Subgroups — C₃₁×#36812 #21493571

Order 7936.

2048 conjugacy classes of subgroups.

The subgroup lattice has 994 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#2854	C₂	1	2	yes	maximal, complemented
2	C₃₁×#2798	C₂	1	2	yes	maximal, complemented
3	C₃₁×#2710	C₂	1	2	yes	maximal, complemented
4	C₃₁×#2705	C₂	1	2	yes	maximal, complemented
5	C₃₁×#2705	C₂	1	2	yes	maximal, complemented
6	C₃₁×#2693	C₂	1	2	yes	maximal, complemented
7	C₃₁×#2678	C₂	1	2	yes	maximal, complemented
8	C₃₁×#2678	C₂	1	2	yes	maximal, complemented
9	C₃₁×#2673	C₂	1	2	yes	maximal, complemented
10	C₃₁×#2648	C₂	1	2	yes	maximal, complemented
11	C₃₁×#2608	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#2559	C₂	1	2	yes	maximal, complemented
13	C₃₁×#2539	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#2471	C₂	1	2	yes	maximal, complemented
15	C₃₁×#2431	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#2404	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#2333	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃₁×#2312	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#2297	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂²×#41×C₃₁	C₂²	1	1	yes	characteristic
21	C₂×C₃₁×#127	C₂²	1	1	yes	characteristic, complemented
22	C₂×C₃₁×#126	C₂²	1	2	yes	complemented
23	C₂×C₃₁×#124	C₂²	1	1	yes	characteristic, complemented
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	complemented
28	C₂×C₃₁×#121	C₂²	1	1	yes	characteristic
29	C₂×C₃₁×#121	C₂²	1	2	yes	—
30	C₂×C₃₁×#121	C₂²	1	2	yes	—
31	C₂×C₃₁×#120	C₂²	1	1	yes	characteristic
32	C₂×C₃₁×#120	C₂²	1	1	yes	characteristic
33	C₂×C₃₁×#120	C₂²	1	2	yes	—
34	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic, complemented
35	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
36	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic, complemented
37	C₃₁×#400	C₂²	1	2	yes	complemented
38	C₃₁×#400	C₂²	1	2	yes	complemented
39	C₃₁×#399	C₂²	1	2	yes	—
40	C₃₁×#399	C₂²	1	2	yes	complemented
41	C₃₁×#397	C₂²	1	2	yes	—
42	C₃₁×#397	C₂²	1	2	yes	—
43	C₃₁×#397	C₂²	1	2	yes	complemented
44	C₃₁×#396	C₂²	1	2	yes	—
45	C₃₁×#396	C₂²	1	2	yes	—
46	C₃₁×#396	C₂²	1	2	yes	complemented
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	2	yes	—
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×#392	C₂²	1	2	yes	—
56	C₃₁×#392	C₂²	1	2	yes	—
57	C₃₁×#392	C₂²	1	2	yes	—
58	C₃₁×#392	C₂²	1	2	yes	—
59	C₃₁×#392	C₂²	1	2	yes	—
60	C₃₁×#392	C₂²	1	2	yes	—
61	C₃₁×#391	C₂²	1	1	yes	characteristic, 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	—
66	C₃₁×#390	C₂²	1	2	yes	—
67	C₃₁×#390	C₂²	1	2	yes	—
68	C₃₁×#390	C₂²	1	2	yes	—
69	C₃₁×#390	C₂²	1	1	yes	characteristic, complemented
70	C₃₁×#389	C₂²	1	2	yes	complemented
71	C₃₁×#389	C₂²	1	2	yes	complemented
72	C₃₁×#389	C₂²	1	2	yes	complemented
73	C₃₁×#388	C₂²	1	2	yes	—
74	C₃₁×#388	C₂²	1	2	yes	—
75	C₃₁×#388	C₂²	1	2	yes	—
76	C₃₁×#388	C₂²	1	2	yes	—
77	C₃₁×#388	C₂²	1	2	yes	—
78	C₃₁×#388	C₂²	1	2	yes	—
79	C₃₁×#388	C₂²	1	2	yes	complemented
80	C₃₁×#388	C₂²	1	2	yes	complemented
81	C₃₁×#387	C₂²	1	2	yes	complemented
82	C₃₁×#387	C₂²	1	2	yes	complemented
83	C₃₁×#387	C₂²	1	2	yes	complemented
84	C₃₁×#387	C₂²	1	2	yes	complemented
85	C₃₁×#386	C₂²	1	2	yes	—
86	C₃₁×#386	C₂²	1	2	yes	—
87	C₃₁×#386	C₂²	1	2	yes	—
88	C₃₁×#386	C₂²	1	1	yes	characteristic
89	C₃₁×#386	C₂²	1	1	yes	characteristic
90	C₃₁×#386	C₂²	1	2	yes	—
91	C₃₁×#386	C₂²	1	2	yes	complemented
92	C₃₁×#386	C₂²	1	2	yes	complemented
93	C₃₁×#386	C₂²	1	2	yes	complemented
94	C₃₁×#386	C₂²	1	2	yes	complemented
95	C₃₁×#386	C₂²	1	2	yes	complemented
96	C₃₁×#385	C₂²	1	2	yes	complemented
97	C₃₁×#381	C₂²	1	1	yes	characteristic
98	C₃₁×#380	C₂²	1	2	yes	—
99	C₃₁×#380	C₂²	1	2	yes	complemented
100	C₃₁×#379	C₂²	1	2	yes	—
101	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
102	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
103	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
104	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	complemented
105	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
106	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
107	C₂⁵×C₃₁	C₂³	1	1	yes	characteristic
108	C₂×#41×C₃₁	—	2	4	no	—
109	C₂×#41×C₃₁	—	4	2	no	—
110	C₂×#41×C₃₁	—	4	2	no	—
111	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
112	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
113	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
114	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
115	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
116	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
117	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
118	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
119	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
120	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
121	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
122	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
123	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
124	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
125	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
126	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
127	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
128	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
129	C₃₁×#127	—	4	2	no	—
130	C₃₁×#126	—	4	4	no	—
131	C₃₁×#124	—	4	2	no	—
132	C₃₁×#123	—	4	4	no	—
133	C₃₁×#123	—	4	4	no	—
134	C₃₁×#123	—	4	4	no	—
135	C₃₁×#123	—	4	4	no	—
136	C₃₁×#121	—	2	4	no	—
137	C₃₁×#121	—	4	4	no	—
138	C₃₁×#121	—	4	4	no	—
139	C₃₁×#120	—	4	2	no	—
140	C₃₁×#120	—	4	4	no	—
141	C₃₁×#120	—	4	2	no	—
142	C₃₁×#117	—	4	2	no	—
143	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
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	1	yes	characteristic
147	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
148	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
149	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
150	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
151	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
152	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
153	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
154	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
155	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
156	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
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	2	yes	—
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	1	yes	characteristic
167	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
168	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
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	2	yes	—
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	2	yes	—
178	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
179	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
180	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
181	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
182	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
183	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
184	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
185	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
186	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
187	C₂×C₄²×C₃₁	—	4	2	no	—
188	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
189	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
190	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
191	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
192	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
193	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
194	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
195	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
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	C₃₁×#95	C₂³	1	2	yes	—
208	C₃₁×#95	C₂³	1	2	yes	—
209	C₃₁×#95	C₂³	1	2	yes	—
210	C₃₁×#95	C₂³	1	2	yes	—
211	C₃₁×#95	C₂³	1	2	yes	—
212	C₃₁×#95	C₂³	1	2	yes	—
213	C₂⁴×C₃₁	—	2	2	no	—
214	C₂⁴×C₃₁	—	4	2	no	—
215	C₂⁴×C₃₁	—	4	2	no	—
216	C₂⁴×C₃₁	—	4	1	no	—
217	C₂⁴×C₃₁	—	4	1	no	—
218	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
219	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
220	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
221	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
222	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
223	#41×C₃₁	—	4	16	no	—
224	C₂×Q₈×C₃₁	—	2	2	no	—
225	C₂×Q₈×C₃₁	—	2	2	no	—
226	C₂×Q₈×C₃₁	—	4	1	no	—
227	C₂×D₄×C₃₁	—	2	2	no	—
228	C₂×D₄×C₃₁	—	2	2	no	—
229	C₂×D₄×C₃₁	—	2	2	no	—
230	C₂×D₄×C₃₁	—	2	2	no	—
231	C₂×D₄×C₃₁	—	2	4	no	—
232	C₂×D₄×C₃₁	—	2	4	no	—
233	C₂×D₄×C₃₁	—	2	4	no	—
234	C₂×D₄×C₃₁	—	2	2	no	—
235	C₂×D₄×C₃₁	—	2	2	no	—
236	C₂×D₄×C₃₁	—	2	2	no	—
237	C₂×D₄×C₃₁	—	2	4	no	—
238	C₂×D₄×C₃₁	—	4	1	no	—
239	C₂×D₄×C₃₁	—	4	1	no	—
240	C₂×D₄×C₃₁	—	4	1	no	—
241	C₂×D₄×C₃₁	—	4	2	no	—
242	C₂×D₄×C₃₁	—	4	2	no	—
243	C₂×D₄×C₃₁	—	4	2	no	—
244	C₂×D₄×C₃₁	—	4	2	no	—
245	C₂×D₄×C₃₁	—	4	2	no	—
246	C₂×D₄×C₃₁	—	4	2	no	—
247	C₂×D₄×C₃₁	—	4	2	no	—
248	C₂×D₄×C₃₁	—	4	2	no	—
249	C₂×D₄×C₃₁	—	4	2	no	—
250	C₂×D₄×C₃₁	—	4	2	no	—
251	C₂×D₄×C₃₁	—	4	1	no	—
252	C₂×D₄×C₃₁	—	4	1	no	—
253	C₂×D₄×C₃₁	—	4	2	no	—
254	C₂×D₄×C₃₁	—	4	2	no	—
255	C₂×D₄×C₃₁	—	4	2	no	—
256	C₂×D₄×C₃₁	—	4	2	no	—
257	C₂×D₄×C₃₁	—	4	2	no	—
258	C₂×D₄×C₃₁	—	4	2	no	—
259	C₂×D₄×C₃₁	—	4	2	no	—
260	C₂²×C₄×C₃₁	—	2	2	no	—
261	C₂²×C₄×C₃₁	—	2	2	no	—
262	C₂²×C₄×C₃₁	—	2	2	no	—
263	C₂²×C₄×C₃₁	—	2	4	no	—
264	C₂²×C₄×C₃₁	—	2	2	no	—
265	C₂²×C₄×C₃₁	—	2	2	no	—
266	C₂²×C₄×C₃₁	—	2	4	no	—
267	C₂²×C₄×C₃₁	—	4	2	no	—
268	C₂²×C₄×C₃₁	—	4	1	no	—
269	C₂²×C₄×C₃₁	—	4	1	no	—
270	C₂²×C₄×C₃₁	—	4	1	no	—
271	C₂²×C₄×C₃₁	—	4	1	no	—
272	C₂²×C₄×C₃₁	—	4	2	no	—
273	C₂²×C₄×C₃₁	—	4	2	no	—
274	C₂²×C₄×C₃₁	—	4	2	no	—
275	C₂²×C₄×C₃₁	—	4	2	no	—
276	C₂²×C₄×C₃₁	#41	1	4	yes	—
277	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
278	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
279	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
280	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
281	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
282	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
283	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
284	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
285	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
286	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
287	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
288	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
289	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
290	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
291	C₄⋊C₄×C₃₁	—	2	2	no	—
292	C₄⋊C₄×C₃₁	—	2	4	no	—
293	C₄⋊C₄×C₃₁	—	2	4	no	—
294	C₄⋊C₄×C₃₁	—	2	4	no	—
295	C₄⋊C₄×C₃₁	—	2	4	no	—
296	C₄⋊C₄×C₃₁	—	4	2	no	—
297	C₄⋊C₄×C₃₁	—	4	2	no	—
298	C₄⋊C₄×C₃₁	—	4	2	no	—
299	C₄⋊C₄×C₃₁	—	4	2	no	—
300	C₄⋊C₄×C₃₁	—	4	2	no	—
301	C₄⋊C₄×C₃₁	—	4	2	no	—
302	C₄⋊C₄×C₃₁	—	4	2	no	—
303	C₄⋊C₄×C₃₁	—	4	2	no	—
304	C₂²⋊C₄×C₃₁	—	2	4	no	—
305	C₂²⋊C₄×C₃₁	—	2	4	no	—
306	C₂²⋊C₄×C₃₁	—	2	4	no	—
307	C₂²⋊C₄×C₃₁	—	2	4	no	—
308	C₂²⋊C₄×C₃₁	—	2	4	no	—
309	C₂²⋊C₄×C₃₁	—	2	4	no	—
310	C₂²⋊C₄×C₃₁	—	2	4	no	—
311	C₂²⋊C₄×C₃₁	—	2	4	no	—
312	C₂²⋊C₄×C₃₁	—	2	4	no	—
313	C₂²⋊C₄×C₃₁	—	4	2	no	—
314	C₂²⋊C₄×C₃₁	—	4	2	no	—
315	C₂²⋊C₄×C₃₁	—	4	2	no	—
316	C₂²⋊C₄×C₃₁	—	4	2	no	—
317	C₂²⋊C₄×C₃₁	—	4	2	no	—
318	C₂²⋊C₄×C₃₁	—	4	2	no	—
319	C₂²⋊C₄×C₃₁	—	4	1	no	—
320	C₂²⋊C₄×C₃₁	—	4	1	no	—
321	C₂²⋊C₄×C₃₁	—	4	2	no	—
322	C₂²⋊C₄×C₃₁	—	4	2	no	—
323	C₂²⋊C₄×C₃₁	—	4	2	no	—
324	C₂²⋊C₄×C₃₁	—	4	2	no	—
325	C₂²⋊C₄×C₃₁	—	4	2	no	—
326	C₂²⋊C₄×C₃₁	—	4	2	no	—
327	C₂²⋊C₄×C₃₁	—	4	2	no	—
328	C₂²⋊C₄×C₃₁	—	4	2	no	—
329	C₂²⋊C₄×C₃₁	—	4	2	no	—
330	C₂²⋊C₄×C₃₁	—	4	2	no	—
331	C₂²⋊C₄×C₃₁	—	4	2	no	—
332	C₂²⋊C₄×C₃₁	—	4	2	no	—
333	C₂²⋊C₄×C₃₁	—	4	2	no	—
334	C₄²×C₃₁	—	4	1	no	—
335	C₄²×C₃₁	—	4	2	no	—
336	C₄²×C₃₁	—	4	1	no	—
337	C₄²×C₃₁	—	4	1	no	—
338	C₄²×C₃₁	—	4	1	no	—
339	C₄²×C₃₁	—	4	1	no	—
340	C₄²×C₃₁	—	4	2	no	—
341	C₄²×C₃₁	—	4	1	no	—
342	#36812	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
343	C₂³×C₃₁	—	2	1	no	—
344	C₂³×C₃₁	—	2	2	no	—
345	C₂³×C₃₁	—	2	1	no	—
346	C₂³×C₃₁	—	2	2	no	—
347	C₂³×C₃₁	—	2	1	no	—
348	C₂³×C₃₁	—	2	1	no	—
349	C₂³×C₃₁	—	2	2	no	—
350	C₂³×C₃₁	—	2	2	no	—
351	C₂³×C₃₁	—	2	2	no	—
352	C₂³×C₃₁	—	2	2	no	—
353	C₂³×C₃₁	—	2	1	no	—
354	C₂³×C₃₁	—	2	2	no	—
355	C₂³×C₃₁	—	2	2	no	—
356	C₂³×C₃₁	—	2	2	no	—
357	C₂³×C₃₁	—	2	2	no	—
358	C₂³×C₃₁	—	2	2	no	—
359	C₂³×C₃₁	—	2	2	no	—
360	C₂³×C₃₁	—	2	2	no	—
361	C₂³×C₃₁	—	2	2	no	—
362	C₂³×C₃₁	—	2	1	no	—
363	C₂³×C₃₁	—	2	1	no	—
364	C₂³×C₃₁	—	2	2	no	—
365	C₂³×C₃₁	—	2	2	no	—
366	C₂³×C₃₁	—	2	2	no	—
367	C₂³×C₃₁	—	2	2	no	—
368	C₂³×C₃₁	—	2	2	no	—
369	C₂³×C₃₁	—	2	2	no	—
370	C₂³×C₃₁	—	4	4	no	—
371	C₂³×C₃₁	—	8	2	no	—
372	C₂³×C₃₁	—	8	2	no	—
373	C₂³×C₃₁	—	8	4	no	—
374	C₂³×C₃₁	—	8	4	no	—
375	C₂³×C₃₁	C₂×#41	1	2	yes	—
376	C₂³×C₃₁	H(5,𝔽₂)	1	2	yes	—
377	C₂³×C₃₁	C₂⁵	1	1	yes	characteristic
378	Q₈×C₃₁	—	4	4	no	—
379	D₄×C₃₁	—	4	4	no	—
380	D₄×C₃₁	—	4	4	no	—
381	D₄×C₃₁	—	4	4	no	—
382	D₄×C₃₁	—	8	2	no	—
383	D₄×C₃₁	—	8	4	no	—
384	D₄×C₃₁	—	8	4	no	—
385	D₄×C₃₁	—	8	4	no	—
386	D₄×C₃₁	—	8	4	no	—
387	D₄×C₃₁	—	8	4	no	—
388	D₄×C₃₁	—	8	4	no	—
389	D₄×C₃₁	—	8	4	no	—
390	C₂×C₄×C₃₁	—	2	8	no	—
391	C₂×C₄×C₃₁	—	2	1	no	—
392	C₂×C₄×C₃₁	—	2	2	no	—
393	C₂×C₄×C₃₁	—	2	1	no	—
394	C₂×C₄×C₃₁	—	2	1	no	—
395	C₂×C₄×C₃₁	—	2	1	no	—
396	C₂×C₄×C₃₁	—	2	1	no	—
397	C₂×C₄×C₃₁	—	2	1	no	—
398	C₂×C₄×C₃₁	—	2	2	no	—
399	C₂×C₄×C₃₁	—	2	2	no	—
400	C₂×C₄×C₃₁	—	2	2	no	—
401	C₂×C₄×C₃₁	—	2	1	no	—
402	C₂×C₄×C₃₁	—	2	2	no	—
403	C₂×C₄×C₃₁	—	2	2	no	—
404	C₂×C₄×C₃₁	—	2	2	no	—
405	C₂×C₄×C₃₁	—	2	2	no	—
406	C₂×C₄×C₃₁	—	2	2	no	—
407	C₂×C₄×C₃₁	—	2	2	no	—
408	C₂×C₄×C₃₁	—	2	2	no	—
409	C₂×C₄×C₃₁	—	2	2	no	—
410	C₂×C₄×C₃₁	—	2	2	no	—
411	C₂×C₄×C₃₁	—	2	2	no	—
412	C₂×C₄×C₃₁	—	2	2	no	—
413	C₂×C₄×C₃₁	—	2	2	no	—
414	C₂×C₄×C₃₁	—	2	2	no	—
415	C₂×C₄×C₃₁	—	2	2	no	—
416	C₂×C₄×C₃₁	—	2	2	no	—
417	C₂×C₄×C₃₁	—	2	2	no	—
418	C₂×C₄×C₃₁	—	2	2	no	—
419	C₂×C₄×C₃₁	—	2	1	no	—
420	C₂×C₄×C₃₁	—	2	1	no	—
421	C₂×C₄×C₃₁	—	2	2	no	—
422	C₂×C₄×C₃₁	—	2	2	no	—
423	C₂×C₄×C₃₁	—	2	2	no	—
424	C₂×C₄×C₃₁	—	2	2	no	—
425	C₂×C₄×C₃₁	—	2	2	no	—
426	C₂×C₄×C₃₁	—	2	2	no	—
427	C₂×C₄×C₃₁	—	2	2	no	—
428	C₂×C₄×C₃₁	—	2	2	no	—
429	C₂×C₄×C₃₁	—	4	4	no	—
430	C₂×C₄×C₃₁	—	4	8	no	—
431	C₂×C₄×C₃₁	—	4	4	no	—
432	C₂×C₄×C₃₁	—	8	2	no	—
433	C₂×C₄×C₃₁	—	8	4	no	—
434	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
435	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
436	C₂×C₄×C₃₁	H(5,𝔽₂)	1	4	yes	—
437	C₂×C₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
438	#2854	C₂×C₃₁	1	2	yes	complemented
439	#2798	C₂×C₃₁	1	2	yes	complemented
440	#2710	C₂×C₃₁	1	2	yes	complemented
441	#2705	C₂×C₃₁	1	2	yes	complemented
442	#2705	C₂×C₃₁	1	2	yes	complemented
443	#2693	C₂×C₃₁	1	2	yes	complemented
444	#2678	C₂×C₃₁	1	2	yes	complemented
445	#2678	C₂×C₃₁	1	2	yes	complemented
446	#2673	C₂×C₃₁	1	2	yes	complemented
447	#2648	C₂×C₃₁	1	2	yes	complemented
448	#2608	C₂×C₃₁	1	1	yes	characteristic, complemented
449	#2559	C₂×C₃₁	1	2	yes	complemented
450	#2539	C₂×C₃₁	1	1	yes	characteristic, complemented
451	#2471	C₂×C₃₁	1	2	yes	complemented
452	#2431	C₂×C₃₁	1	1	yes	characteristic, complemented
453	#2404	C₂×C₃₁	1	1	yes	characteristic, complemented
454	#2333	C₂×C₃₁	1	1	yes	characteristic, complemented
455	#2312	C₂×C₃₁	1	1	yes	characteristic, complemented
456	#2297	C₂×C₃₁	1	1	yes	characteristic, complemented
457	C₂²×C₃₁	—	2	2	no	—
458	C₂²×C₃₁	—	2	2	no	—
459	C₂²×C₃₁	—	2	2	no	—
460	C₂²×C₃₁	—	2	2	no	—
461	C₂²×C₃₁	—	2	4	no	—
462	C₂²×C₃₁	—	4	1	no	—
463	C₂²×C₃₁	—	4	1	no	—
464	C₂²×C₃₁	—	4	2	no	—
465	C₂²×C₃₁	—	4	2	no	—
466	C₂²×C₃₁	—	4	2	no	—
467	C₂²×C₃₁	—	4	2	no	—
468	C₂²×C₃₁	—	4	1	no	—
469	C₂²×C₃₁	—	4	2	no	—
470	C₂²×C₃₁	—	4	1	no	—
471	C₂²×C₃₁	—	4	2	no	—
472	C₂²×C₃₁	—	4	2	no	—
473	C₂²×C₃₁	—	4	2	no	—
474	C₂²×C₃₁	—	4	1	no	—
475	C₂²×C₃₁	—	4	2	no	—
476	C₂²×C₃₁	—	4	2	no	—
477	C₂²×C₃₁	—	4	2	no	—
478	C₂²×C₃₁	—	4	2	no	—
479	C₂²×C₃₁	—	4	2	no	—
480	C₂²×C₃₁	—	4	2	no	—
481	C₂²×C₃₁	—	4	2	no	—
482	C₂²×C₃₁	—	4	2	no	—
483	C₂²×C₃₁	—	4	2	no	—
484	C₂²×C₃₁	—	4	2	no	—
485	C₂²×C₃₁	—	4	2	no	—
486	C₂²×C₃₁	—	8	8	no	—
487	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
488	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
489	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
490	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	2	yes	—
491	C₂²×C₃₁	#585	1	2	yes	—
492	C₄×C₃₁	—	2	2	no	—
493	C₄×C₃₁	—	2	2	no	—
494	C₄×C₃₁	—	2	2	no	—
495	C₄×C₃₁	—	2	4	no	—
496	C₄×C₃₁	—	4	1	no	—
497	C₄×C₃₁	—	4	2	no	—
498	C₄×C₃₁	—	4	2	no	—
499	C₄×C₃₁	—	4	2	no	—
500	C₄×C₃₁	—	4	2	no	—
501	C₄×C₃₁	—	4	2	no	—
502	C₄×C₃₁	—	4	2	no	—
503	C₄×C₃₁	—	4	2	no	—
504	C₄×C₃₁	—	4	2	no	—
505	C₄×C₃₁	—	4	2	no	—
506	C₂²×#41	C₂²×C₃₁	1	1	yes	characteristic
507	C₂×#127	C₂²×C₃₁	1	1	yes	characteristic, complemented
508	C₂×#126	C₂²×C₃₁	1	2	yes	complemented
509	C₂×#124	C₂²×C₃₁	1	1	yes	characteristic, complemented
510	C₂×#123	C₂²×C₃₁	1	2	yes	—
511	C₂×#123	C₂²×C₃₁	1	2	yes	—
512	C₂×#123	C₂²×C₃₁	1	2	yes	—
513	C₂×#123	C₂²×C₃₁	1	2	yes	complemented
514	C₂×#121	C₂²×C₃₁	1	1	yes	characteristic
515	C₂×#121	C₂²×C₃₁	1	2	yes	—
516	C₂×#121	C₂²×C₃₁	1	2	yes	—
517	C₂×#120	C₂²×C₃₁	1	1	yes	characteristic
518	C₂×#120	C₂²×C₃₁	1	1	yes	characteristic
519	C₂×#120	C₂²×C₃₁	1	2	yes	—
520	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic, complemented
521	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
522	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic, complemented
523	#400	C₂²×C₃₁	1	2	yes	complemented
524	#400	C₂²×C₃₁	1	2	yes	complemented
525	#399	C₂²×C₃₁	1	2	yes	—
526	#399	C₂²×C₃₁	1	2	yes	complemented
527	#397	C₂²×C₃₁	1	2	yes	—
528	#397	C₂²×C₃₁	1	2	yes	—
529	#397	C₂²×C₃₁	1	2	yes	complemented
530	#396	C₂²×C₃₁	1	2	yes	—
531	#396	C₂²×C₃₁	1	2	yes	—
532	#396	C₂²×C₃₁	1	2	yes	complemented
533	#396	C₂²×C₃₁	1	2	yes	complemented
534	#394	C₂²×C₃₁	1	2	yes	—
535	#394	C₂²×C₃₁	1	2	yes	—
536	#394	C₂²×C₃₁	1	2	yes	—
537	#394	C₂²×C₃₁	1	2	yes	—
538	#394	C₂²×C₃₁	1	2	yes	complemented
539	#394	C₂²×C₃₁	1	2	yes	complemented
540	#393	C₂²×C₃₁	1	2	yes	—
541	#392	C₂²×C₃₁	1	2	yes	—
542	#392	C₂²×C₃₁	1	2	yes	—
543	#392	C₂²×C₃₁	1	2	yes	—
544	#392	C₂²×C₃₁	1	2	yes	—
545	#392	C₂²×C₃₁	1	2	yes	—
546	#392	C₂²×C₃₁	1	2	yes	—
547	#391	C₂²×C₃₁	1	1	yes	characteristic, complemented
548	#391	C₂²×C₃₁	1	2	yes	complemented
549	#390	C₂²×C₃₁	1	2	yes	—
550	#390	C₂²×C₃₁	1	2	yes	—
551	#390	C₂²×C₃₁	1	2	yes	—
552	#390	C₂²×C₃₁	1	2	yes	—
553	#390	C₂²×C₃₁	1	2	yes	—
554	#390	C₂²×C₃₁	1	2	yes	—
555	#390	C₂²×C₃₁	1	1	yes	characteristic, complemented
556	#389	C₂²×C₃₁	1	2	yes	complemented
557	#389	C₂²×C₃₁	1	2	yes	complemented
558	#389	C₂²×C₃₁	1	2	yes	complemented
559	#388	C₂²×C₃₁	1	2	yes	—
560	#388	C₂²×C₃₁	1	2	yes	—
561	#388	C₂²×C₃₁	1	2	yes	—
562	#388	C₂²×C₃₁	1	2	yes	—
563	#388	C₂²×C₃₁	1	2	yes	—
564	#388	C₂²×C₃₁	1	2	yes	—
565	#388	C₂²×C₃₁	1	2	yes	complemented
566	#388	C₂²×C₃₁	1	2	yes	complemented
567	#387	C₂²×C₃₁	1	2	yes	complemented
568	#387	C₂²×C₃₁	1	2	yes	complemented
569	#387	C₂²×C₃₁	1	2	yes	complemented
570	#387	C₂²×C₃₁	1	2	yes	complemented
571	#386	C₂²×C₃₁	1	2	yes	—
572	#386	C₂²×C₃₁	1	2	yes	—
573	#386	C₂²×C₃₁	1	2	yes	—
574	#386	C₂²×C₃₁	1	1	yes	characteristic
575	#386	C₂²×C₃₁	1	1	yes	characteristic
576	#386	C₂²×C₃₁	1	2	yes	—
577	#386	C₂²×C₃₁	1	2	yes	complemented
578	#386	C₂²×C₃₁	1	2	yes	complemented
579	#386	C₂²×C₃₁	1	2	yes	complemented
580	#386	C₂²×C₃₁	1	2	yes	complemented
581	#386	C₂²×C₃₁	1	2	yes	complemented
582	#385	C₂²×C₃₁	1	2	yes	complemented
583	#381	C₂²×C₃₁	1	1	yes	characteristic
584	#380	C₂²×C₃₁	1	2	yes	—
585	#380	C₂²×C₃₁	1	2	yes	complemented
586	#379	C₂²×C₃₁	1	2	yes	—
587	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
588	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
589	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
590	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	complemented
591	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
592	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
593	C₂×C₃₁	—	4	2	no	—
594	C₂×C₃₁	—	4	2	no	—
595	C₂×C₃₁	—	8	1	no	—
596	C₂×C₃₁	—	8	2	no	—
597	C₂×C₃₁	—	8	2	no	—
598	C₂×C₃₁	#3455	1	1	yes	characteristic
599	C₂×C₃₁	#3490	1	1	yes	characteristic
600	C₂×C₃₁	#3508	1	1	yes	characteristic
601	C₂×C₃₁	#3534	1	2	yes	—
602	C₂×C₃₁	#3546	1	2	yes	—
603	C₂⁵	C₂³×C₃₁	1	1	yes	characteristic
604	C₂×#41	—	2	4	no	—
605	C₂×#41	—	4	2	no	—
606	C₂×#41	—	4	2	no	—
607	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
608	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
609	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
610	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
611	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
612	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
613	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
614	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
615	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
616	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
617	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
618	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
619	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
620	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
621	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
622	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
623	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
624	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
625	#127	—	4	2	no	—
626	#126	—	4	4	no	—
627	#124	—	4	2	no	—
628	#123	—	4	4	no	—
629	#123	—	4	4	no	—
630	#123	—	4	4	no	—
631	#123	—	4	4	no	—
632	#121	—	2	4	no	—
633	#121	—	4	4	no	—
634	#121	—	4	4	no	—
635	#120	—	4	2	no	—
636	#120	—	4	4	no	—
637	#120	—	4	2	no	—
638	#117	—	4	2	no	—
639	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
640	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
641	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
642	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
643	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
644	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
645	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
646	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
647	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
648	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
649	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
650	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
651	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
652	C₂×C₂²⋊C₄	—	2	4	no	—
653	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
654	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
655	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
656	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
657	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
658	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
659	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
660	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
661	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
662	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
663	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
664	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
665	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
666	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
667	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
668	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
669	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
670	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
671	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
672	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
673	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
674	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
675	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
676	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
677	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
678	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
679	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
680	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
681	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
682	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
683	C₂×C₄²	—	4	2	no	—
684	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
685	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
686	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
687	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
688	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
689	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
690	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
691	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
692	#95	C₂³×C₃₁	1	2	yes	—
693	#95	C₂³×C₃₁	1	2	yes	—
694	#95	C₂³×C₃₁	1	2	yes	—
695	#95	C₂³×C₃₁	1	2	yes	—
696	#95	C₂³×C₃₁	1	2	yes	—
697	#95	C₂³×C₃₁	1	2	yes	—
698	#95	C₂³×C₃₁	1	2	yes	—
699	#95	C₂³×C₃₁	1	2	yes	—
700	#95	C₂³×C₃₁	1	2	yes	—
701	#95	C₂³×C₃₁	1	2	yes	—
702	#95	C₂³×C₃₁	1	2	yes	—
703	#95	C₂³×C₃₁	1	2	yes	—
704	#95	C₂³×C₃₁	1	2	yes	—
705	#95	C₂³×C₃₁	1	2	yes	—
706	#95	C₂³×C₃₁	1	2	yes	—
707	#95	C₂³×C₃₁	1	2	yes	—
708	#95	C₂³×C₃₁	1	2	yes	—
709	C₃₁	#36812	1	1	yes	characteristic, direct product factor, Sylow
710	C₂⁴	—	2	2	no	—
711	C₂⁴	—	4	2	no	—
712	C₂⁴	—	4	2	no	—
713	C₂⁴	—	4	1	no	—
714	C₂⁴	—	4	1	no	—
715	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
716	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
717	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
718	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
719	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
720	#41	—	4	16	no	—
721	C₂×Q₈	—	2	2	no	—
722	C₂×Q₈	—	2	2	no	—
723	C₂×Q₈	—	4	1	no	—
724	C₂×D₄	—	2	2	no	—
725	C₂×D₄	—	2	2	no	—
726	C₂×D₄	—	2	2	no	—
727	C₂×D₄	—	2	2	no	—
728	C₂×D₄	—	2	4	no	—
729	C₂×D₄	—	2	4	no	—
730	C₂×D₄	—	2	4	no	—
731	C₂×D₄	—	2	2	no	—
732	C₂×D₄	—	2	2	no	—
733	C₂×D₄	—	2	2	no	—
734	C₂×D₄	—	2	4	no	—
735	C₂×D₄	—	4	1	no	—
736	C₂×D₄	—	4	1	no	—
737	C₂×D₄	—	4	1	no	—
738	C₂×D₄	—	4	2	no	—
739	C₂×D₄	—	4	2	no	—
740	C₂×D₄	—	4	2	no	—
741	C₂×D₄	—	4	2	no	—
742	C₂×D₄	—	4	2	no	—
743	C₂×D₄	—	4	2	no	—
744	C₂×D₄	—	4	2	no	—
745	C₂×D₄	—	4	2	no	—
746	C₂×D₄	—	4	2	no	—
747	C₂×D₄	—	4	2	no	—
748	C₂×D₄	—	4	1	no	—
749	C₂×D₄	—	4	1	no	—
750	C₂×D₄	—	4	2	no	—
751	C₂×D₄	—	4	2	no	—
752	C₂×D₄	—	4	2	no	—
753	C₂×D₄	—	4	2	no	—
754	C₂×D₄	—	4	2	no	—
755	C₂×D₄	—	4	2	no	—
756	C₂×D₄	—	4	2	no	—
757	C₂²×C₄	—	2	2	no	—
758	C₂²×C₄	—	2	2	no	—
759	C₂²×C₄	—	2	2	no	—
760	C₂²×C₄	—	2	4	no	—
761	C₂²×C₄	—	2	2	no	—
762	C₂²×C₄	—	2	2	no	—
763	C₂²×C₄	—	2	4	no	—
764	C₂²×C₄	—	4	2	no	—
765	C₂²×C₄	—	4	1	no	—
766	C₂²×C₄	—	4	1	no	—
767	C₂²×C₄	—	4	1	no	—
768	C₂²×C₄	—	4	1	no	—
769	C₂²×C₄	—	4	2	no	—
770	C₂²×C₄	—	4	2	no	—
771	C₂²×C₄	—	4	2	no	—
772	C₂²×C₄	—	4	2	no	—
773	C₂²×C₄	#41×C₃₁	1	4	yes	—
774	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
775	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
776	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
777	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
778	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
779	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
780	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
781	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
782	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
783	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
784	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
785	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
786	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
787	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
788	C₄⋊C₄	—	2	2	no	—
789	C₄⋊C₄	—	2	4	no	—
790	C₄⋊C₄	—	2	4	no	—
791	C₄⋊C₄	—	2	4	no	—
792	C₄⋊C₄	—	2	4	no	—
793	C₄⋊C₄	—	4	2	no	—
794	C₄⋊C₄	—	4	2	no	—
795	C₄⋊C₄	—	4	2	no	—
796	C₄⋊C₄	—	4	2	no	—
797	C₄⋊C₄	—	4	2	no	—
798	C₄⋊C₄	—	4	2	no	—
799	C₄⋊C₄	—	4	2	no	—
800	C₄⋊C₄	—	4	2	no	—
801	C₂²⋊C₄	—	2	4	no	—
802	C₂²⋊C₄	—	2	4	no	—
803	C₂²⋊C₄	—	2	4	no	—
804	C₂²⋊C₄	—	2	4	no	—
805	C₂²⋊C₄	—	2	4	no	—
806	C₂²⋊C₄	—	2	4	no	—
807	C₂²⋊C₄	—	2	4	no	—
808	C₂²⋊C₄	—	2	4	no	—
809	C₂²⋊C₄	—	2	4	no	—
810	C₂²⋊C₄	—	4	2	no	—
811	C₂²⋊C₄	—	4	2	no	—
812	C₂²⋊C₄	—	4	2	no	—
813	C₂²⋊C₄	—	4	2	no	—
814	C₂²⋊C₄	—	4	2	no	—
815	C₂²⋊C₄	—	4	2	no	—
816	C₂²⋊C₄	—	4	1	no	—
817	C₂²⋊C₄	—	4	1	no	—
818	C₂²⋊C₄	—	4	2	no	—
819	C₂²⋊C₄	—	4	2	no	—
820	C₂²⋊C₄	—	4	2	no	—
821	C₂²⋊C₄	—	4	2	no	—
822	C₂²⋊C₄	—	4	2	no	—
823	C₂²⋊C₄	—	4	2	no	—
824	C₂²⋊C₄	—	4	2	no	—
825	C₂²⋊C₄	—	4	2	no	—
826	C₂²⋊C₄	—	4	2	no	—
827	C₂²⋊C₄	—	4	2	no	—
828	C₂²⋊C₄	—	4	2	no	—
829	C₂²⋊C₄	—	4	2	no	—
830	C₂²⋊C₄	—	4	2	no	—
831	C₄²	—	4	1	no	—
832	C₄²	—	4	2	no	—
833	C₄²	—	4	1	no	—
834	C₄²	—	4	1	no	—
835	C₄²	—	4	1	no	—
836	C₄²	—	4	1	no	—
837	C₄²	—	4	2	no	—
838	C₄²	—	4	1	no	—
839	C₂³	—	2	1	no	—
840	C₂³	—	2	2	no	—
841	C₂³	—	2	1	no	—
842	C₂³	—	2	2	no	—
843	C₂³	—	2	1	no	—
844	C₂³	—	2	1	no	—
845	C₂³	—	2	2	no	—
846	C₂³	—	2	2	no	—
847	C₂³	—	2	2	no	—
848	C₂³	—	2	2	no	—
849	C₂³	—	2	1	no	—
850	C₂³	—	2	2	no	—
851	C₂³	—	2	2	no	—
852	C₂³	—	2	2	no	—
853	C₂³	—	2	2	no	—
854	C₂³	—	2	2	no	—
855	C₂³	—	2	2	no	—
856	C₂³	—	2	2	no	—
857	C₂³	—	2	2	no	—
858	C₂³	—	2	1	no	—
859	C₂³	—	2	1	no	—
860	C₂³	—	2	2	no	—
861	C₂³	—	2	2	no	—
862	C₂³	—	2	2	no	—
863	C₂³	—	2	2	no	—
864	C₂³	—	2	2	no	—
865	C₂³	—	2	2	no	—
866	C₂³	—	4	4	no	—
867	C₂³	—	8	2	no	—
868	C₂³	—	8	2	no	—
869	C₂³	—	8	4	no	—
870	C₂³	—	8	4	no	—
871	C₂³	C₂×#41×C₃₁	1	2	yes	—
872	C₂³	C₃₁×H(5,𝔽₂)	1	2	yes	—
873	C₂³	C₂⁵×C₃₁	1	1	yes	characteristic
874	Q₈	—	4	4	no	—
875	D₄	—	4	4	no	—
876	D₄	—	4	4	no	—
877	D₄	—	4	4	no	—
878	D₄	—	8	2	no	—
879	D₄	—	8	4	no	—
880	D₄	—	8	4	no	—
881	D₄	—	8	4	no	—
882	D₄	—	8	4	no	—
883	D₄	—	8	4	no	—
884	D₄	—	8	4	no	—
885	D₄	—	8	4	no	—
886	C₂×C₄	—	2	8	no	—
887	C₂×C₄	—	2	1	no	—
888	C₂×C₄	—	2	2	no	—
889	C₂×C₄	—	2	1	no	—
890	C₂×C₄	—	2	1	no	—
891	C₂×C₄	—	2	1	no	—
892	C₂×C₄	—	2	1	no	—
893	C₂×C₄	—	2	1	no	—
894	C₂×C₄	—	2	2	no	—
895	C₂×C₄	—	2	2	no	—
896	C₂×C₄	—	2	2	no	—
897	C₂×C₄	—	2	1	no	—
898	C₂×C₄	—	2	2	no	—
899	C₂×C₄	—	2	2	no	—
900	C₂×C₄	—	2	2	no	—
901	C₂×C₄	—	2	2	no	—
902	C₂×C₄	—	2	2	no	—
903	C₂×C₄	—	2	2	no	—
904	C₂×C₄	—	2	2	no	—
905	C₂×C₄	—	2	2	no	—
906	C₂×C₄	—	2	2	no	—
907	C₂×C₄	—	2	2	no	—
908	C₂×C₄	—	2	2	no	—
909	C₂×C₄	—	2	2	no	—
910	C₂×C₄	—	2	2	no	—
911	C₂×C₄	—	2	2	no	—
912	C₂×C₄	—	2	2	no	—
913	C₂×C₄	—	2	2	no	—
914	C₂×C₄	—	2	2	no	—
915	C₂×C₄	—	2	1	no	—
916	C₂×C₄	—	2	1	no	—
917	C₂×C₄	—	2	2	no	—
918	C₂×C₄	—	2	2	no	—
919	C₂×C₄	—	2	2	no	—
920	C₂×C₄	—	2	2	no	—
921	C₂×C₄	—	2	2	no	—
922	C₂×C₄	—	2	2	no	—
923	C₂×C₄	—	2	2	no	—
924	C₂×C₄	—	2	2	no	—
925	C₂×C₄	—	4	4	no	—
926	C₂×C₄	—	4	8	no	—
927	C₂×C₄	—	4	4	no	—
928	C₂×C₄	—	8	2	no	—
929	C₂×C₄	—	8	4	no	—
930	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
931	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
932	C₂×C₄	C₃₁×H(5,𝔽₂)	1	4	yes	—
933	C₂×C₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
934	C₂²	—	2	2	no	—
935	C₂²	—	2	2	no	—
936	C₂²	—	2	2	no	—
937	C₂²	—	2	2	no	—
938	C₂²	—	2	4	no	—
939	C₂²	—	4	1	no	—
940	C₂²	—	4	1	no	—
941	C₂²	—	4	2	no	—
942	C₂²	—	4	2	no	—
943	C₂²	—	4	2	no	—
944	C₂²	—	4	2	no	—
945	C₂²	—	4	2	no	—
946	C₂²	—	4	1	no	—
947	C₂²	—	4	1	no	—
948	C₂²	—	4	2	no	—
949	C₂²	—	4	2	no	—
950	C₂²	—	4	2	no	—
951	C₂²	—	4	2	no	—
952	C₂²	—	4	1	no	—
953	C₂²	—	4	2	no	—
954	C₂²	—	4	2	no	—
955	C₂²	—	4	2	no	—
956	C₂²	—	4	2	no	—
957	C₂²	—	4	2	no	—
958	C₂²	—	4	2	no	—
959	C₂²	—	4	2	no	—
960	C₂²	—	4	2	no	—
961	C₂²	—	4	2	no	—
962	C₂²	—	4	2	no	—
963	C₂²	—	8	8	no	—
964	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
965	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
966	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
967	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	2	yes	—
968	C₂²	C₃₁×#585	1	2	yes	—
969	C₄	—	2	2	no	—
970	C₄	—	2	2	no	—
971	C₄	—	2	2	no	—
972	C₄	—	2	4	no	—
973	C₄	—	4	1	no	—
974	C₄	—	4	2	no	—
975	C₄	—	4	2	no	—
976	C₄	—	4	2	no	—
977	C₄	—	4	2	no	—
978	C₄	—	4	2	no	—
979	C₄	—	4	2	no	—
980	C₄	—	4	2	no	—
981	C₄	—	4	2	no	—
982	C₄	—	4	2	no	—
983	C₂	—	4	2	no	—
984	C₂	—	4	2	no	—
985	C₂	—	8	2	no	—
986	C₂	—	8	1	no	—
987	C₂	—	8	2	no	—
988	C₂	C₃₁×#3455	1	1	yes	characteristic
989	C₂	C₃₁×#3490	1	1	yes	characteristic
990	C₂	C₃₁×#3508	1	1	yes	characteristic
991	C₂	C₃₁×#3534	1	2	yes	—
992	C₂	C₃₁×#3546	1	2	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. C₃₁×#2854	C₂	semidirect
2. C₃₁×#2798	C₂	semidirect
3. C₃₁×#2710	C₂	semidirect
4. C₃₁×#2705	C₂	semidirect
5. C₃₁×#2705	C₂	semidirect
6. C₃₁×#2693	C₂	semidirect
7. C₃₁×#2678	C₂	semidirect
8. C₃₁×#2678	C₂	semidirect
9. C₃₁×#2673	C₂	semidirect
10. C₃₁×#2648	C₂	semidirect
11. C₃₁×#2608	C₂	semidirect
12. C₃₁×#2559	C₂	semidirect
13. C₃₁×#2539	C₂	semidirect
14. C₃₁×#2471	C₂	semidirect
15. C₃₁×#2431	C₂	semidirect
16. C₃₁×#2404	C₂	semidirect
17. C₃₁×#2333	C₂	semidirect
18. C₃₁×#2312	C₂	semidirect
19. C₃₁×#2297	C₂	semidirect
21. C₂×C₃₁×#127	C₂²	semidirect
22. C₂×C₃₁×#126	C₂²	semidirect
23. C₂×C₃₁×#124	C₂²	semidirect
27. C₂×C₃₁×#123	C₂²	semidirect
34. C₂×C₃₁×#117	C₂²	semidirect
36. C₂²×C₄²×C₃₁	C₂²	semidirect
37. C₃₁×#400	C₂²	semidirect
38. C₃₁×#400	C₂²	semidirect
40. C₃₁×#399	C₂²	semidirect
43. C₃₁×#397	C₂²	semidirect
46. C₃₁×#396	C₂²	semidirect
47. C₃₁×#396	C₂²	semidirect
52. C₃₁×#394	C₂²	semidirect
53. C₃₁×#394	C₂²	semidirect
61. C₃₁×#391	C₂²	semidirect
62. C₃₁×#391	C₂²	semidirect
69. C₃₁×#390	C₂²	semidirect
70. C₃₁×#389	C₂²	semidirect
71. C₃₁×#389	C₂²	semidirect
72. C₃₁×#389	C₂²	semidirect
79. C₃₁×#388	C₂²	semidirect
80. C₃₁×#388	C₂²	semidirect
81. C₃₁×#387	C₂²	semidirect
82. C₃₁×#387	C₂²	semidirect
83. C₃₁×#387	C₂²	semidirect
84. C₃₁×#387	C₂²	semidirect
91. C₃₁×#386	C₂²	semidirect
92. C₃₁×#386	C₂²	semidirect
93. C₃₁×#386	C₂²	semidirect
94. C₃₁×#386	C₂²	semidirect
95. C₃₁×#386	C₂²	semidirect
96. C₃₁×#385	C₂²	semidirect
99. C₃₁×#380	C₂²	semidirect
104. C₄×C₂²⋊C₄×C₃₁	C₂²	semidirect
105. C₄×C₂²⋊C₄×C₃₁	C₂²	semidirect
106. C₄×C₂²⋊C₄×C₃₁	C₂²	semidirect
342. #36812	C₃₁	direct (N × H)
438. #2854	C₂×C₃₁	semidirect
439. #2798	C₂×C₃₁	semidirect
440. #2710	C₂×C₃₁	semidirect
441. #2705	C₂×C₃₁	semidirect
442. #2705	C₂×C₃₁	semidirect
443. #2693	C₂×C₃₁	semidirect
444. #2678	C₂×C₃₁	semidirect
445. #2678	C₂×C₃₁	semidirect
446. #2673	C₂×C₃₁	semidirect
447. #2648	C₂×C₃₁	semidirect
448. #2608	C₂×C₃₁	semidirect
449. #2559	C₂×C₃₁	semidirect
450. #2539	C₂×C₃₁	semidirect
451. #2471	C₂×C₃₁	semidirect
452. #2431	C₂×C₃₁	semidirect
453. #2404	C₂×C₃₁	semidirect
454. #2333	C₂×C₃₁	semidirect
455. #2312	C₂×C₃₁	semidirect
456. #2297	C₂×C₃₁	semidirect
507. C₂×#127	C₂²×C₃₁	semidirect
508. C₂×#126	C₂²×C₃₁	semidirect
509. C₂×#124	C₂²×C₃₁	semidirect
513. C₂×#123	C₂²×C₃₁	semidirect
520. C₂×#117	C₂²×C₃₁	semidirect
522. C₂²×C₄²	C₂²×C₃₁	semidirect
523. #400	C₂²×C₃₁	semidirect
524. #400	C₂²×C₃₁	semidirect
526. #399	C₂²×C₃₁	semidirect
529. #397	C₂²×C₃₁	semidirect
532. #396	C₂²×C₃₁	semidirect
533. #396	C₂²×C₃₁	semidirect
538. #394	C₂²×C₃₁	semidirect
539. #394	C₂²×C₃₁	semidirect
547. #391	C₂²×C₃₁	semidirect
548. #391	C₂²×C₃₁	semidirect
555. #390	C₂²×C₃₁	semidirect
556. #389	C₂²×C₃₁	semidirect
557. #389	C₂²×C₃₁	semidirect
558. #389	C₂²×C₃₁	semidirect
565. #388	C₂²×C₃₁	semidirect
566. #388	C₂²×C₃₁	semidirect
567. #387	C₂²×C₃₁	semidirect
568. #387	C₂²×C₃₁	semidirect
569. #387	C₂²×C₃₁	semidirect
570. #387	C₂²×C₃₁	semidirect
577. #386	C₂²×C₃₁	semidirect
578. #386	C₂²×C₃₁	semidirect
579. #386	C₂²×C₃₁	semidirect
580. #386	C₂²×C₃₁	semidirect
581. #386	C₂²×C₃₁	semidirect
582. #385	C₂²×C₃₁	semidirect
585. #380	C₂²×C₃₁	semidirect
590. C₄×C₂²⋊C₄	C₂²×C₃₁	semidirect
591. C₄×C₂²⋊C₄	C₂²×C₃₁	semidirect
592. C₄×C₂²⋊C₄	C₂²×C₃₁	semidirect
709. C₃₁	#36812	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×#2854	2
C₃₁×#2798	2
C₃₁×#2710	2
C₃₁×#2705	2
C₃₁×#2693	2
C₃₁×#2678	2
C₃₁×#2673	2
C₃₁×#2648	2
C₃₁×#2608	2
C₃₁×#2559	2
C₃₁×#2539	2
C₃₁×#2471	2
C₃₁×#2431	2
C₃₁×#2404	2
C₃₁×#2333	2
C₃₁×#2312	2
C₃₁×#2297	2
#36812	31

Subgroups — C31×#36812 #21493571

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#36812 #21493571