Subgroups — C₃₁×#36822 #21493581

Order 7936.

1792 conjugacy classes of subgroups.

The subgroup lattice has 912 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#2853	C₂	1	2	yes	maximal, complemented
2	C₃₁×#2798	C₂	1	2	yes	maximal, complemented
3	C₃₁×#2752	C₂	1	2	yes	maximal, complemented
4	C₃₁×#2743	C₂	1	2	yes	maximal, complemented
5	C₃₁×#2740	C₂	1	2	yes	maximal, complemented
6	C₃₁×#2716	C₂	1	2	yes	maximal, complemented
7	C₃₁×#2710	C₂	1	2	yes	maximal, complemented
8	C₃₁×#2697	C₂	1	2	yes	maximal, complemented
9	C₃₁×#2685	C₂	1	2	yes	maximal, complemented
10	C₃₁×#2649	C₂	1	2	yes	maximal, complemented
11	C₃₁×#2608	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#2595	C₂	1	2	yes	maximal, complemented
13	C₃₁×#2561	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#2479	C₂	1	2	yes	maximal, complemented
15	C₃₁×#2432	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#2404	C₂	1	1	yes	maximal, characteristic
17	C₃₁×#2332	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×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
22	C₂×C₃₁×#126	C₂²	1	2	yes	—
23	C₂×C₃₁×#124	C₂²	1	1	yes	characteristic, complemented
24	C₂×C₃₁×#123	C₂²	1	2	yes	—
25	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
26	C₂×C₃₁×#120	C₂²	1	1	yes	characteristic
27	C₂×C₃₁×#120	C₂²	1	1	yes	characteristic
28	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic, complemented
29	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
30	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic, complemented
31	C₃₁×#400	C₂²	1	2	yes	complemented
32	C₃₁×#400	C₂²	1	2	yes	complemented
33	C₃₁×#400	C₂²	1	2	yes	complemented
34	C₃₁×#399	C₂²	1	2	yes	—
35	C₃₁×#399	C₂²	1	2	yes	complemented
36	C₃₁×#399	C₂²	1	2	yes	complemented
37	C₃₁×#398	C₂²	1	2	yes	complemented
38	C₃₁×#397	C₂²	1	2	yes	—
39	C₃₁×#397	C₂²	1	2	yes	—
40	C₃₁×#397	C₂²	1	2	yes	—
41	C₃₁×#397	C₂²	1	2	yes	complemented
42	C₃₁×#397	C₂²	1	2	yes	complemented
43	C₃₁×#396	C₂²	1	2	yes	—
44	C₃₁×#396	C₂²	1	2	yes	—
45	C₃₁×#396	C₂²	1	2	yes	—
46	C₃₁×#394	C₂²	1	2	yes	—
47	C₃₁×#394	C₂²	1	2	yes	—
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×#393	C₂²	1	2	yes	—
53	C₃₁×#393	C₂²	1	2	yes	—
54	C₃₁×#392	C₂²	1	2	yes	—
55	C₃₁×#391	C₂²	1	2	yes	complemented
56	C₃₁×#391	C₂²	1	1	yes	characteristic, complemented
57	C₃₁×#391	C₂²	1	2	yes	complemented
58	C₃₁×#390	C₂²	1	2	yes	—
59	C₃₁×#390	C₂²	1	2	yes	—
60	C₃₁×#390	C₂²	1	2	yes	—
61	C₃₁×#390	C₂²	1	1	yes	characteristic, complemented
62	C₃₁×#389	C₂²	1	2	yes	complemented
63	C₃₁×#389	C₂²	1	2	yes	complemented
64	C₃₁×#388	C₂²	1	2	yes	—
65	C₃₁×#388	C₂²	1	2	yes	—
66	C₃₁×#388	C₂²	1	2	yes	—
67	C₃₁×#388	C₂²	1	2	yes	—
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	—
74	C₃₁×#388	C₂²	1	2	yes	—
75	C₃₁×#388	C₂²	1	2	yes	complemented
76	C₃₁×#388	C₂²	1	2	yes	complemented
77	C₃₁×#387	C₂²	1	2	yes	complemented
78	C₃₁×#387	C₂²	1	2	yes	complemented
79	C₃₁×#387	C₂²	1	2	yes	complemented
80	C₃₁×#387	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×#385	C₂²	1	2	yes	complemented
93	C₃₁×#385	C₂²	1	2	yes	complemented
94	C₃₁×#385	C₂²	1	2	yes	complemented
95	C₃₁×#381	C₂²	1	1	yes	characteristic
96	C₃₁×#381	C₂²	1	2	yes	—
97	C₃₁×#381	C₂²	1	2	yes	complemented
98	C₃₁×#380	C₂²	1	2	yes	—
99	C₃₁×#379	C₂²	1	2	yes	—
100	C₃₁×#379	C₂²	1	2	yes	—
101	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	complemented
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	1	yes	characteristic
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×Q₈×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	1	yes	characteristic
116	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
117	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
118	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
119	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
120	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
121	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
122	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
123	C₃₁×C₄⋊Q₈	—	4	2	no	—
124	C₃₁×#126	—	4	4	no	—
125	C₃₁×#124	—	4	2	no	—
126	C₃₁×#123	—	4	4	no	—
127	C₃₁×C₂²⋊Q₈	—	2	4	no	—
128	C₃₁×#120	—	4	2	no	—
129	C₃₁×#120	—	4	2	no	—
130	C₃₁×#117	—	4	2	no	—
131	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
132	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
133	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
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	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	2	yes	—
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×C₂²⋊C₄×C₃₁	—	2	4	no	—
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	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	1	yes	characteristic
153	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
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	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	2	yes	—
167	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
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×C₄²×C₃₁	—	4	2	no	—
175	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
176	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
177	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
178	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
179	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
180	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
181	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
182	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
183	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
184	C₃₁×#95	C₂³	1	2	yes	—
185	C₃₁×#95	C₂³	1	2	yes	—
186	C₃₁×#95	C₂³	1	2	yes	—
187	C₃₁×#95	C₂³	1	2	yes	—
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	2	yes	—
192	C₃₁×#95	C₂³	1	2	yes	—
193	C₃₁×#95	C₂³	1	2	yes	—
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	—	4	2	no	—
209	C₂⁴×C₃₁	—	4	1	no	—
210	C₂⁴×C₃₁	—	4	1	no	—
211	C₂⁴×C₃₁	—	4	2	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	1	yes	characteristic
216	#41×C₃₁	—	4	16	no	—
217	C₂×Q₈×C₃₁	—	2	2	no	—
218	C₂×Q₈×C₃₁	—	2	2	no	—
219	C₂×Q₈×C₃₁	—	2	2	no	—
220	C₂×Q₈×C₃₁	—	4	1	no	—
221	C₂×Q₈×C₃₁	—	4	1	no	—
222	C₂×Q₈×C₃₁	—	4	1	no	—
223	C₂×D₄×C₃₁	—	2	2	no	—
224	C₂×D₄×C₃₁	—	2	2	no	—
225	C₂×D₄×C₃₁	—	2	2	no	—
226	C₂×D₄×C₃₁	—	2	2	no	—
227	C₂×D₄×C₃₁	—	2	4	no	—
228	C₂×D₄×C₃₁	—	2	2	no	—
229	C₂×D₄×C₃₁	—	2	2	no	—
230	C₂×D₄×C₃₁	—	4	1	no	—
231	C₂×D₄×C₃₁	—	4	1	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	C₂²×C₄×C₃₁	—	2	2	no	—
239	C₂²×C₄×C₃₁	—	2	2	no	—
240	C₂²×C₄×C₃₁	—	2	2	no	—
241	C₂²×C₄×C₃₁	—	2	4	no	—
242	C₂²×C₄×C₃₁	—	2	2	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	1	no	—
247	C₂²×C₄×C₃₁	—	4	1	no	—
248	C₂²×C₄×C₃₁	—	4	1	no	—
249	C₂²×C₄×C₃₁	—	4	1	no	—
250	C₂²×C₄×C₃₁	—	4	2	no	—
251	C₂²×C₄×C₃₁	#41	1	4	yes	—
252	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
253	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
254	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
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	2	yes	—
260	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
261	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
262	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
263	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
264	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
265	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
266	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
267	C₄⋊C₄×C₃₁	—	2	2	no	—
268	C₄⋊C₄×C₃₁	—	2	4	no	—
269	C₄⋊C₄×C₃₁	—	2	4	no	—
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	2	no	—
276	C₄⋊C₄×C₃₁	—	4	2	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	2	no	—
282	C₂²⋊C₄×C₃₁	—	2	4	no	—
283	C₂²⋊C₄×C₃₁	—	2	4	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	—	4	2	no	—
288	C₂²⋊C₄×C₃₁	—	4	2	no	—
289	C₂²⋊C₄×C₃₁	—	4	2	no	—
290	C₂²⋊C₄×C₃₁	—	4	2	no	—
291	C₂²⋊C₄×C₃₁	—	4	2	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	2	no	—
300	C₂²⋊C₄×C₃₁	—	4	2	no	—
301	C₂²⋊C₄×C₃₁	—	4	1	no	—
302	C₂²⋊C₄×C₃₁	—	4	1	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	C₄²×C₃₁	—	4	1	no	—
310	C₄²×C₃₁	—	4	1	no	—
311	C₄²×C₃₁	—	4	2	no	—
312	C₄²×C₃₁	—	4	2	no	—
313	C₄²×C₃₁	—	4	1	no	—
314	C₄²×C₃₁	—	4	1	no	—
315	C₄²×C₃₁	—	4	1	no	—
316	C₄²×C₃₁	—	4	2	no	—
317	C₄²×C₃₁	—	4	1	no	—
318	#36822	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
319	C₂³×C₃₁	—	2	1	no	—
320	C₂³×C₃₁	—	2	1	no	—
321	C₂³×C₃₁	—	2	1	no	—
322	C₂³×C₃₁	—	2	1	no	—
323	C₂³×C₃₁	—	2	2	no	—
324	C₂³×C₃₁	—	2	2	no	—
325	C₂³×C₃₁	—	2	2	no	—
326	C₂³×C₃₁	—	2	2	no	—
327	C₂³×C₃₁	—	2	2	no	—
328	C₂³×C₃₁	—	2	1	no	—
329	C₂³×C₃₁	—	2	2	no	—
330	C₂³×C₃₁	—	2	2	no	—
331	C₂³×C₃₁	—	2	1	no	—
332	C₂³×C₃₁	—	2	1	no	—
333	C₂³×C₃₁	—	2	2	no	—
334	C₂³×C₃₁	—	2	2	no	—
335	C₂³×C₃₁	—	2	2	no	—
336	C₂³×C₃₁	—	2	2	no	—
337	C₂³×C₃₁	—	2	2	no	—
338	C₂³×C₃₁	—	2	2	no	—
339	C₂³×C₃₁	—	4	4	no	—
340	C₂³×C₃₁	—	8	2	no	—
341	C₂³×C₃₁	—	8	2	no	—
342	C₂³×C₃₁	—	8	4	no	—
343	C₂³×C₃₁	—	8	4	no	—
344	C₂³×C₃₁	C₂×#41	1	2	yes	—
345	C₂³×C₃₁	H(5,𝔽₂)	1	2	yes	—
346	C₂³×C₃₁	C₂⁵	1	1	yes	characteristic
347	Q₈×C₃₁	—	4	4	no	—
348	Q₈×C₃₁	—	8	2	no	—
349	D₄×C₃₁	—	4	4	no	—
350	D₄×C₃₁	—	4	4	no	—
351	D₄×C₃₁	—	4	4	no	—
352	D₄×C₃₁	—	8	4	no	—
353	D₄×C₃₁	—	8	4	no	—
354	C₂×C₄×C₃₁	—	2	8	no	—
355	C₂×C₄×C₃₁	—	2	1	no	—
356	C₂×C₄×C₃₁	—	2	1	no	—
357	C₂×C₄×C₃₁	—	2	1	no	—
358	C₂×C₄×C₃₁	—	2	1	no	—
359	C₂×C₄×C₃₁	—	2	1	no	—
360	C₂×C₄×C₃₁	—	2	1	no	—
361	C₂×C₄×C₃₁	—	2	2	no	—
362	C₂×C₄×C₃₁	—	2	2	no	—
363	C₂×C₄×C₃₁	—	2	2	no	—
364	C₂×C₄×C₃₁	—	2	1	no	—
365	C₂×C₄×C₃₁	—	2	2	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	1	no	—
376	C₂×C₄×C₃₁	—	2	1	no	—
377	C₂×C₄×C₃₁	—	2	2	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	2	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	—	2	2	no	—
397	C₂×C₄×C₃₁	—	4	4	no	—
398	C₂×C₄×C₃₁	—	4	4	no	—
399	C₂×C₄×C₃₁	—	4	8	no	—
400	C₂×C₄×C₃₁	—	8	2	no	—
401	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
402	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
403	C₂×C₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
404	#2853	C₂×C₃₁	1	2	yes	complemented
405	#2798	C₂×C₃₁	1	2	yes	complemented
406	#2752	C₂×C₃₁	1	2	yes	complemented
407	#2743	C₂×C₃₁	1	2	yes	complemented
408	#2740	C₂×C₃₁	1	2	yes	complemented
409	#2716	C₂×C₃₁	1	2	yes	complemented
410	#2710	C₂×C₃₁	1	2	yes	complemented
411	#2697	C₂×C₃₁	1	2	yes	complemented
412	#2685	C₂×C₃₁	1	2	yes	complemented
413	#2649	C₂×C₃₁	1	2	yes	complemented
414	#2608	C₂×C₃₁	1	1	yes	characteristic, complemented
415	#2595	C₂×C₃₁	1	2	yes	complemented
416	#2561	C₂×C₃₁	1	1	yes	characteristic, complemented
417	#2479	C₂×C₃₁	1	2	yes	complemented
418	#2432	C₂×C₃₁	1	1	yes	characteristic, complemented
419	#2404	C₂×C₃₁	1	1	yes	characteristic
420	#2332	C₂×C₃₁	1	1	yes	characteristic, complemented
421	#2312	C₂×C₃₁	1	1	yes	characteristic, complemented
422	#2297	C₂×C₃₁	1	1	yes	characteristic, complemented
423	C₂²×C₃₁	—	2	2	no	—
424	C₂²×C₃₁	—	2	2	no	—
425	C₂²×C₃₁	—	2	2	no	—
426	C₂²×C₃₁	—	2	2	no	—
427	C₂²×C₃₁	—	2	4	no	—
428	C₂²×C₃₁	—	4	1	no	—
429	C₂²×C₃₁	—	4	1	no	—
430	C₂²×C₃₁	—	4	2	no	—
431	C₂²×C₃₁	—	4	2	no	—
432	C₂²×C₃₁	—	4	2	no	—
433	C₂²×C₃₁	—	4	1	no	—
434	C₂²×C₃₁	—	4	2	no	—
435	C₂²×C₃₁	—	4	1	no	—
436	C₂²×C₃₁	—	4	2	no	—
437	C₂²×C₃₁	—	4	1	no	—
438	C₂²×C₃₁	—	4	2	no	—
439	C₂²×C₃₁	—	4	2	no	—
440	C₂²×C₃₁	—	4	2	no	—
441	C₂²×C₃₁	—	4	2	no	—
442	C₂²×C₃₁	—	4	2	no	—
443	C₂²×C₃₁	—	4	2	no	—
444	C₂²×C₃₁	—	4	2	no	—
445	C₂²×C₃₁	—	8	8	no	—
446	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
447	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
448	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
449	C₂²×C₃₁	#585	1	2	yes	—
450	C₂²×C₃₁	#585	1	2	yes	—
451	C₄×C₃₁	—	2	2	no	—
452	C₄×C₃₁	—	2	2	no	—
453	C₄×C₃₁	—	2	2	no	—
454	C₄×C₃₁	—	4	2	no	—
455	C₄×C₃₁	—	4	1	no	—
456	C₄×C₃₁	—	4	2	no	—
457	C₄×C₃₁	—	4	2	no	—
458	C₄×C₃₁	—	4	2	no	—
459	C₄×C₃₁	—	4	2	no	—
460	C₄×C₃₁	—	4	2	no	—
461	C₄×C₃₁	—	4	2	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	C₂²×#41	C₂²×C₃₁	1	1	yes	characteristic
467	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
468	C₂×#126	C₂²×C₃₁	1	2	yes	—
469	C₂×#124	C₂²×C₃₁	1	1	yes	characteristic, complemented
470	C₂×#123	C₂²×C₃₁	1	2	yes	—
471	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
472	C₂×#120	C₂²×C₃₁	1	1	yes	characteristic
473	C₂×#120	C₂²×C₃₁	1	1	yes	characteristic
474	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic, complemented
475	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
476	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic, complemented
477	#400	C₂²×C₃₁	1	2	yes	complemented
478	#400	C₂²×C₃₁	1	2	yes	complemented
479	#400	C₂²×C₃₁	1	2	yes	complemented
480	#399	C₂²×C₃₁	1	2	yes	—
481	#399	C₂²×C₃₁	1	2	yes	complemented
482	#399	C₂²×C₃₁	1	2	yes	complemented
483	#398	C₂²×C₃₁	1	2	yes	complemented
484	#397	C₂²×C₃₁	1	2	yes	—
485	#397	C₂²×C₃₁	1	2	yes	—
486	#397	C₂²×C₃₁	1	2	yes	—
487	#397	C₂²×C₃₁	1	2	yes	complemented
488	#397	C₂²×C₃₁	1	2	yes	complemented
489	#396	C₂²×C₃₁	1	2	yes	—
490	#396	C₂²×C₃₁	1	2	yes	—
491	#396	C₂²×C₃₁	1	2	yes	—
492	#394	C₂²×C₃₁	1	2	yes	—
493	#394	C₂²×C₃₁	1	2	yes	—
494	#394	C₂²×C₃₁	1	2	yes	—
495	#394	C₂²×C₃₁	1	2	yes	—
496	#394	C₂²×C₃₁	1	2	yes	—
497	#394	C₂²×C₃₁	1	2	yes	—
498	#393	C₂²×C₃₁	1	2	yes	—
499	#393	C₂²×C₃₁	1	2	yes	—
500	#392	C₂²×C₃₁	1	2	yes	—
501	#391	C₂²×C₃₁	1	2	yes	complemented
502	#391	C₂²×C₃₁	1	1	yes	characteristic, complemented
503	#391	C₂²×C₃₁	1	2	yes	complemented
504	#390	C₂²×C₃₁	1	2	yes	—
505	#390	C₂²×C₃₁	1	2	yes	—
506	#390	C₂²×C₃₁	1	2	yes	—
507	#390	C₂²×C₃₁	1	1	yes	characteristic, complemented
508	#389	C₂²×C₃₁	1	2	yes	complemented
509	#389	C₂²×C₃₁	1	2	yes	complemented
510	#388	C₂²×C₃₁	1	2	yes	—
511	#388	C₂²×C₃₁	1	2	yes	—
512	#388	C₂²×C₃₁	1	2	yes	—
513	#388	C₂²×C₃₁	1	2	yes	—
514	#388	C₂²×C₃₁	1	2	yes	—
515	#388	C₂²×C₃₁	1	2	yes	—
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	#387	C₂²×C₃₁	1	2	yes	complemented
524	#387	C₂²×C₃₁	1	2	yes	complemented
525	#387	C₂²×C₃₁	1	2	yes	complemented
526	#387	C₂²×C₃₁	1	2	yes	complemented
527	#387	C₂²×C₃₁	1	2	yes	complemented
528	#387	C₂²×C₃₁	1	2	yes	complemented
529	#387	C₂²×C₃₁	1	2	yes	complemented
530	#387	C₂²×C₃₁	1	2	yes	complemented
531	#386	C₂²×C₃₁	1	2	yes	—
532	#386	C₂²×C₃₁	1	2	yes	—
533	#386	C₂²×C₃₁	1	2	yes	—
534	#386	C₂²×C₃₁	1	1	yes	characteristic
535	#386	C₂²×C₃₁	1	1	yes	characteristic
536	#386	C₂²×C₃₁	1	2	yes	—
537	#386	C₂²×C₃₁	1	2	yes	complemented
538	#385	C₂²×C₃₁	1	2	yes	complemented
539	#385	C₂²×C₃₁	1	2	yes	complemented
540	#385	C₂²×C₃₁	1	2	yes	complemented
541	#381	C₂²×C₃₁	1	2	yes	—
542	#381	C₂²×C₃₁	1	1	yes	characteristic
543	#381	C₂²×C₃₁	1	2	yes	complemented
544	#380	C₂²×C₃₁	1	2	yes	—
545	#379	C₂²×C₃₁	1	2	yes	—
546	#379	C₂²×C₃₁	1	2	yes	—
547	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	complemented
548	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
549	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
550	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
551	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
552	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
553	C₂×C₃₁	—	4	2	no	—
554	C₂×C₃₁	—	4	2	no	—
555	C₂×C₃₁	—	8	1	no	—
556	C₂×C₃₁	—	8	2	no	—
557	C₂×C₃₁	#3455	1	1	yes	characteristic
558	C₂×C₃₁	#3490	1	1	yes	characteristic
559	C₂×C₃₁	#3510	1	1	yes	characteristic
560	C₂×C₃₁	#3533	1	2	yes	—
561	C₂×C₃₁	#3562	1	2	yes	—
562	C₂⁵	C₂³×C₃₁	1	1	yes	characteristic
563	C₂×#41	—	2	4	no	—
564	C₂×#41	—	4	2	no	—
565	C₂×#41	—	4	2	no	—
566	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
567	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
568	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
569	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
570	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
571	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
572	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
573	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
574	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
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	C₄⋊Q₈	—	4	2	no	—
579	#126	—	4	4	no	—
580	#124	—	4	2	no	—
581	#123	—	4	4	no	—
582	C₂²⋊Q₈	—	2	4	no	—
583	#120	—	4	2	no	—
584	#120	—	4	2	no	—
585	#117	—	4	2	no	—
586	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
587	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
588	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
589	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
590	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
591	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
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	2	yes	—
595	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
596	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
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×C₂²⋊C₄	—	2	4	no	—
602	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
603	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
604	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
605	C₂×C₂²⋊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	1	yes	characteristic
609	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
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	2	yes	—
615	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
616	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
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	2	yes	—
627	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
628	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
629	C₂×C₄²	—	4	2	no	—
630	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
631	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
632	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
633	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
634	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
635	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
636	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
637	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
638	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
639	#95	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	2	yes	—
656	#95	C₂³×C₃₁	1	2	yes	—
657	#95	C₂³×C₃₁	1	2	yes	—
658	#95	C₂³×C₃₁	1	2	yes	—
659	#95	C₂³×C₃₁	1	2	yes	—
660	#95	C₂³×C₃₁	1	2	yes	—
661	#95	C₂³×C₃₁	1	2	yes	—
662	C₃₁	#36822	1	1	yes	characteristic, direct product factor, Sylow
663	C₂⁴	—	2	2	no	—
664	C₂⁴	—	4	2	no	—
665	C₂⁴	—	4	1	no	—
666	C₂⁴	—	4	1	no	—
667	C₂⁴	—	4	2	no	—
668	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
669	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
670	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
671	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
672	#41	—	4	16	no	—
673	C₂×Q₈	—	2	2	no	—
674	C₂×Q₈	—	2	2	no	—
675	C₂×Q₈	—	2	2	no	—
676	C₂×Q₈	—	4	1	no	—
677	C₂×Q₈	—	4	1	no	—
678	C₂×Q₈	—	4	1	no	—
679	C₂×D₄	—	2	2	no	—
680	C₂×D₄	—	2	2	no	—
681	C₂×D₄	—	2	2	no	—
682	C₂×D₄	—	2	2	no	—
683	C₂×D₄	—	2	4	no	—
684	C₂×D₄	—	2	2	no	—
685	C₂×D₄	—	2	2	no	—
686	C₂×D₄	—	4	1	no	—
687	C₂×D₄	—	4	1	no	—
688	C₂×D₄	—	4	1	no	—
689	C₂×D₄	—	4	2	no	—
690	C₂×D₄	—	4	2	no	—
691	C₂×D₄	—	4	2	no	—
692	C₂×D₄	—	4	2	no	—
693	C₂×D₄	—	4	2	no	—
694	C₂²×C₄	—	2	2	no	—
695	C₂²×C₄	—	2	2	no	—
696	C₂²×C₄	—	2	2	no	—
697	C₂²×C₄	—	2	4	no	—
698	C₂²×C₄	—	2	2	no	—
699	C₂²×C₄	—	2	2	no	—
700	C₂²×C₄	—	4	2	no	—
701	C₂²×C₄	—	4	2	no	—
702	C₂²×C₄	—	4	1	no	—
703	C₂²×C₄	—	4	1	no	—
704	C₂²×C₄	—	4	1	no	—
705	C₂²×C₄	—	4	1	no	—
706	C₂²×C₄	—	4	2	no	—
707	C₂²×C₄	#41×C₃₁	1	4	yes	—
708	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
709	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
710	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
711	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
712	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
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	2	yes	—
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	1	yes	characteristic
722	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
723	C₄⋊C₄	—	2	2	no	—
724	C₄⋊C₄	—	2	4	no	—
725	C₄⋊C₄	—	2	4	no	—
726	C₄⋊C₄	—	2	4	no	—
727	C₄⋊C₄	—	4	2	no	—
728	C₄⋊C₄	—	4	2	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	2	no	—
734	C₄⋊C₄	—	4	2	no	—
735	C₄⋊C₄	—	4	2	no	—
736	C₄⋊C₄	—	4	2	no	—
737	C₄⋊C₄	—	4	2	no	—
738	C₂²⋊C₄	—	2	4	no	—
739	C₂²⋊C₄	—	2	4	no	—
740	C₂²⋊C₄	—	2	4	no	—
741	C₂²⋊C₄	—	2	4	no	—
742	C₂²⋊C₄	—	2	4	no	—
743	C₂²⋊C₄	—	4	2	no	—
744	C₂²⋊C₄	—	4	2	no	—
745	C₂²⋊C₄	—	4	2	no	—
746	C₂²⋊C₄	—	4	2	no	—
747	C₂²⋊C₄	—	4	2	no	—
748	C₂²⋊C₄	—	4	2	no	—
749	C₂²⋊C₄	—	4	2	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	2	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	C₄²	—	4	1	no	—
766	C₄²	—	4	1	no	—
767	C₄²	—	4	2	no	—
768	C₄²	—	4	2	no	—
769	C₄²	—	4	1	no	—
770	C₄²	—	4	1	no	—
771	C₄²	—	4	1	no	—
772	C₄²	—	4	2	no	—
773	C₄²	—	4	1	no	—
774	C₂³	—	2	1	no	—
775	C₂³	—	2	1	no	—
776	C₂³	—	2	1	no	—
777	C₂³	—	2	1	no	—
778	C₂³	—	2	2	no	—
779	C₂³	—	2	2	no	—
780	C₂³	—	2	2	no	—
781	C₂³	—	2	2	no	—
782	C₂³	—	2	2	no	—
783	C₂³	—	2	1	no	—
784	C₂³	—	2	2	no	—
785	C₂³	—	2	2	no	—
786	C₂³	—	2	1	no	—
787	C₂³	—	2	1	no	—
788	C₂³	—	2	2	no	—
789	C₂³	—	2	2	no	—
790	C₂³	—	2	2	no	—
791	C₂³	—	2	2	no	—
792	C₂³	—	2	2	no	—
793	C₂³	—	2	2	no	—
794	C₂³	—	4	4	no	—
795	C₂³	—	8	2	no	—
796	C₂³	—	8	2	no	—
797	C₂³	—	8	4	no	—
798	C₂³	—	8	4	no	—
799	C₂³	C₂×#41×C₃₁	1	2	yes	—
800	C₂³	C₃₁×H(5,𝔽₂)	1	2	yes	—
801	C₂³	C₂⁵×C₃₁	1	1	yes	characteristic
802	Q₈	—	4	4	no	—
803	Q₈	—	8	2	no	—
804	D₄	—	4	4	no	—
805	D₄	—	4	4	no	—
806	D₄	—	4	4	no	—
807	D₄	—	8	4	no	—
808	D₄	—	8	4	no	—
809	C₂×C₄	—	2	8	no	—
810	C₂×C₄	—	2	1	no	—
811	C₂×C₄	—	2	1	no	—
812	C₂×C₄	—	2	1	no	—
813	C₂×C₄	—	2	1	no	—
814	C₂×C₄	—	2	1	no	—
815	C₂×C₄	—	2	1	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	2	no	—
822	C₂×C₄	—	2	2	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	1	no	—
831	C₂×C₄	—	2	1	no	—
832	C₂×C₄	—	2	2	no	—
833	C₂×C₄	—	2	2	no	—
834	C₂×C₄	—	2	2	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	2	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	—	4	4	no	—
853	C₂×C₄	—	4	4	no	—
854	C₂×C₄	—	4	8	no	—
855	C₂×C₄	—	8	2	no	—
856	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
857	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
858	C₂×C₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
859	C₂²	—	2	2	no	—
860	C₂²	—	2	2	no	—
861	C₂²	—	2	2	no	—
862	C₂²	—	2	2	no	—
863	C₂²	—	2	4	no	—
864	C₂²	—	4	1	no	—
865	C₂²	—	4	1	no	—
866	C₂²	—	4	2	no	—
867	C₂²	—	4	2	no	—
868	C₂²	—	4	2	no	—
869	C₂²	—	4	2	no	—
870	C₂²	—	4	1	no	—
871	C₂²	—	4	1	no	—
872	C₂²	—	4	2	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	2	no	—
880	C₂²	—	4	2	no	—
881	C₂²	—	8	8	no	—
882	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
883	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
884	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
885	C₂²	C₃₁×#585	1	2	yes	—
886	C₂²	C₃₁×#585	1	2	yes	—
887	C₄	—	2	2	no	—
888	C₄	—	2	2	no	—
889	C₄	—	2	2	no	—
890	C₄	—	4	2	no	—
891	C₄	—	4	1	no	—
892	C₄	—	4	2	no	—
893	C₄	—	4	2	no	—
894	C₄	—	4	2	no	—
895	C₄	—	4	2	no	—
896	C₄	—	4	2	no	—
897	C₄	—	4	2	no	—
898	C₄	—	4	2	no	—
899	C₄	—	4	2	no	—
900	C₄	—	4	2	no	—
901	C₄	—	4	2	no	—
902	C₂	—	4	2	no	—
903	C₂	—	4	2	no	—
904	C₂	—	8	2	no	—
905	C₂	—	8	1	no	—
906	C₂	C₃₁×#3455	1	1	yes	characteristic
907	C₂	C₃₁×#3490	1	1	yes	characteristic
908	C₂	C₃₁×#3510	1	1	yes	characteristic
909	C₂	C₃₁×#3533	1	2	yes	—
910	C₂	C₃₁×#3562	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃₁	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₃₁
prime radical	C₃₁×#2404	C₂
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×#2853	C₂	semidirect
2. C₃₁×#2798	C₂	semidirect
3. C₃₁×#2752	C₂	semidirect
4. C₃₁×#2743	C₂	semidirect
5. C₃₁×#2740	C₂	semidirect
6. C₃₁×#2716	C₂	semidirect
7. C₃₁×#2710	C₂	semidirect
8. C₃₁×#2697	C₂	semidirect
9. C₃₁×#2685	C₂	semidirect
10. C₃₁×#2649	C₂	semidirect
11. C₃₁×#2608	C₂	semidirect
12. C₃₁×#2595	C₂	semidirect
13. C₃₁×#2561	C₂	semidirect
14. C₃₁×#2479	C₂	semidirect
15. C₃₁×#2432	C₂	semidirect
17. C₃₁×#2332	C₂	semidirect
18. C₃₁×#2312	C₂	semidirect
19. C₃₁×#2297	C₂	semidirect
21. C₂×C₃₁×C₄⋊Q₈	C₂²	semidirect
23. C₂×C₃₁×#124	C₂²	semidirect
28. C₂×C₃₁×#117	C₂²	semidirect
30. C₂²×C₄²×C₃₁	C₂²	semidirect
31. C₃₁×#400	C₂²	semidirect
32. C₃₁×#400	C₂²	semidirect
33. C₃₁×#400	C₂²	semidirect
35. C₃₁×#399	C₂²	semidirect
36. C₃₁×#399	C₂²	semidirect
37. C₃₁×#398	C₂²	semidirect
41. C₃₁×#397	C₂²	semidirect
42. C₃₁×#397	C₂²	semidirect
55. C₃₁×#391	C₂²	semidirect
56. C₃₁×#391	C₂²	semidirect
57. C₃₁×#391	C₂²	semidirect
61. C₃₁×#390	C₂²	semidirect
62. C₃₁×#389	C₂²	semidirect
63. C₃₁×#389	C₂²	semidirect
75. C₃₁×#388	C₂²	semidirect
76. C₃₁×#388	C₂²	semidirect
77. C₃₁×#387	C₂²	semidirect
78. C₃₁×#387	C₂²	semidirect
79. C₃₁×#387	C₂²	semidirect
80. C₃₁×#387	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×#385	C₂²	semidirect
93. C₃₁×#385	C₂²	semidirect
94. C₃₁×#385	C₂²	semidirect
97. C₃₁×#381	C₂²	semidirect
101. C₄×C₄⋊C₄×C₃₁	C₂²	semidirect
105. C₄×C₂²⋊C₄×C₃₁	C₂²	semidirect
106. C₄×C₂²⋊C₄×C₃₁	C₂²	semidirect
318. #36822	C₃₁	direct (N × H)
404. #2853	C₂×C₃₁	semidirect
405. #2798	C₂×C₃₁	semidirect
406. #2752	C₂×C₃₁	semidirect
407. #2743	C₂×C₃₁	semidirect
408. #2740	C₂×C₃₁	semidirect
409. #2716	C₂×C₃₁	semidirect
410. #2710	C₂×C₃₁	semidirect
411. #2697	C₂×C₃₁	semidirect
412. #2685	C₂×C₃₁	semidirect
413. #2649	C₂×C₃₁	semidirect
414. #2608	C₂×C₃₁	semidirect
415. #2595	C₂×C₃₁	semidirect
416. #2561	C₂×C₃₁	semidirect
417. #2479	C₂×C₃₁	semidirect
418. #2432	C₂×C₃₁	semidirect
420. #2332	C₂×C₃₁	semidirect
421. #2312	C₂×C₃₁	semidirect
422. #2297	C₂×C₃₁	semidirect
467. C₂×C₄⋊Q₈	C₂²×C₃₁	semidirect
469. C₂×#124	C₂²×C₃₁	semidirect
474. C₂×#117	C₂²×C₃₁	semidirect
476. C₂²×C₄²	C₂²×C₃₁	semidirect
477. #400	C₂²×C₃₁	semidirect
478. #400	C₂²×C₃₁	semidirect
479. #400	C₂²×C₃₁	semidirect
481. #399	C₂²×C₃₁	semidirect
482. #399	C₂²×C₃₁	semidirect
483. #398	C₂²×C₃₁	semidirect
487. #397	C₂²×C₃₁	semidirect
488. #397	C₂²×C₃₁	semidirect
501. #391	C₂²×C₃₁	semidirect
502. #391	C₂²×C₃₁	semidirect
503. #391	C₂²×C₃₁	semidirect
507. #390	C₂²×C₃₁	semidirect
508. #389	C₂²×C₃₁	semidirect
509. #389	C₂²×C₃₁	semidirect
521. #388	C₂²×C₃₁	semidirect
522. #388	C₂²×C₃₁	semidirect
523. #387	C₂²×C₃₁	semidirect
524. #387	C₂²×C₃₁	semidirect
525. #387	C₂²×C₃₁	semidirect
526. #387	C₂²×C₃₁	semidirect
527. #387	C₂²×C₃₁	semidirect
528. #387	C₂²×C₃₁	semidirect
529. #387	C₂²×C₃₁	semidirect
530. #387	C₂²×C₃₁	semidirect
537. #386	C₂²×C₃₁	semidirect
538. #385	C₂²×C₃₁	semidirect
539. #385	C₂²×C₃₁	semidirect
540. #385	C₂²×C₃₁	semidirect
543. #381	C₂²×C₃₁	semidirect
547. C₄×C₄⋊C₄	C₂²×C₃₁	semidirect
551. C₄×C₂²⋊C₄	C₂²×C₃₁	semidirect
552. C₄×C₂²⋊C₄	C₂²×C₃₁	semidirect
662. C₃₁	#36822	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×#2853	2
C₃₁×#2798	2
C₃₁×#2752	2
C₃₁×#2743	2
C₃₁×#2740	2
C₃₁×#2716	2
C₃₁×#2710	2
C₃₁×#2697	2
C₃₁×#2685	2
C₃₁×#2649	2
C₃₁×#2608	2
C₃₁×#2595	2
C₃₁×#2561	2
C₃₁×#2479	2
C₃₁×#2432	2
C₃₁×#2404	2
C₃₁×#2332	2
C₃₁×#2312	2
C₃₁×#2297	2
#36822	31

Subgroups — C31×#36822 #21493581

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#36822 #21493581