	D₄	—	4	4	no	—
746	D₄	—	4	8	no	—
747	D₄	—	4	8	no	—
748	D₄	—	4	8	no	—
749	C₂×C₄	—	2	8	no	—
750	C₂×C₄	—	2	2	no	—
751	C₂×C₄	—	2	4	no	—
752	C₂×C₄	—	2	2	no	—
753	C₂×C₄	—	2	4	no	—
754	C₂×C₄	—	2	2	no	—
755	C₂×C₄	—	2	2	no	—
756	C₂×C₄	—	2	2	no	—
757	C₂×C₄	—	2	8	no	—
758	C₂×C₄	—	2	8	no	—
759	C₂×C₄	—	2	8	no	—
760	C₂×C₄	—	2	2	no	—
761	C₂×C₄	—	2	2	no	—
762	C₂×C₄	—	2	2	no	—
763	C₂×C₄	—	2	2	no	—
764	C₂×C₄	—	2	2	no	—
765	C₂×C₄	—	2	4	no	—
766	C₂×C₄	—	2	4	no	—
767	C₂×C₄	—	2	2	no	—
768	C₂×C₄	—	2	4	no	—
769	C₂×C₄	—	2	4	no	—
770	C₂×C₄	—	2	2	no	—
771	C₂×C₄	—	2	4	no	—
772	C₂×C₄	—	2	4	no	—
773	C₂×C₄	—	2	4	no	—
774	C₂×C₄	—	4	4	no	—
775	C₂×C₄	—	4	4	no	—
776	C₂×C₄	—	4	4	no	—
777	C₂×C₄	—	4	16	no	—
778	C₂×C₄	—	4	8	no	—
779	C₂×C₄	—	4	4	no	—
780	C₂×C₄	—	4	4	no	—
781	C₂×C₄	—	4	8	no	—
782	C₂×C₄	—	4	8	no	—
783	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
784	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
785	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
786	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
787	C₂×C₄	C₂×#41×C₃₁	1	8	yes	—
788	C₂×C₄	C₂×#41×C₃₁	1	4	yes	—
789	C₂×C₄	C₃₁×H(5,𝔽₂)	1	4	yes	—
790	C₂²	—	2	2	no	—
791	C₂²	—	2	2	no	—
792	C₂²	—	2	2	no	—
793	C₂²	—	2	2	no	—
794	C₂²	—	2	8	no	—
795	C₂²	—	2	8	no	—
796	C₂²	—	2	2	no	—
797	C₂²	—	2	4	no	—
798	C₂²	—	2	2	no	—
799	C₂²	—	2	2	no	—
800	C₂²	—	2	8	no	—
801	C₂²	—	4	16	no	—
802	C₂²	—	4	16	no	—
803	C₂²	—	4	2	no	—
804	C₂²	—	4	2	no	—
805	C₂²	—	4	4	no	—
806	C₂²	—	4	4	no	—
807	C₂²	—	4	2	no	—
808	C₂²	—	4	2	no	—
809	C₂²	—	4	2	no	—
810	C₂²	—	4	4	no	—
811	C₂²	—	4	4	no	—
812	C₂²	C₃₁×#525	1	4	yes	—
813	C₂²	C₃₁×#532	1	4	yes	—
814	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
815	C₂²	C₂²×#41×C₃₁	1	2	yes	—
816	C₂²	C₂²×#41×C₃₁	1	2	yes	—
817	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	2	yes	—
818	C₄	—	2	4	no	—
819	C₄	—	2	2	no	—
820	C₄	—	2	2	no	—
821	C₄	—	2	2	no	—
822	C₄	—	2	8	no	—
823	C₄	—	4	2	no	—
824	C₄	—	4	2	no	—
825	C₄	—	4	2	no	—
826	C₄	—	4	2	no	—
827	C₄	—	4	2	no	—
828	C₄	—	4	4	no	—
829	C₄	C₃₁×#534	1	4	yes	—
830	C₂	—	2	4	no	—
831	C₂	—	2	4	no	—
832	C₂	—	4	2	no	—
833	C₂	—	4	4	no	—
834	C₂	—	8	2	no	—
835	C₂	C₂×C₃₁×#525	1	1	yes	characteristic
836	C₂	C₂×C₃₁×#532	1	1	yes	characteristic
837	C₂	C₂×C₃₁×#534	1	1	yes	characteristic
838	C₂	C₃₁×#3481	1	4	yes	—

	subgroup	G/H
center	C₂²×C₄×C₃₁	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₃₁
socle	C₂³×C₃₁	C₂⁵
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×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×C₄×D₄×C₃₁	C₂	semidirect
3. C₃₁×#2602	C₂	semidirect
4. C₃₁×#2591	C₂	semidirect
5. C₃₁×#2583	C₂	semidirect
6. C₃₁×#2564	C₂	semidirect
7. C₃₁×#2561	C₂	semidirect
8. C₃₁×#2543	C₂	semidirect
9. C₃₁×#2539	C₂	semidirect
10. C₃₁×#2412	C₂	semidirect
11. C₃₁×#2410	C₂	semidirect
12. C₃₁×#2395	C₂	semidirect
13. C₃₁×#2388	C₂	semidirect
14. C₄×C₃₁×#123	C₂	semidirect
15. C₄×C₃₁×#121	C₂	semidirect
16. C₄×C₃₁×#120	C₂	semidirect
17. C₂×C₄×C₂²⋊C₄×C₃₁	C₂	semidirect
18. C₂²×#41×C₃₁	C₂²	semidirect
24. C₂×C₃₁×#123	C₂²	semidirect
26. C₂×C₃₁×C₂²⋊Q₈	C₂²	semidirect
29. C₂×C₃₁×#121	C₂²	semidirect
38. C₂×C₄×D₄×C₃₁	C₂²	semidirect
39. C₂×C₄×D₄×C₃₁	C₂²	semidirect
40. C₂×C₃₁×#117	C₂²	semidirect
46. C₂²×C₄²×C₃₁	C₂²	semidirect
47. C₃₁×#400	C₂²	semidirect
48. C₃₁×#399	C₂²	semidirect
49. C₃₁×#398	C₂²	semidirect
50. C₃₁×#397	C₂²	semidirect
51. C₃₁×#397	C₂²	semidirect
52. C₃₁×#395	C₂²	semidirect
54. C₃₁×#394	C₂²	semidirect
55. C₃₁×#394	C₂²	semidirect
56. C₃₁×#393	C₂²	semidirect
58. C₃₁×#392	C₂²	semidirect
59. C₃₁×#390	C₂²	semidirect
60. C₃₁×#389	C₂²	semidirect
61. C₃₁×#388	C₂²	semidirect
62. C₃₁×#388	C₂²	semidirect
63. C₃₁×#388	C₂²	semidirect
64. C₃₁×#387	C₂²	semidirect
68. C₃₁×#386	C₂²	semidirect
69. C₃₁×#386	C₂²	semidirect
72. C₃₁×#385	C₂²	semidirect
74. C₃₁×#380	C₂²	semidirect
76. C₄×C₄⋊C₄×C₃₁	C₂²	semidirect
80. C₄×C₂²⋊C₄×C₃₁	C₂²	semidirect
81. C₄×C₂²⋊C₄×C₃₁	C₂²	semidirect
82. C₄×C₂²⋊C₄×C₃₁	C₂²	semidirect
83. C₄×C₂²⋊C₄×C₃₁	C₂²	semidirect
84. C₂×C₃₁×#95	C₂²	semidirect
102. C₂³×C₄×C₃₁	D₄	semidirect
215. C₂×D₄×C₃₁	#41	semidirect
283. C₂²⋊C₄×C₃₁	#41	semidirect
290. #34957	C₃₁	direct (N × H)
371. C₂×#525	C₂×C₃₁	semidirect
372. C₂²×C₄×D₄	C₂×C₃₁	semidirect
373. #2602	C₂×C₃₁	semidirect
374. #2591	C₂×C₃₁	semidirect
375. #2583	C₂×C₃₁	semidirect
376. #2564	C₂×C₃₁	semidirect
377. #2561	C₂×C₃₁	semidirect
378. #2543	C₂×C₃₁	semidirect
379. #2539	C₂×C₃₁	semidirect
380. #2412	C₂×C₃₁	semidirect
381. #2410	C₂×C₃₁	semidirect
382. #2395	C₂×C₃₁	semidirect
383. #2388	C₂×C₃₁	semidirect
384. C₄×#123	C₂×C₃₁	semidirect
385. C₄×#121	C₂×C₃₁	semidirect
386. C₄×#120	C₂×C₃₁	semidirect
387. C₂×C₄×C₂²⋊C₄	C₂×C₃₁	semidirect
428. C₂²×#41	C₂²×C₃₁	semidirect
434. C₂×#123	C₂²×C₃₁	semidirect
436. C₂×C₂²⋊Q₈	C₂²×C₃₁	semidirect
439. C₂×#121	C₂²×C₃₁	semidirect
448. C₂×C₄×D₄	C₂²×C₃₁	semidirect
449. C₂×C₄×D₄	C₂²×C₃₁	semidirect
450. C₂×#117	C₂²×C₃₁	semidirect
456. C₂²×C₄²	C₂²×C₃₁	semidirect
457. #400	C₂²×C₃₁	semidirect
458. #399	C₂²×C₃₁	semidirect
459. #398	C₂²×C₃₁	semidirect
460. #397	C₂²×C₃₁	semidirect
461. #397	C₂²×C₃₁	semidirect
462. #395	C₂²×C₃₁	semidirect
464. #394	C₂²×C₃₁	semidirect
465. #394	C₂²×C₃₁	semidirect
466. #393	C₂²×C₃₁	semidirect
468. #392	C₂²×C₃₁	semidirect
469. #390	C₂²×C₃₁	semidirect
470. #389	C₂²×C₃₁	semidirect
471. #388	C₂²×C₃₁	semidirect
472. #388	C₂²×C₃₁	semidirect
473. #388	C₂²×C₃₁	semidirect
474. #387	C₂²×C₃₁	semidirect
478. #386	C₂²×C₃₁	semidirect
479. #386	C₂²×C₃₁	semidirect
482. #385	C₂²×C₃₁	semidirect
484. #380	C₂²×C₃₁	semidirect
486. C₄×C₄⋊C₄	C₂²×C₃₁	semidirect
490. C₄×C₂²⋊C₄	C₂²×C₃₁	semidirect
491. C₄×C₂²⋊C₄	C₂²×C₃₁	semidirect
492. C₄×C₂²⋊C₄	C₂²×C₃₁	semidirect
493. C₄×C₂²⋊C₄	C₂²×C₃₁	semidirect
494. C₂×#95	C₂²×C₃₁	semidirect
521. C₂³×C₄	D₄×C₃₁	semidirect
600. C₃₁	#34957	direct (N × H)
635. C₂×D₄	#41×C₃₁	semidirect
703. 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×C₄×D₄×C₃₁	2
C₃₁×#2602	2
C₃₁×#2591	2
C₃₁×#2583	2
C₃₁×#2564	2
C₃₁×#2561	2
C₃₁×#2543	2
C₃₁×#2539	2
C₃₁×#2412	2
C₃₁×#2410	2
C₃₁×#2395	2
C₃₁×#2388	2
C₄×C₃₁×#123	2
C₄×C₃₁×#121	2
C₄×C₃₁×#120	2
C₂×C₄×C₂²⋊C₄×C₃₁	2
#34957	31

Subgroups — C31×#34957 #21491716

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#34957 #21491716