Subgroups — C₃₁×#36842 #21493601

Order 7936.

1966 conjugacy classes of subgroups.

The subgroup lattice has 916 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#2849	C₂	1	2	yes	maximal, complemented
2	C₃₁×#2807	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#2764	C₂	1	2	yes	maximal, complemented
4	C₃₁×#2749	C₂	1	2	yes	maximal, complemented
5	C₃₁×#2749	C₂	1	2	yes	maximal, complemented
6	C₃₁×#2735	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#2712	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#2710	C₂	1	2	yes	maximal, complemented
9	C₃₁×#2701	C₂	1	2	yes	maximal, complemented
10	C₃₁×#2670	C₂	1	2	yes	maximal, complemented
11	C₃₁×#2668	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#2635	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#2633	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#2572	C₂	1	2	yes	maximal, complemented
15	C₃₁×#2558	C₂	1	2	yes	maximal, complemented
16	C₃₁×#2464	C₂	1	2	yes	maximal, complemented
17	C₃₁×#2447	C₂	1	2	yes	maximal, complemented
18	C₃₁×#2337	C₂	1	2	yes	maximal, complemented
19	C₄×C₃₁×#120	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂⁴×C₄×C₃₁	C₂²	1	1	yes	characteristic
21	C₂×C₃₁×#125	C₂²	1	1	yes	characteristic, complemented
22	C₂×C₃₁×#124	C₂²	1	2	yes	—
23	C₂×C₃₁×#124	C₂²	1	2	yes	—
24	C₂×C₃₁×#123	C₂²	1	2	yes	—
25	C₂×C₃₁×#123	C₂²	1	2	yes	—
26	C₂×C₃₁×#121	C₂²	1	2	yes	—
27	C₂×C₃₁×#121	C₂²	1	1	yes	characteristic, complemented
28	C₂×C₃₁×#120	C₂²	1	1	yes	characteristic
29	C₂×C₃₁×#120	C₂²	1	2	yes	—
30	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
31	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
32	C₃₁×#400	C₂²	1	2	yes	complemented
33	C₃₁×#400	C₂²	1	1	yes	characteristic, complemented
34	C₃₁×#400	C₂²	1	2	yes	complemented
35	C₃₁×#399	C₂²	1	1	yes	characteristic
36	C₃₁×#399	C₂²	1	1	yes	characteristic
37	C₃₁×#399	C₂²	1	1	yes	characteristic, complemented
38	C₃₁×#398	C₂²	1	2	yes	complemented
39	C₃₁×#398	C₂²	1	2	yes	complemented
40	C₃₁×#397	C₂²	1	1	yes	characteristic
41	C₃₁×#397	C₂²	1	2	yes	—
42	C₃₁×#397	C₂²	1	2	yes	—
43	C₃₁×#397	C₂²	1	1	yes	characteristic, complemented
44	C₃₁×#397	C₂²	1	2	yes	complemented
45	C₃₁×#397	C₂²	1	2	yes	complemented
46	C₃₁×#396	C₂²	1	2	yes	—
47	C₃₁×#396	C₂²	1	2	yes	complemented
48	C₃₁×#394	C₂²	1	2	yes	—
49	C₃₁×#394	C₂²	1	2	yes	—
50	C₃₁×#394	C₂²	1	2	yes	—
51	C₃₁×#394	C₂²	1	1	yes	characteristic, complemented
52	C₃₁×#394	C₂²	1	2	yes	complemented
53	C₃₁×#394	C₂²	1	2	yes	complemented
54	C₃₁×#393	C₂²	1	2	yes	—
55	C₃₁×#393	C₂²	1	2	yes	complemented
56	C₃₁×#392	C₂²	1	1	yes	characteristic
57	C₃₁×#392	C₂²	1	2	yes	—
58	C₃₁×#392	C₂²	1	2	yes	—
59	C₃₁×#392	C₂²	1	2	yes	—
60	C₃₁×#391	C₂²	1	2	yes	complemented
61	C₃₁×#391	C₂²	1	2	yes	complemented
62	C₃₁×#391	C₂²	1	2	yes	complemented
63	C₃₁×#390	C₂²	1	2	yes	—
64	C₃₁×#390	C₂²	1	2	yes	—
65	C₃₁×#390	C₂²	1	2	yes	complemented
66	C₃₁×#389	C₂²	1	2	yes	complemented
67	C₃₁×#389	C₂²	1	2	yes	complemented
68	C₃₁×#388	C₂²	1	2	yes	—
69	C₃₁×#388	C₂²	1	2	yes	—
70	C₃₁×#388	C₂²	1	2	yes	—
71	C₃₁×#388	C₂²	1	2	yes	—
72	C₃₁×#388	C₂²	1	2	yes	—
73	C₃₁×#388	C₂²	1	2	yes	complemented
74	C₃₁×#388	C₂²	1	2	yes	complemented
75	C₃₁×#388	C₂²	1	2	yes	complemented
76	C₃₁×#388	C₂²	1	2	yes	complemented
77	C₃₁×#386	C₂²	1	2	yes	—
78	C₃₁×#386	C₂²	1	2	yes	—
79	C₃₁×#386	C₂²	1	2	yes	—
80	C₃₁×#386	C₂²	1	2	yes	—
81	C₃₁×#386	C₂²	1	2	yes	—
82	C₃₁×#386	C₂²	1	2	yes	—
83	C₃₁×#386	C₂²	1	2	yes	—
84	C₃₁×#386	C₂²	1	1	yes	characteristic
85	C₃₁×#386	C₂²	1	2	yes	complemented
86	C₃₁×#385	C₂²	1	2	yes	—
87	C₃₁×#385	C₂²	1	2	yes	—
88	C₃₁×#385	C₂²	1	2	yes	—
89	C₃₁×#385	C₂²	1	2	yes	—
90	C₃₁×#385	C₂²	1	2	yes	—
91	C₃₁×#385	C₂²	1	1	yes	characteristic
92	C₃₁×#385	C₂²	1	2	yes	complemented
93	C₃₁×#385	C₂²	1	2	yes	complemented
94	C₃₁×#383	C₂²	1	1	yes	characteristic, complemented
95	C₃₁×#383	C₂²	1	2	yes	complemented
96	C₃₁×#383	C₂²	1	2	yes	complemented
97	C₃₁×#381	C₂²	1	2	yes	—
98	C₃₁×#381	C₂²	1	2	yes	—
99	C₃₁×#381	C₂²	1	2	yes	complemented
100	C₃₁×#381	C₂²	1	1	yes	characteristic, complemented
101	C₃₁×#379	C₂²	1	2	yes	—
102	C₃₁×#379	C₂²	1	1	yes	characteristic
103	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	complemented
104	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
105	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
106	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	complemented
107	C₂⁵×C₃₁	C₂³	1	1	yes	characteristic
108	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
109	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
110	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
111	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
112	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
113	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
114	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
115	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
116	C₂³×C₄×C₃₁	—	4	2	no	—
117	C₂³×C₄×C₃₁	—	4	4	no	—
118	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
119	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
120	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
121	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
122	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
123	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
124	C₃₁×#125	—	4	2	no	—
125	C₃₁×#124	—	2	8	no	—
126	C₃₁×#124	—	4	4	no	—
127	C₃₁×#123	—	4	4	no	—
128	C₃₁×#123	—	4	4	no	—
129	C₃₁×#121	—	4	2	no	—
130	C₃₁×#121	—	4	4	no	—
131	C₃₁×#120	—	2	4	no	—
132	C₃₁×#120	—	4	4	no	—
133	C₄×D₄×C₃₁	—	4	2	no	—
134	C₄×D₄×C₃₁	—	4	4	no	—
135	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
136	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
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	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	1	yes	characteristic
143	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
144	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
145	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
146	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
147	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
148	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
149	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	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	2	yes	—
160	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
161	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
162	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
163	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
164	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
165	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
166	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
167	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
168	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
169	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
170	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
171	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
172	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
173	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
174	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
175	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
176	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
177	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
178	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
179	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
180	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
181	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
182	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
183	C₃₁×#95	C₂³	1	2	yes	—
184	C₃₁×#95	C₂³	1	2	yes	—
185	C₃₁×#95	C₂³	1	2	yes	—
186	C₃₁×#95	C₂³	1	1	yes	characteristic
187	C₃₁×#95	C₂³	1	1	yes	characteristic
188	C₃₁×#95	C₂³	1	2	yes	—
189	C₃₁×#95	C₂³	1	2	yes	—
190	C₃₁×#95	C₂³	1	2	yes	—
191	C₃₁×#95	C₂³	1	1	yes	characteristic
192	C₃₁×#95	C₂³	1	2	yes	—
193	C₃₁×#95	C₂³	1	1	yes	characteristic
194	C₃₁×#95	C₂³	1	2	yes	—
195	C₃₁×#95	C₂³	1	2	yes	—
196	C₃₁×#95	C₂³	1	2	yes	—
197	C₃₁×#95	C₂³	1	2	yes	—
198	C₃₁×#95	C₂³	1	2	yes	—
199	C₃₁×#95	C₂³	1	2	yes	—
200	C₃₁×#95	C₂³	1	2	yes	—
201	C₃₁×#95	C₂³	1	2	yes	—
202	C₃₁×#95	C₂³	1	2	yes	—
203	C₃₁×#95	C₂³	1	2	yes	—
204	C₃₁×#95	C₂³	1	2	yes	—
205	C₃₁×#95	C₂³	1	2	yes	—
206	C₃₁×#95	C₂³	1	2	yes	—
207	C₂⁴×C₃₁	—	2	2	no	—
208	C₂⁴×C₃₁	—	2	4	no	—
209	C₂⁴×C₃₁	—	4	1	no	—
210	C₂⁴×C₃₁	—	4	2	no	—
211	C₂⁴×C₃₁	—	4	1	no	—
212	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
213	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
214	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
215	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
216	C₂×Q₈×C₃₁	—	2	4	no	—
217	C₂×Q₈×C₃₁	—	4	2	no	—
218	C₂×Q₈×C₃₁	—	4	2	no	—
219	C₂×D₄×C₃₁	—	2	2	no	—
220	C₂×D₄×C₃₁	—	2	4	no	—
221	C₂×D₄×C₃₁	—	2	4	no	—
222	C₂×D₄×C₃₁	—	2	4	no	—
223	C₂×D₄×C₃₁	—	2	4	no	—
224	C₂×D₄×C₃₁	—	2	4	no	—
225	C₂×D₄×C₃₁	—	4	1	no	—
226	C₂×D₄×C₃₁	—	4	2	no	—
227	C₂×D₄×C₃₁	—	4	1	no	—
228	C₂×D₄×C₃₁	—	4	2	no	—
229	C₂×D₄×C₃₁	—	4	2	no	—
230	C₂×D₄×C₃₁	—	4	2	no	—
231	C₂×D₄×C₃₁	—	4	2	no	—
232	C₂×D₄×C₃₁	—	4	1	no	—
233	C₂×D₄×C₃₁	—	4	2	no	—
234	C₂×D₄×C₃₁	—	4	2	no	—
235	C₂×D₄×C₃₁	—	4	2	no	—
236	C₂×D₄×C₃₁	—	4	2	no	—
237	C₂×D₄×C₃₁	—	4	2	no	—
238	C₂×D₄×C₃₁	—	4	2	no	—
239	C₂²×C₄×C₃₁	—	2	4	no	—
240	C₂²×C₄×C₃₁	—	2	4	no	—
241	C₂²×C₄×C₃₁	—	2	2	no	—
242	C₂²×C₄×C₃₁	—	2	4	no	—
243	C₂²×C₄×C₃₁	—	2	2	no	—
244	C₂²×C₄×C₃₁	—	4	2	no	—
245	C₂²×C₄×C₃₁	—	4	2	no	—
246	C₂²×C₄×C₃₁	—	4	2	no	—
247	C₂²×C₄×C₃₁	—	4	2	no	—
248	C₂²×C₄×C₃₁	—	4	1	no	—
249	C₂²×C₄×C₃₁	—	4	2	no	—
250	C₂²×C₄×C₃₁	—	4	2	no	—
251	C₂²×C₄×C₃₁	—	4	2	no	—
252	C₂²×C₄×C₃₁	—	4	2	no	—
253	C₂²×C₄×C₃₁	—	4	2	no	—
254	C₂²×C₄×C₃₁	—	4	16	no	—
255	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
256	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
257	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
258	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
259	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
260	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
261	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
262	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
263	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
264	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
265	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
266	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
267	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
268	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
269	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
270	C₄⋊C₄×C₃₁	—	2	4	no	—
271	C₄⋊C₄×C₃₁	—	4	2	no	—
272	C₄⋊C₄×C₃₁	—	4	2	no	—
273	C₄⋊C₄×C₃₁	—	4	2	no	—
274	C₄⋊C₄×C₃₁	—	4	2	no	—
275	C₄⋊C₄×C₃₁	—	4	1	no	—
276	C₄⋊C₄×C₃₁	—	4	1	no	—
277	C₄⋊C₄×C₃₁	—	4	2	no	—
278	C₄⋊C₄×C₃₁	—	4	2	no	—
279	C₄⋊C₄×C₃₁	—	4	2	no	—
280	C₄⋊C₄×C₃₁	—	4	2	no	—
281	C₄⋊C₄×C₃₁	—	4	1	no	—
282	C₄⋊C₄×C₃₁	—	4	1	no	—
283	C₄⋊C₄×C₃₁	—	4	2	no	—
284	C₂²⋊C₄×C₃₁	—	2	4	no	—
285	C₂²⋊C₄×C₃₁	—	2	4	no	—
286	C₂²⋊C₄×C₃₁	—	2	4	no	—
287	C₂²⋊C₄×C₃₁	—	2	4	no	—
288	C₂²⋊C₄×C₃₁	—	2	4	no	—
289	C₂²⋊C₄×C₃₁	—	2	4	no	—
290	C₂²⋊C₄×C₃₁	—	2	4	no	—
291	C₂²⋊C₄×C₃₁	—	2	4	no	—
292	C₂²⋊C₄×C₃₁	—	4	2	no	—
293	C₂²⋊C₄×C₃₁	—	4	2	no	—
294	C₂²⋊C₄×C₃₁	—	4	2	no	—
295	C₂²⋊C₄×C₃₁	—	4	2	no	—
296	C₂²⋊C₄×C₃₁	—	4	2	no	—
297	C₂²⋊C₄×C₃₁	—	4	2	no	—
298	C₂²⋊C₄×C₃₁	—	4	2	no	—
299	C₂²⋊C₄×C₃₁	—	4	1	no	—
300	C₂²⋊C₄×C₃₁	—	4	1	no	—
301	C₂²⋊C₄×C₃₁	—	4	1	no	—
302	C₂²⋊C₄×C₃₁	—	4	2	no	—
303	C₂²⋊C₄×C₃₁	—	4	2	no	—
304	C₂²⋊C₄×C₃₁	—	4	2	no	—
305	C₂²⋊C₄×C₃₁	—	4	2	no	—
306	C₂²⋊C₄×C₃₁	—	4	2	no	—
307	C₂²⋊C₄×C₃₁	—	4	2	no	—
308	C₂²⋊C₄×C₃₁	—	4	2	no	—
309	C₂²⋊C₄×C₃₁	—	4	2	no	—
310	C₂²⋊C₄×C₃₁	—	4	2	no	—
311	C₂²⋊C₄×C₃₁	—	4	2	no	—
312	C₂²⋊C₄×C₃₁	#41	1	4	yes	—
313	C₄²×C₃₁	—	2	4	no	—
314	C₄²×C₃₁	—	2	2	no	—
315	C₄²×C₃₁	—	4	2	no	—
316	C₄²×C₃₁	—	4	2	no	—
317	C₄²×C₃₁	—	4	2	no	—
318	#36842	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
319	C₂³×C₃₁	—	2	2	no	—
320	C₂³×C₃₁	—	2	1	no	—
321	C₂³×C₃₁	—	2	2	no	—
322	C₂³×C₃₁	—	2	2	no	—
323	C₂³×C₃₁	—	2	2	no	—
324	C₂³×C₃₁	—	2	1	no	—
325	C₂³×C₃₁	—	2	2	no	—
326	C₂³×C₃₁	—	2	2	no	—
327	C₂³×C₃₁	—	2	2	no	—
328	C₂³×C₃₁	—	2	2	no	—
329	C₂³×C₃₁	—	2	2	no	—
330	C₂³×C₃₁	—	2	1	no	—
331	C₂³×C₃₁	—	2	2	no	—
332	C₂³×C₃₁	—	2	2	no	—
333	C₂³×C₃₁	—	2	2	no	—
334	C₂³×C₃₁	—	2	1	no	—
335	C₂³×C₃₁	—	2	2	no	—
336	C₂³×C₃₁	—	2	1	no	—
337	C₂³×C₃₁	—	2	2	no	—
338	C₂³×C₃₁	—	2	2	no	—
339	C₂³×C₃₁	—	2	2	no	—
340	C₂³×C₃₁	—	2	2	no	—
341	C₂³×C₃₁	—	4	4	no	—
342	C₂³×C₃₁	—	4	8	no	—
343	C₂³×C₃₁	—	4	4	no	—
344	C₂³×C₃₁	—	4	8	no	—
345	C₂³×C₃₁	—	4	4	no	—
346	C₂³×C₃₁	C₂×#41	1	2	yes	—
347	C₂³×C₃₁	H(5,𝔽₂)	1	4	yes	—
348	C₂³×C₃₁	C₂⁵	1	1	yes	characteristic
349	Q₈×C₃₁	—	8	4	no	—
350	D₄×C₃₁	—	4	8	no	—
351	D₄×C₃₁	—	4	4	no	—
352	D₄×C₃₁	—	8	4	no	—
353	D₄×C₃₁	—	8	4	no	—
354	D₄×C₃₁	—	8	4	no	—
355	D₄×C₃₁	—	8	2	no	—
356	D₄×C₃₁	—	8	4	no	—
357	C₂×C₄×C₃₁	—	2	2	no	—
358	C₂×C₄×C₃₁	—	2	2	no	—
359	C₂×C₄×C₃₁	—	2	2	no	—
360	C₂×C₄×C₃₁	—	2	2	no	—
361	C₂×C₄×C₃₁	—	2	2	no	—
362	C₂×C₄×C₃₁	—	2	1	no	—
363	C₂×C₄×C₃₁	—	2	2	no	—
364	C₂×C₄×C₃₁	—	2	1	no	—
365	C₂×C₄×C₃₁	—	2	1	no	—
366	C₂×C₄×C₃₁	—	2	2	no	—
367	C₂×C₄×C₃₁	—	2	2	no	—
368	C₂×C₄×C₃₁	—	2	2	no	—
369	C₂×C₄×C₃₁	—	2	2	no	—
370	C₂×C₄×C₃₁	—	2	2	no	—
371	C₂×C₄×C₃₁	—	2	2	no	—
372	C₂×C₄×C₃₁	—	2	2	no	—
373	C₂×C₄×C₃₁	—	2	2	no	—
374	C₂×C₄×C₃₁	—	2	2	no	—
375	C₂×C₄×C₃₁	—	2	2	no	—
376	C₂×C₄×C₃₁	—	2	1	no	—
377	C₂×C₄×C₃₁	—	2	1	no	—
378	C₂×C₄×C₃₁	—	2	2	no	—
379	C₂×C₄×C₃₁	—	2	2	no	—
380	C₂×C₄×C₃₁	—	2	2	no	—
381	C₂×C₄×C₃₁	—	2	2	no	—
382	C₂×C₄×C₃₁	—	2	2	no	—
383	C₂×C₄×C₃₁	—	2	2	no	—
384	C₂×C₄×C₃₁	—	2	2	no	—
385	C₂×C₄×C₃₁	—	2	2	no	—
386	C₂×C₄×C₃₁	—	2	2	no	—
387	C₂×C₄×C₃₁	—	2	2	no	—
388	C₂×C₄×C₃₁	—	2	2	no	—
389	C₂×C₄×C₃₁	—	2	1	no	—
390	C₂×C₄×C₃₁	—	2	2	no	—
391	C₂×C₄×C₃₁	—	2	2	no	—
392	C₂×C₄×C₃₁	—	2	2	no	—
393	C₂×C₄×C₃₁	—	2	2	no	—
394	C₂×C₄×C₃₁	—	2	2	no	—
395	C₂×C₄×C₃₁	—	2	2	no	—
396	C₂×C₄×C₃₁	—	4	8	no	—
397	C₂×C₄×C₃₁	—	4	4	no	—
398	C₂×C₄×C₃₁	—	4	8	no	—
399	C₂×C₄×C₃₁	—	4	4	no	—
400	C₂×C₄×C₃₁	—	8	2	no	—
401	C₂×C₄×C₃₁	—	8	4	no	—
402	C₂×C₄×C₃₁	C₂×#41	1	4	yes	—
403	C₂×C₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
404	#2849	C₂×C₃₁	1	2	yes	complemented
405	#2807	C₂×C₃₁	1	1	yes	characteristic, complemented
406	#2764	C₂×C₃₁	1	2	yes	complemented
407	#2749	C₂×C₃₁	1	2	yes	complemented
408	#2749	C₂×C₃₁	1	2	yes	complemented
409	#2735	C₂×C₃₁	1	1	yes	characteristic, complemented
410	#2712	C₂×C₃₁	1	1	yes	characteristic, complemented
411	#2710	C₂×C₃₁	1	2	yes	complemented
412	#2701	C₂×C₃₁	1	2	yes	complemented
413	#2670	C₂×C₃₁	1	2	yes	complemented
414	#2668	C₂×C₃₁	1	1	yes	characteristic, complemented
415	#2635	C₂×C₃₁	1	1	yes	characteristic, complemented
416	#2633	C₂×C₃₁	1	1	yes	characteristic, complemented
417	#2572	C₂×C₃₁	1	2	yes	complemented
418	#2558	C₂×C₃₁	1	2	yes	complemented
419	#2464	C₂×C₃₁	1	2	yes	complemented
420	#2447	C₂×C₃₁	1	2	yes	complemented
421	#2337	C₂×C₃₁	1	2	yes	complemented
422	C₄×#120	C₂×C₃₁	1	1	yes	characteristic, complemented
423	C₂²×C₃₁	—	2	2	no	—
424	C₂²×C₃₁	—	2	4	no	—
425	C₂²×C₃₁	—	2	4	no	—
426	C₂²×C₃₁	—	2	4	no	—
427	C₂²×C₃₁	—	2	4	no	—
428	C₂²×C₃₁	—	4	16	no	—
429	C₂²×C₃₁	—	4	2	no	—
430	C₂²×C₃₁	—	4	2	no	—
431	C₂²×C₃₁	—	4	1	no	—
432	C₂²×C₃₁	—	4	2	no	—
433	C₂²×C₃₁	—	4	2	no	—
434	C₂²×C₃₁	—	4	1	no	—
435	C₂²×C₃₁	—	4	2	no	—
436	C₂²×C₃₁	—	4	1	no	—
437	C₂²×C₃₁	—	4	2	no	—
438	C₂²×C₃₁	—	4	2	no	—
439	C₂²×C₃₁	—	4	2	no	—
440	C₂²×C₃₁	—	4	2	no	—
441	C₂²×C₃₁	—	4	1	no	—
442	C₂²×C₃₁	—	4	2	no	—
443	C₂²×C₃₁	—	4	2	no	—
444	C₂²×C₃₁	—	4	2	no	—
445	C₂²×C₃₁	—	4	2	no	—
446	C₂²×C₃₁	—	4	1	no	—
447	C₂²×C₃₁	—	4	2	no	—
448	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
449	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
450	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	2	yes	—
451	C₂²×C₃₁	#585	1	1	yes	characteristic
452	C₂²×C₃₁	#585	1	2	yes	—
453	C₄×C₃₁	—	2	4	no	—
454	C₄×C₃₁	—	2	2	no	—
455	C₄×C₃₁	—	4	2	no	—
456	C₄×C₃₁	—	4	1	no	—
457	C₄×C₃₁	—	4	2	no	—
458	C₄×C₃₁	—	4	2	no	—
459	C₄×C₃₁	—	4	2	no	—
460	C₄×C₃₁	—	4	1	no	—
461	C₄×C₃₁	—	4	1	no	—
462	C₄×C₃₁	—	4	2	no	—
463	C₄×C₃₁	—	4	2	no	—
464	C₄×C₃₁	—	4	2	no	—
465	C₄×C₃₁	—	4	2	no	—
466	C₄×C₃₁	—	4	1	no	—
467	C₄×C₃₁	—	4	2	no	—
468	C₂⁴×C₄	C₂²×C₃₁	1	1	yes	characteristic
469	C₂×#125	C₂²×C₃₁	1	1	yes	characteristic, complemented
470	C₂×#124	C₂²×C₃₁	1	2	yes	—
471	C₂×#124	C₂²×C₃₁	1	2	yes	—
472	C₂×#123	C₂²×C₃₁	1	2	yes	—
473	C₂×#123	C₂²×C₃₁	1	2	yes	—
474	C₂×#121	C₂²×C₃₁	1	2	yes	—
475	C₂×#121	C₂²×C₃₁	1	1	yes	characteristic, complemented
476	C₂×#120	C₂²×C₃₁	1	1	yes	characteristic
477	C₂×#120	C₂²×C₃₁	1	2	yes	—
478	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
479	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
480	#400	C₂²×C₃₁	1	2	yes	complemented
481	#400	C₂²×C₃₁	1	1	yes	characteristic, complemented
482	#400	C₂²×C₃₁	1	2	yes	complemented
483	#399	C₂²×C₃₁	1	1	yes	characteristic
484	#399	C₂²×C₃₁	1	1	yes	characteristic
485	#399	C₂²×C₃₁	1	1	yes	characteristic, complemented
486	#398	C₂²×C₃₁	1	2	yes	complemented
487	#398	C₂²×C₃₁	1	2	yes	complemented
488	#397	C₂²×C₃₁	1	1	yes	characteristic
489	#397	C₂²×C₃₁	1	2	yes	—
490	#397	C₂²×C₃₁	1	2	yes	—
491	#397	C₂²×C₃₁	1	1	yes	characteristic, complemented
492	#397	C₂²×C₃₁	1	2	yes	complemented
493	#397	C₂²×C₃₁	1	2	yes	complemented
494	#396	C₂²×C₃₁	1	2	yes	—
495	#396	C₂²×C₃₁	1	2	yes	complemented
496	#394	C₂²×C₃₁	1	2	yes	—
497	#394	C₂²×C₃₁	1	2	yes	—
498	#394	C₂²×C₃₁	1	2	yes	—
499	#394	C₂²×C₃₁	1	1	yes	characteristic, complemented
500	#394	C₂²×C₃₁	1	2	yes	complemented
501	#394	C₂²×C₃₁	1	2	yes	complemented
502	#393	C₂²×C₃₁	1	2	yes	—
503	#393	C₂²×C₃₁	1	2	yes	complemented
504	#392	C₂²×C₃₁	1	1	yes	characteristic
505	#392	C₂²×C₃₁	1	2	yes	—
506	#392	C₂²×C₃₁	1	2	yes	—
507	#392	C₂²×C₃₁	1	2	yes	—
508	#391	C₂²×C₃₁	1	2	yes	complemented
509	#391	C₂²×C₃₁	1	2	yes	complemented
510	#391	C₂²×C₃₁	1	2	yes	complemented
511	#390	C₂²×C₃₁	1	2	yes	—
512	#390	C₂²×C₃₁	1	2	yes	—
513	#390	C₂²×C₃₁	1	2	yes	complemented
514	#389	C₂²×C₃₁	1	2	yes	complemented
515	#389	C₂²×C₃₁	1	2	yes	complemented
516	#388	C₂²×C₃₁	1	2	yes	—
517	#388	C₂²×C₃₁	1	2	yes	—
518	#388	C₂²×C₃₁	1	2	yes	—
519	#388	C₂²×C₃₁	1	2	yes	—
520	#388	C₂²×C₃₁	1	2	yes	—
521	#388	C₂²×C₃₁	1	2	yes	complemented
522	#388	C₂²×C₃₁	1	2	yes	complemented
523	#388	C₂²×C₃₁	1	2	yes	complemented
524	#388	C₂²×C₃₁	1	2	yes	complemented
525	#386	C₂²×C₃₁	1	2	yes	—
526	#386	C₂²×C₃₁	1	2	yes	—
527	#386	C₂²×C₃₁	1	2	yes	—
528	#386	C₂²×C₃₁	1	2	yes	—
529	#386	C₂²×C₃₁	1	2	yes	—
530	#386	C₂²×C₃₁	1	2	yes	—
531	#386	C₂²×C₃₁	1	2	yes	—
532	#386	C₂²×C₃₁	1	1	yes	characteristic
533	#386	C₂²×C₃₁	1	2	yes	complemented
534	#385	C₂²×C₃₁	1	2	yes	—
535	#385	C₂²×C₃₁	1	2	yes	—
536	#385	C₂²×C₃₁	1	2	yes	—
537	#385	C₂²×C₃₁	1	2	yes	—
538	#385	C₂²×C₃₁	1	2	yes	—
539	#385	C₂²×C₃₁	1	1	yes	characteristic
540	#385	C₂²×C₃₁	1	2	yes	complemented
541	#385	C₂²×C₃₁	1	2	yes	complemented
542	#383	C₂²×C₃₁	1	1	yes	characteristic, complemented
543	#383	C₂²×C₃₁	1	2	yes	complemented
544	#383	C₂²×C₃₁	1	2	yes	complemented
545	#381	C₂²×C₃₁	1	2	yes	—
546	#381	C₂²×C₃₁	1	2	yes	—
547	#381	C₂²×C₃₁	1	2	yes	complemented
548	#381	C₂²×C₃₁	1	1	yes	characteristic, complemented
549	#379	C₂²×C₃₁	1	2	yes	—
550	#379	C₂²×C₃₁	1	1	yes	characteristic
551	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	complemented
552	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
553	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
554	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	complemented
555	C₂×C₃₁	—	4	2	no	—
556	C₂×C₃₁	—	4	4	no	—
557	C₂×C₃₁	—	8	1	no	—
558	C₂×C₃₁	—	8	2	no	—
559	C₂×C₃₁	#3460	1	1	yes	characteristic
560	C₂×C₃₁	#3513	1	2	yes	—
561	C₂×C₃₁	#3532	1	1	yes	characteristic
562	C₂×C₃₁	#3533	1	2	yes	—
563	C₂×C₃₁	#3540	1	1	yes	characteristic
564	C₂⁵	C₂³×C₃₁	1	1	yes	characteristic
565	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
566	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
567	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
568	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
569	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
570	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
571	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
572	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
573	C₂³×C₄	—	4	2	no	—
574	C₂³×C₄	—	4	4	no	—
575	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
576	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
577	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
578	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
579	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
580	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
581	#125	—	4	2	no	—
582	#124	—	2	8	no	—
583	#124	—	4	4	no	—
584	#123	—	4	4	no	—
585	#123	—	4	4	no	—
586	#121	—	4	2	no	—
587	#121	—	4	4	no	—
588	#120	—	2	4	no	—
589	#120	—	4	4	no	—
590	C₄×D₄	—	4	2	no	—
591	C₄×D₄	—	4	4	no	—
592	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
593	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
594	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
595	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
596	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
597	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
598	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
599	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
600	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
601	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
602	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
603	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
604	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
605	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
606	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
607	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
608	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
609	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
610	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
611	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
612	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
613	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
614	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
615	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
616	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
617	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
618	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
619	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
620	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
621	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
622	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
623	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
624	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
625	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
626	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
627	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
628	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
629	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
630	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
631	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
632	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
633	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
634	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
635	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
636	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
637	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
638	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
639	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
640	#95	C₂³×C₃₁	1	2	yes	—
641	#95	C₂³×C₃₁	1	2	yes	—
642	#95	C₂³×C₃₁	1	2	yes	—
643	#95	C₂³×C₃₁	1	2	yes	—
644	#95	C₂³×C₃₁	1	2	yes	—
645	#95	C₂³×C₃₁	1	2	yes	—
646	#95	C₂³×C₃₁	1	2	yes	—
647	#95	C₂³×C₃₁	1	2	yes	—
648	#95	C₂³×C₃₁	1	2	yes	—
649	#95	C₂³×C₃₁	1	2	yes	—
650	#95	C₂³×C₃₁	1	2	yes	—
651	#95	C₂³×C₃₁	1	2	yes	—
652	#95	C₂³×C₃₁	1	2	yes	—
653	#95	C₂³×C₃₁	1	2	yes	—
654	#95	C₂³×C₃₁	1	2	yes	—
655	#95	C₂³×C₃₁	1	1	yes	characteristic
656	#95	C₂³×C₃₁	1	1	yes	characteristic
657	#95	C₂³×C₃₁	1	2	yes	—
658	#95	C₂³×C₃₁	1	1	yes	characteristic
659	#95	C₂³×C₃₁	1	2	yes	—
660	#95	C₂³×C₃₁	1	1	yes	characteristic
661	#95	C₂³×C₃₁	1	2	yes	—
662	#95	C₂³×C₃₁	1	2	yes	—
663	#95	C₂³×C₃₁	1	2	yes	—
664	C₃₁	#36842	1	1	yes	characteristic, direct product factor, Sylow
665	C₂⁴	—	2	2	no	—
666	C₂⁴	—	2	4	no	—
667	C₂⁴	—	4	1	no	—
668	C₂⁴	—	4	2	no	—
669	C₂⁴	—	4	1	no	—
670	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
671	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
672	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
673	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
674	C₂×Q₈	—	2	4	no	—
675	C₂×Q₈	—	4	2	no	—
676	C₂×Q₈	—	4	2	no	—
677	C₂×D₄	—	2	2	no	—
678	C₂×D₄	—	2	4	no	—
679	C₂×D₄	—	2	4	no	—
680	C₂×D₄	—	2	4	no	—
681	C₂×D₄	—	2	4	no	—
682	C₂×D₄	—	2	4	no	—
683	C₂×D₄	—	4	1	no	—
684	C₂×D₄	—	4	2	no	—
685	C₂×D₄	—	4	1	no	—
686	C₂×D₄	—	4	2	no	—
687	C₂×D₄	—	4	2	no	—
688	C₂×D₄	—	4	2	no	—
689	C₂×D₄	—	4	2	no	—
690	C₂×D₄	—	4	1	no	—
691	C₂×D₄	—	4	2	no	—
692	C₂×D₄	—	4	2	no	—
693	C₂×D₄	—	4	2	no	—
694	C₂×D₄	—	4	2	no	—
695	C₂×D₄	—	4	2	no	—
696	C₂×D₄	—	4	2	no	—
697	C₂²×C₄	—	2	4	no	—
698	C₂²×C₄	—	2	4	no	—
699	C₂²×C₄	—	2	2	no	—
700	C₂²×C₄	—	2	4	no	—
701	C₂²×C₄	—	2	2	no	—
702	C₂²×C₄	—	4	2	no	—
703	C₂²×C₄	—	4	2	no	—
704	C₂²×C₄	—	4	2	no	—
705	C₂²×C₄	—	4	2	no	—
706	C₂²×C₄	—	4	1	no	—
707	C₂²×C₄	—	4	2	no	—
708	C₂²×C₄	—	4	2	no	—
709	C₂²×C₄	—	4	2	no	—
710	C₂²×C₄	—	4	2	no	—
711	C₂²×C₄	—	4	2	no	—
712	C₂²×C₄	—	4	16	no	—
713	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
714	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
715	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
716	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
717	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
718	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
719	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
720	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
721	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
722	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
723	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
724	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
725	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
726	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
727	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
728	C₄⋊C₄	—	2	4	no	—
729	C₄⋊C₄	—	4	2	no	—
730	C₄⋊C₄	—	4	2	no	—
731	C₄⋊C₄	—	4	2	no	—
732	C₄⋊C₄	—	4	2	no	—
733	C₄⋊C₄	—	4	1	no	—
734	C₄⋊C₄	—	4	1	no	—
735	C₄⋊C₄	—	4	2	no	—
736	C₄⋊C₄	—	4	2	no	—
737	C₄⋊C₄	—	4	2	no	—
738	C₄⋊C₄	—	4	2	no	—
739	C₄⋊C₄	—	4	1	no	—
740	C₄⋊C₄	—	4	1	no	—
741	C₄⋊C₄	—	4	2	no	—
742	C₂²⋊C₄	—	2	4	no	—
743	C₂²⋊C₄	—	2	4	no	—
744	C₂²⋊C₄	—	2	4	no	—
745	C₂²⋊C₄	—	2	4	no	—
746	C₂²⋊C₄	—	2	4	no	—
747	C₂²⋊C₄	—	2	4	no	—
748	C₂²⋊C₄	—	2	4	no	—
749	C₂²⋊C₄	—	2	4	no	—
750	C₂²⋊C₄	—	4	2	no	—
751	C₂²⋊C₄	—	4	2	no	—
752	C₂²⋊C₄	—	4	2	no	—
753	C₂²⋊C₄	—	4	2	no	—
754	C₂²⋊C₄	—	4	2	no	—
755	C₂²⋊C₄	—	4	2	no	—
756	C₂²⋊C₄	—	4	2	no	—
757	C₂²⋊C₄	—	4	1	no	—
758	C₂²⋊C₄	—	4	1	no	—
759	C₂²⋊C₄	—	4	1	no	—
760	C₂²⋊C₄	—	4	2	no	—
761	C₂²⋊C₄	—	4	2	no	—
762	C₂²⋊C₄	—	4	2	no	—
763	C₂²⋊C₄	—	4	2	no	—
764	C₂²⋊C₄	—	4	2	no	—
765	C₂²⋊C₄	—	4	2	no	—
766	C₂²⋊C₄	—	4	2	no	—
767	C₂²⋊C₄	—	4	2	no	—
768	C₂²⋊C₄	—	4	2	no	—
769	C₂²⋊C₄	—	4	2	no	—
770	C₂²⋊C₄	#41×C₃₁	1	4	yes	—
771	C₄²	—	2	4	no	—
772	C₄²	—	2	2	no	—
773	C₄²	—	4	2	no	—
774	C₄²	—	4	2	no	—
775	C₄²	—	4	2	no	—
776	C₂³	—	2	2	no	—
777	C₂³	—	2	1	no	—
778	C₂³	—	2	2	no	—
779	C₂³	—	2	2	no	—
780	C₂³	—	2	2	no	—
781	C₂³	—	2	1	no	—
782	C₂³	—	2	2	no	—
783	C₂³	—	2	2	no	—
784	C₂³	—	2	2	no	—
785	C₂³	—	2	2	no	—
786	C₂³	—	2	2	no	—
787	C₂³	—	2	1	no	—
788	C₂³	—	2	2	no	—
789	C₂³	—	2	2	no	—
790	C₂³	—	2	2	no	—
791	C₂³	—	2	1	no	—
792	C₂³	—	2	2	no	—
793	C₂³	—	2	1	no	—
794	C₂³	—	2	2	no	—
795	C₂³	—	2	2	no	—
796	C₂³	—	2	2	no	—
797	C₂³	—	2	2	no	—
798	C₂³	—	4	4	no	—
799	C₂³	—	4	8	no	—
800	C₂³	—	4	4	no	—
801	C₂³	—	4	8	no	—
802	C₂³	—	4	4	no	—
803	C₂³	C₂×#41×C₃₁	1	2	yes	—
804	C₂³	C₃₁×H(5,𝔽₂)	1	4	yes	—
805	C₂³	C₂⁵×C₃₁	1	1	yes	characteristic
806	Q₈	—	8	4	no	—
807	D₄	—	4	8	no	—
808	D₄	—	4	4	no	—
809	D₄	—	8	4	no	—
810	D₄	—	8	4	no	—
811	D₄	—	8	4	no	—
812	D₄	—	8	2	no	—
813	D₄	—	8	4	no	—
814	C₂×C₄	—	2	2	no	—
815	C₂×C₄	—	2	2	no	—
816	C₂×C₄	—	2	2	no	—
817	C₂×C₄	—	2	2	no	—
818	C₂×C₄	—	2	2	no	—
819	C₂×C₄	—	2	1	no	—
820	C₂×C₄	—	2	2	no	—
821	C₂×C₄	—	2	1	no	—
822	C₂×C₄	—	2	1	no	—
823	C₂×C₄	—	2	2	no	—
824	C₂×C₄	—	2	2	no	—
825	C₂×C₄	—	2	2	no	—
826	C₂×C₄	—	2	2	no	—
827	C₂×C₄	—	2	2	no	—
828	C₂×C₄	—	2	2	no	—
829	C₂×C₄	—	2	2	no	—
830	C₂×C₄	—	2	2	no	—
831	C₂×C₄	—	2	2	no	—
832	C₂×C₄	—	2	2	no	—
833	C₂×C₄	—	2	1	no	—
834	C₂×C₄	—	2	1	no	—
835	C₂×C₄	—	2	2	no	—
836	C₂×C₄	—	2	2	no	—
837	C₂×C₄	—	2	2	no	—
838	C₂×C₄	—	2	2	no	—
839	C₂×C₄	—	2	2	no	—
840	C₂×C₄	—	2	2	no	—
841	C₂×C₄	—	2	2	no	—
842	C₂×C₄	—	2	2	no	—
843	C₂×C₄	—	2	2	no	—
844	C₂×C₄	—	2	2	no	—
845	C₂×C₄	—	2	2	no	—
846	C₂×C₄	—	2	1	no	—
847	C₂×C₄	—	2	2	no	—
848	C₂×C₄	—	2	2	no	—
849	C₂×C₄	—	2	2	no	—
850	C₂×C₄	—	2	2	no	—
851	C₂×C₄	—	2	2	no	—
852	C₂×C₄	—	2	2	no	—
853	C₂×C₄	—	4	8	no	—
854	C₂×C₄	—	4	4	no	—
855	C₂×C₄	—	4	8	no	—
856	C₂×C₄	—	4	4	no	—
857	C₂×C₄	—	8	2	no	—
858	C₂×C₄	—	8	4	no	—
859	C₂×C₄	C₂×#41×C₃₁	1	4	yes	—
860	C₂×C₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
861	C₂²	—	2	2	no	—
862	C₂²	—	2	4	no	—
863	C₂²	—	2	4	no	—
864	C₂²	—	2	4	no	—
865	C₂²	—	2	4	no	—
866	C₂²	—	4	16	no	—
867	C₂²	—	4	2	no	—
868	C₂²	—	4	2	no	—
869	C₂²	—	4	1	no	—
870	C₂²	—	4	2	no	—
871	C₂²	—	4	2	no	—
872	C₂²	—	4	1	no	—
873	C₂²	—	4	2	no	—
874	C₂²	—	4	1	no	—
875	C₂²	—	4	2	no	—
876	C₂²	—	4	2	no	—
877	C₂²	—	4	2	no	—
878	C₂²	—	4	2	no	—
879	C₂²	—	4	1	no	—
880	C₂²	—	4	2	no	—
881	C₂²	—	4	2	no	—
882	C₂²	—	4	2	no	—
883	C₂²	—	4	2	no	—
884	C₂²	—	4	1	no	—
885	C₂²	—	4	2	no	—
886	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
887	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
888	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	2	yes	—
889	C₂²	C₃₁×#585	1	1	yes	characteristic
890	C₂²	C₃₁×#585	1	2	yes	—
891	C₄	—	2	4	no	—
892	C₄	—	2	2	no	—
893	C₄	—	4	1	no	—
894	C₄	—	4	2	no	—
895	C₄	—	4	2	no	—
896	C₄	—	4	2	no	—
897	C₄	—	4	2	no	—
898	C₄	—	4	1	no	—
899	C₄	—	4	1	no	—
900	C₄	—	4	2	no	—
901	C₄	—	4	2	no	—
902	C₄	—	4	2	no	—
903	C₄	—	4	2	no	—
904	C₄	—	4	2	no	—
905	C₄	—	4	1	no	—
906	C₂	—	4	2	no	—
907	C₂	—	4	4	no	—
908	C₂	—	8	1	no	—
909	C₂	—	8	2	no	—
910	C₂	C₃₁×#3460	1	1	yes	characteristic
911	C₂	C₃₁×#3513	1	2	yes	—
912	C₂	C₃₁×#3532	1	1	yes	characteristic
913	C₂	C₃₁×#3533	1	2	yes	—
914	C₂	C₃₁×#3540	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. C₃₁×#2849	C₂	semidirect
2. C₃₁×#2807	C₂	semidirect
3. C₃₁×#2764	C₂	semidirect
4. C₃₁×#2749	C₂	semidirect
5. C₃₁×#2749	C₂	semidirect
6. C₃₁×#2735	C₂	semidirect
7. C₃₁×#2712	C₂	semidirect
8. C₃₁×#2710	C₂	semidirect
9. C₃₁×#2701	C₂	semidirect
10. C₃₁×#2670	C₂	semidirect
11. C₃₁×#2668	C₂	semidirect
12. C₃₁×#2635	C₂	semidirect
13. C₃₁×#2633	C₂	semidirect
14. C₃₁×#2572	C₂	semidirect
15. C₃₁×#2558	C₂	semidirect
16. C₃₁×#2464	C₂	semidirect
17. C₃₁×#2447	C₂	semidirect
18. C₃₁×#2337	C₂	semidirect
19. C₄×C₃₁×#120	C₂	semidirect
21. C₂×C₃₁×#125	C₂²	semidirect
27. C₂×C₃₁×#121	C₂²	semidirect
32. C₃₁×#400	C₂²	semidirect
33. C₃₁×#400	C₂²	semidirect
34. C₃₁×#400	C₂²	semidirect
37. C₃₁×#399	C₂²	semidirect
38. C₃₁×#398	C₂²	semidirect
39. C₃₁×#398	C₂²	semidirect
43. C₃₁×#397	C₂²	semidirect
44. C₃₁×#397	C₂²	semidirect
45. C₃₁×#397	C₂²	semidirect
47. C₃₁×#396	C₂²	semidirect
51. C₃₁×#394	C₂²	semidirect
52. C₃₁×#394	C₂²	semidirect
53. C₃₁×#394	C₂²	semidirect
55. C₃₁×#393	C₂²	semidirect
60. C₃₁×#391	C₂²	semidirect
61. C₃₁×#391	C₂²	semidirect
62. C₃₁×#391	C₂²	semidirect
65. C₃₁×#390	C₂²	semidirect
66. C₃₁×#389	C₂²	semidirect
67. C₃₁×#389	C₂²	semidirect
73. C₃₁×#388	C₂²	semidirect
74. C₃₁×#388	C₂²	semidirect
75. C₃₁×#388	C₂²	semidirect
76. C₃₁×#388	C₂²	semidirect
85. C₃₁×#386	C₂²	semidirect
92. C₃₁×#385	C₂²	semidirect
93. C₃₁×#385	C₂²	semidirect
94. C₃₁×#383	C₂²	semidirect
95. C₃₁×#383	C₂²	semidirect
96. C₃₁×#383	C₂²	semidirect
99. C₃₁×#381	C₂²	semidirect
100. C₃₁×#381	C₂²	semidirect
103. C₄×C₄⋊C₄×C₃₁	C₂²	semidirect
106. C₄×C₂²⋊C₄×C₃₁	C₂²	semidirect
318. #36842	C₃₁	direct (N × H)
404. #2849	C₂×C₃₁	semidirect
405. #2807	C₂×C₃₁	semidirect
406. #2764	C₂×C₃₁	semidirect
407. #2749	C₂×C₃₁	semidirect
408. #2749	C₂×C₃₁	semidirect
409. #2735	C₂×C₃₁	semidirect
410. #2712	C₂×C₃₁	semidirect
411. #2710	C₂×C₃₁	semidirect
412. #2701	C₂×C₃₁	semidirect
413. #2670	C₂×C₃₁	semidirect
414. #2668	C₂×C₃₁	semidirect
415. #2635	C₂×C₃₁	semidirect
416. #2633	C₂×C₃₁	semidirect
417. #2572	C₂×C₃₁	semidirect
418. #2558	C₂×C₃₁	semidirect
419. #2464	C₂×C₃₁	semidirect
420. #2447	C₂×C₃₁	semidirect
421. #2337	C₂×C₃₁	semidirect
422. C₄×#120	C₂×C₃₁	semidirect
469. C₂×#125	C₂²×C₃₁	semidirect
475. C₂×#121	C₂²×C₃₁	semidirect
480. #400	C₂²×C₃₁	semidirect
481. #400	C₂²×C₃₁	semidirect
482. #400	C₂²×C₃₁	semidirect
485. #399	C₂²×C₃₁	semidirect
486. #398	C₂²×C₃₁	semidirect
487. #398	C₂²×C₃₁	semidirect
491. #397	C₂²×C₃₁	semidirect
492. #397	C₂²×C₃₁	semidirect
493. #397	C₂²×C₃₁	semidirect
495. #396	C₂²×C₃₁	semidirect
499. #394	C₂²×C₃₁	semidirect
500. #394	C₂²×C₃₁	semidirect
501. #394	C₂²×C₃₁	semidirect
503. #393	C₂²×C₃₁	semidirect
508. #391	C₂²×C₃₁	semidirect
509. #391	C₂²×C₃₁	semidirect
510. #391	C₂²×C₃₁	semidirect
513. #390	C₂²×C₃₁	semidirect
514. #389	C₂²×C₃₁	semidirect
515. #389	C₂²×C₃₁	semidirect
521. #388	C₂²×C₃₁	semidirect
522. #388	C₂²×C₃₁	semidirect
523. #388	C₂²×C₃₁	semidirect
524. #388	C₂²×C₃₁	semidirect
533. #386	C₂²×C₃₁	semidirect
540. #385	C₂²×C₃₁	semidirect
541. #385	C₂²×C₃₁	semidirect
542. #383	C₂²×C₃₁	semidirect
543. #383	C₂²×C₃₁	semidirect
544. #383	C₂²×C₃₁	semidirect
547. #381	C₂²×C₃₁	semidirect
548. #381	C₂²×C₃₁	semidirect
551. C₄×C₄⋊C₄	C₂²×C₃₁	semidirect
554. C₄×C₂²⋊C₄	C₂²×C₃₁	semidirect
664. C₃₁	#36842	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃₁×#2849	2
C₃₁×#2807	2
C₃₁×#2764	2
C₃₁×#2749	2
C₃₁×#2735	2
C₃₁×#2712	2
C₃₁×#2710	2
C₃₁×#2701	2
C₃₁×#2670	2
C₃₁×#2668	2
C₃₁×#2635	2
C₃₁×#2633	2
C₃₁×#2572	2
C₃₁×#2558	2
C₃₁×#2464	2
C₃₁×#2447	2
C₃₁×#2337	2
C₄×C₃₁×#120	2
#36842	31

Subgroups — C31×#36842 #21493601

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#36842 #21493601