Subgroups — C₃₁×#36752 #21493511

Order 7936.

1570 conjugacy classes of subgroups.

The subgroup lattice has 814 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#2857	C₂	1	1	yes	maximal, characteristic
2	C₃₁×#2851	C₂	1	1	yes	maximal, characteristic
3	C₃₁×#2805	C₂	1	2	yes	maximal, complemented
4	C₃₁×#2802	C₂	1	2	yes	maximal, complemented
5	C₃₁×#2792	C₂	1	2	yes	maximal, complemented
6	C₃₁×#2791	C₂	1	2	yes	maximal, complemented
7	C₃₁×#2791	C₂	1	2	yes	maximal, complemented
8	C₃₁×#2755	C₂	1	2	yes	maximal, complemented
9	C₃₁×#2734	C₂	1	2	yes	maximal, complemented
10	C₃₁×#2713	C₂	1	2	yes	maximal, complemented
11	C₃₁×#2659	C₂	1	1	yes	maximal, characteristic
12	C₃₁×#2646	C₂	1	1	yes	maximal, characteristic
13	C₃₁×#2569	C₂	1	2	yes	maximal
14	C₃₁×#2440	C₂	1	2	yes	maximal
15	C₃₁×#2438	C₂	1	2	yes	maximal
16	C₃₁×#2438	C₂	1	2	yes	maximal
17	C₃₁×#2316	C₂	1	1	yes	maximal, characteristic
18	C₃₁×#2313	C₂	1	1	yes	maximal, characteristic
19	C₂×C₃₁×#387	C₂	1	1	yes	maximal, characteristic
20	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
21	C₂×C₃₁×C₄⋊Q₈	C₂²	1	2	yes	—
22	C₂×C₃₁×#125	C₂²	1	1	yes	characteristic
23	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	—
24	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	—
25	C₂×C₃₁×#117	C₂²	1	2	yes	—
26	C₂²×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
27	C₂²×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
28	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
29	C₃₁×#400	C₂²	1	2	yes	—
30	C₃₁×#400	C₂²	1	2	yes	—
31	C₃₁×#400	C₂²	1	2	yes	—
32	C₃₁×#400	C₂²	1	2	yes	—
33	C₃₁×#400	C₂²	1	2	yes	—
34	C₃₁×#400	C₂²	1	2	yes	—
35	C₃₁×#398	C₂²	1	2	yes	—
36	C₃₁×#398	C₂²	1	2	yes	—
37	C₃₁×#398	C₂²	1	2	yes	—
38	C₃₁×#398	C₂²	1	2	yes	—
39	C₃₁×#398	C₂²	1	2	yes	—
40	C₃₁×#398	C₂²	1	2	yes	—
41	C₃₁×#398	C₂²	1	2	yes	—
42	C₃₁×#398	C₂²	1	2	yes	—
43	C₃₁×#398	C₂²	1	2	yes	—
44	C₃₁×#398	C₂²	1	2	yes	—
45	C₃₁×#398	C₂²	1	2	yes	—
46	C₃₁×#398	C₂²	1	2	yes	—
47	C₃₁×#395	C₂²	1	2	yes	—
48	C₃₁×#395	C₂²	1	2	yes	—
49	C₃₁×#395	C₂²	1	2	yes	—
50	C₃₁×#395	C₂²	1	2	yes	—
51	C₃₁×#395	C₂²	1	2	yes	—
52	C₃₁×#395	C₂²	1	2	yes	—
53	C₃₁×#391	C₂²	1	2	yes	—
54	C₃₁×#391	C₂²	1	2	yes	—
55	C₃₁×#391	C₂²	1	2	yes	—
56	C₃₁×#389	C₂²	1	2	yes	—
57	C₃₁×#389	C₂²	1	2	yes	—
58	C₃₁×#389	C₂²	1	2	yes	—
59	C₃₁×#389	C₂²	1	2	yes	—
60	C₃₁×#389	C₂²	1	1	yes	characteristic
61	C₃₁×#389	C₂²	1	1	yes	characteristic
62	C₃₁×#389	C₂²	1	1	yes	characteristic
63	C₃₁×#389	C₂²	1	2	yes	—
64	C₃₁×#389	C₂²	1	1	yes	characteristic
65	C₃₁×#389	C₂²	1	2	yes	—
66	C₃₁×#389	C₂²	1	2	yes	—
67	C₃₁×#389	C₂²	1	2	yes	—
68	C₃₁×#389	C₂²	1	2	yes	—
69	C₃₁×#387	C₂²	1	2	yes	—
70	C₃₁×#387	C₂²	1	2	yes	—
71	C₃₁×#387	C₂²	1	2	yes	—
72	C₃₁×#387	C₂²	1	2	yes	—
73	C₃₁×#387	C₂²	1	2	yes	—
74	C₃₁×#387	C₂²	1	2	yes	—
75	C₃₁×#387	C₂²	1	2	yes	—
76	C₃₁×#387	C₂²	1	2	yes	—
77	C₃₁×#387	C₂²	1	2	yes	—
78	C₃₁×#387	C₂²	1	2	yes	—
79	C₃₁×#387	C₂²	1	2	yes	—
80	C₃₁×#387	C₂²	1	2	yes	—
81	C₃₁×#387	C₂²	1	2	yes	—
82	C₃₁×#387	C₂²	1	2	yes	—
83	C₃₁×#387	C₂²	1	2	yes	—
84	C₃₁×#387	C₂²	1	2	yes	—
85	C₃₁×#387	C₂²	1	2	yes	—
86	C₃₁×#387	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×#384	C₂²	1	1	yes	characteristic
92	C₃₁×#384	C₂²	1	2	yes	—
93	C₃₁×#382	C₂²	1	1	yes	characteristic
94	C₃₁×#381	C₂²	1	2	yes	—
95	C₃₁×#380	C₂²	1	1	yes	characteristic
96	C₃₁×#380	C₂²	1	1	yes	characteristic
97	C₃₁×#380	C₂²	1	2	yes	—
98	C₃₁×#380	C₂²	1	2	yes	—
99	C₃₁×#380	C₂²	1	2	yes	—
100	C₃₁×#380	C₂²	1	1	yes	characteristic
101	C₃₁×#380	C₂²	1	1	yes	characteristic
102	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
103	C₂×C₃₁×#95	C₂²	1	1	yes	characteristic
104	C₂×C₃₁×#95	C₂²	1	1	yes	characteristic
105	C₂×C₃₁×#95	C₂²	1	1	yes	characteristic
106	C₂×C₃₁×#95	C₂²	1	1	yes	characteristic
107	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
108	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
109	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
110	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
111	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
112	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
113	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
114	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
115	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
116	C₃₁×C₄⋊Q₈	—	4	2	no	—
117	C₃₁×C₄⋊Q₈	—	4	4	no	—
118	C₃₁×#125	—	4	2	no	—
119	C₃₁×C₂²⋊Q₈	—	4	4	no	—
120	C₃₁×C₂²⋊Q₈	—	4	4	no	—
121	C₃₁×#117	—	4	4	no	—
122	C₂×C₄⋊C₄×C₃₁	—	4	2	no	—
123	C₂×C₄⋊C₄×C₃₁	Q₈	1	8	yes	complemented
124	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
125	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
126	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
127	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
128	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
129	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
130	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
131	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
132	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
133	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
134	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
135	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
136	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
137	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
138	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
139	C₂×C₄⋊C₄×C₃₁	C₂³	1	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×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
147	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
148	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
149	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
150	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
155	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
156	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
157	C₂×C₄⋊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×C₄²×C₃₁	—	4	2	no	—
163	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
164	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
165	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
166	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
167	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
168	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
169	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
170	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
171	C₃₁×#95	C₂³	1	2	yes	—
172	C₃₁×#95	C₂³	1	2	yes	—
173	C₃₁×#95	C₂³	1	2	yes	—
174	C₃₁×#95	C₂³	1	2	yes	—
175	C₃₁×#95	C₂³	1	2	yes	—
176	C₃₁×#95	C₂³	1	2	yes	—
177	C₃₁×#95	C₂³	1	2	yes	—
178	C₃₁×#95	C₂³	1	2	yes	—
179	C₃₁×#95	C₂³	1	2	yes	—
180	C₃₁×#95	C₂³	1	2	yes	—
181	C₃₁×#95	C₂³	1	2	yes	—
182	C₃₁×#95	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	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	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
204	C₂×Q₈×C₃₁	—	2	4	no	—
205	C₂×Q₈×C₃₁	—	4	2	no	—
206	C₂×Q₈×C₃₁	—	4	2	no	—
207	C₂×Q₈×C₃₁	—	4	2	no	—
208	C₂×Q₈×C₃₁	—	4	2	no	—
209	C₂×Q₈×C₃₁	—	4	2	no	—
210	C₂²×C₄×C₃₁	—	2	2	no	—
211	C₂²×C₄×C₃₁	—	2	2	no	—
212	C₂²×C₄×C₃₁	—	2	2	no	—
213	C₂²×C₄×C₃₁	—	2	2	no	—
214	C₂²×C₄×C₃₁	—	2	2	no	—
215	C₂²×C₄×C₃₁	—	2	2	no	—
216	C₂²×C₄×C₃₁	—	2	2	no	—
217	C₂²×C₄×C₃₁	—	2	2	no	—
218	C₂²×C₄×C₃₁	—	4	1	no	—
219	C₂²×C₄×C₃₁	—	4	1	no	—
220	C₂²×C₄×C₃₁	—	4	1	no	—
221	C₂²×C₄×C₃₁	—	4	1	no	—
222	C₂²×C₄×C₃₁	—	4	1	no	—
223	C₂²×C₄×C₃₁	—	4	1	no	—
224	C₂²×C₄×C₃₁	—	4	1	no	—
225	C₂²×C₄×C₃₁	—	4	1	no	—
226	C₂²×C₄×C₃₁	—	4	1	no	—
227	C₂²×C₄×C₃₁	—	4	1	no	—
228	C₂²×C₄×C₃₁	C₂×Q₈	1	4	yes	—
229	C₂²×C₄×C₃₁	C₂×Q₈	1	4	yes	—
230	C₂²×C₄×C₃₁	C₂×Q₈	1	4	yes	—
231	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
232	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
233	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
234	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
235	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
236	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
237	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
238	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
239	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
240	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
241	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
242	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
243	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
244	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
245	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
246	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
247	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
248	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
249	C₄⋊C₄×C₃₁	—	2	4	no	—
250	C₄⋊C₄×C₃₁	—	2	4	no	—
251	C₄⋊C₄×C₃₁	—	2	4	no	—
252	C₄⋊C₄×C₃₁	—	2	4	no	—
253	C₄⋊C₄×C₃₁	—	4	2	no	—
254	C₄⋊C₄×C₃₁	—	4	2	no	—
255	C₄⋊C₄×C₃₁	—	4	1	no	—
256	C₄⋊C₄×C₃₁	—	4	1	no	—
257	C₄⋊C₄×C₃₁	—	4	1	no	—
258	C₄⋊C₄×C₃₁	—	4	1	no	—
259	C₄⋊C₄×C₃₁	—	4	2	no	—
260	C₄⋊C₄×C₃₁	—	4	2	no	—
261	C₄⋊C₄×C₃₁	—	4	2	no	—
262	C₄⋊C₄×C₃₁	—	4	2	no	—
263	C₄⋊C₄×C₃₁	—	4	2	no	—
264	C₄⋊C₄×C₃₁	—	4	2	no	—
265	C₄⋊C₄×C₃₁	—	4	2	no	—
266	C₄⋊C₄×C₃₁	—	4	2	no	—
267	C₄⋊C₄×C₃₁	—	4	2	no	—
268	C₄⋊C₄×C₃₁	—	4	2	no	—
269	C₄⋊C₄×C₃₁	—	4	2	no	—
270	C₄⋊C₄×C₃₁	—	4	2	no	—
271	C₄⋊C₄×C₃₁	—	4	2	no	—
272	C₄⋊C₄×C₃₁	—	4	2	no	—
273	C₄⋊C₄×C₃₁	—	4	1	no	—
274	C₄⋊C₄×C₃₁	—	4	1	no	—
275	C₄⋊C₄×C₃₁	—	4	2	no	—
276	C₄⋊C₄×C₃₁	—	4	1	no	—
277	C₄⋊C₄×C₃₁	—	4	2	no	—
278	C₄⋊C₄×C₃₁	—	4	1	no	—
279	C₄⋊C₄×C₃₁	—	4	2	no	—
280	C₄⋊C₄×C₃₁	—	4	2	no	—
281	C₄⋊C₄×C₃₁	C₂×Q₈	1	8	yes	—
282	C₄⋊C₄×C₃₁	C₂×Q₈	1	8	yes	—
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	C₄²×C₃₁	—	2	2	no	—
288	C₄²×C₃₁	—	2	2	no	—
289	C₄²×C₃₁	—	4	1	no	—
290	C₄²×C₃₁	—	4	1	no	—
291	C₄²×C₃₁	—	4	2	no	—
292	C₄²×C₃₁	—	4	2	no	—
293	C₄²×C₃₁	—	4	2	no	—
294	C₄²×C₃₁	—	4	2	no	—
295	#36752	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
296	C₂³×C₃₁	—	2	1	no	—
297	C₂³×C₃₁	—	2	1	no	—
298	C₂³×C₃₁	—	2	1	no	—
299	C₂³×C₃₁	—	2	1	no	—
300	C₂³×C₃₁	C₂²×Q₈	1	2	yes	—
301	C₂³×C₃₁	H(5,𝔽₂)	1	2	yes	—
302	C₂³×C₃₁	2₋¹⁺⁴	1	2	yes	—
303	C₂³×C₃₁	C₂⁵	1	1	yes	characteristic
304	Q₈×C₃₁	—	8	4	no	—
305	Q₈×C₃₁	—	8	4	no	—
306	C₂×C₄×C₃₁	—	2	8	no	—
307	C₂×C₄×C₃₁	—	2	1	no	—
308	C₂×C₄×C₃₁	—	2	1	no	—
309	C₂×C₄×C₃₁	—	2	1	no	—
310	C₂×C₄×C₃₁	—	2	2	no	—
311	C₂×C₄×C₃₁	—	2	2	no	—
312	C₂×C₄×C₃₁	—	2	1	no	—
313	C₂×C₄×C₃₁	—	2	2	no	—
314	C₂×C₄×C₃₁	—	2	1	no	—
315	C₂×C₄×C₃₁	—	2	2	no	—
316	C₂×C₄×C₃₁	—	2	1	no	—
317	C₂×C₄×C₃₁	—	2	1	no	—
318	C₂×C₄×C₃₁	—	2	1	no	—
319	C₂×C₄×C₃₁	—	2	1	no	—
320	C₂×C₄×C₃₁	—	2	1	no	—
321	C₂×C₄×C₃₁	—	2	2	no	—
322	C₂×C₄×C₃₁	—	2	2	no	—
323	C₂×C₄×C₃₁	—	2	2	no	—
324	C₂×C₄×C₃₁	—	2	2	no	—
325	C₂×C₄×C₃₁	—	2	2	no	—
326	C₂×C₄×C₃₁	—	2	2	no	—
327	C₂×C₄×C₃₁	—	2	2	no	—
328	C₂×C₄×C₃₁	—	2	2	no	—
329	C₂×C₄×C₃₁	—	2	2	no	—
330	C₂×C₄×C₃₁	—	2	2	no	—
331	C₂×C₄×C₃₁	—	2	1	no	—
332	C₂×C₄×C₃₁	—	2	2	no	—
333	C₂×C₄×C₃₁	—	2	2	no	—
334	C₂×C₄×C₃₁	—	2	2	no	—
335	C₂×C₄×C₃₁	—	2	2	no	—
336	C₂×C₄×C₃₁	—	2	2	no	—
337	C₂×C₄×C₃₁	—	2	2	no	—
338	C₂×C₄×C₃₁	—	2	2	no	—
339	C₂×C₄×C₃₁	—	2	2	no	—
340	C₂×C₄×C₃₁	—	2	1	no	—
341	C₂×C₄×C₃₁	—	2	1	no	—
342	C₂×C₄×C₃₁	—	2	2	no	—
343	C₂×C₄×C₃₁	—	2	2	no	—
344	C₂×C₄×C₃₁	—	2	2	no	—
345	C₂×C₄×C₃₁	—	2	2	no	—
346	C₂×C₄×C₃₁	—	2	2	no	—
347	C₂×C₄×C₃₁	—	2	2	no	—
348	C₂×C₄×C₃₁	—	2	1	no	—
349	C₂×C₄×C₃₁	—	2	2	no	—
350	C₂×C₄×C₃₁	—	2	2	no	—
351	C₂×C₄×C₃₁	—	2	2	no	—
352	C₂×C₄×C₃₁	—	2	2	no	—
353	C₂×C₄×C₃₁	—	2	2	no	—
354	C₂×C₄×C₃₁	—	2	2	no	—
355	C₂×C₄×C₃₁	—	4	4	no	—
356	C₂×C₄×C₃₁	—	4	4	no	—
357	C₂×C₄×C₃₁	—	4	4	no	—
358	C₂×C₄×C₃₁	—	4	4	no	—
359	C₂×C₄×C₃₁	—	8	2	no	—
360	C₂×C₄×C₃₁	—	8	2	no	—
361	C₂×C₄×C₃₁	C₂²×Q₈	1	4	yes	—
362	C₂×C₄×C₃₁	C₂²×Q₈	1	2	yes	—
363	C₂×C₄×C₃₁	C₂²×Q₈	1	2	yes	—
364	C₂×C₄×C₃₁	C₂²×Q₈	1	4	yes	—
365	C₂×C₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
366	C₂×C₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
367	#2857	C₂×C₃₁	1	1	yes	characteristic
368	#2851	C₂×C₃₁	1	1	yes	characteristic
369	#2805	C₂×C₃₁	1	2	yes	complemented
370	#2802	C₂×C₃₁	1	2	yes	complemented
371	#2792	C₂×C₃₁	1	2	yes	complemented
372	#2791	C₂×C₃₁	1	2	yes	complemented
373	#2791	C₂×C₃₁	1	2	yes	complemented
374	#2755	C₂×C₃₁	1	2	yes	complemented
375	#2734	C₂×C₃₁	1	2	yes	complemented
376	#2713	C₂×C₃₁	1	2	yes	complemented
377	#2659	C₂×C₃₁	1	1	yes	characteristic
378	#2646	C₂×C₃₁	1	1	yes	characteristic
379	#2569	C₂×C₃₁	1	2	yes	—
380	#2440	C₂×C₃₁	1	2	yes	—
381	#2438	C₂×C₃₁	1	2	yes	—
382	#2438	C₂×C₃₁	1	2	yes	—
383	#2316	C₂×C₃₁	1	1	yes	characteristic
384	#2313	C₂×C₃₁	1	1	yes	characteristic
385	C₂×#387	C₂×C₃₁	1	1	yes	characteristic
386	C₂²×C₃₁	—	2	2	no	—
387	C₂²×C₃₁	—	2	2	no	—
388	C₂²×C₃₁	—	2	2	no	—
389	C₂²×C₃₁	—	2	2	no	—
390	C₂²×C₃₁	—	2	2	no	—
391	C₂²×C₃₁	—	2	2	no	—
392	C₂²×C₃₁	#544	1	4	yes	—
393	C₂²×C₃₁	C₂³×Q₈	1	1	yes	characteristic
394	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
395	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
396	C₂²×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
397	C₂²×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
398	C₂²×C₃₁	#585	1	1	yes	characteristic
399	C₂²×C₃₁	#585	1	1	yes	characteristic
400	C₄×C₃₁	—	2	4	no	—
401	C₄×C₃₁	—	2	2	no	—
402	C₄×C₃₁	—	2	2	no	—
403	C₄×C₃₁	—	2	4	no	—
404	C₄×C₃₁	—	2	2	no	—
405	C₄×C₃₁	—	2	2	no	—
406	C₄×C₃₁	—	4	1	no	—
407	C₄×C₃₁	—	4	2	no	—
408	C₄×C₃₁	—	4	2	no	—
409	C₄×C₃₁	—	4	2	no	—
410	C₄×C₃₁	—	4	2	no	—
411	C₄×C₃₁	—	4	2	no	—
412	C₄×C₃₁	—	4	1	no	—
413	C₄×C₃₁	—	4	2	no	—
414	C₄×C₃₁	—	4	2	no	—
415	C₄×C₃₁	—	4	2	no	—
416	C₄×C₃₁	—	4	2	no	—
417	C₄×C₃₁	—	4	2	no	—
418	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
419	C₂×C₄⋊Q₈	C₂²×C₃₁	1	2	yes	—
420	C₂×#125	C₂²×C₃₁	1	1	yes	characteristic
421	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	—
422	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	—
423	C₂×#117	C₂²×C₃₁	1	2	yes	—
424	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
425	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
426	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
427	#400	C₂²×C₃₁	1	2	yes	—
428	#400	C₂²×C₃₁	1	2	yes	—
429	#400	C₂²×C₃₁	1	2	yes	—
430	#400	C₂²×C₃₁	1	2	yes	—
431	#400	C₂²×C₃₁	1	2	yes	—
432	#400	C₂²×C₃₁	1	2	yes	—
433	#398	C₂²×C₃₁	1	2	yes	—
434	#398	C₂²×C₃₁	1	2	yes	—
435	#398	C₂²×C₃₁	1	2	yes	—
436	#398	C₂²×C₃₁	1	2	yes	—
437	#398	C₂²×C₃₁	1	2	yes	—
438	#398	C₂²×C₃₁	1	2	yes	—
439	#398	C₂²×C₃₁	1	2	yes	—
440	#398	C₂²×C₃₁	1	2	yes	—
441	#398	C₂²×C₃₁	1	2	yes	—
442	#398	C₂²×C₃₁	1	2	yes	—
443	#398	C₂²×C₃₁	1	2	yes	—
444	#398	C₂²×C₃₁	1	2	yes	—
445	#395	C₂²×C₃₁	1	2	yes	—
446	#395	C₂²×C₃₁	1	2	yes	—
447	#395	C₂²×C₃₁	1	2	yes	—
448	#395	C₂²×C₃₁	1	2	yes	—
449	#395	C₂²×C₃₁	1	2	yes	—
450	#395	C₂²×C₃₁	1	2	yes	—
451	#391	C₂²×C₃₁	1	2	yes	—
452	#391	C₂²×C₃₁	1	2	yes	—
453	#391	C₂²×C₃₁	1	2	yes	—
454	#389	C₂²×C₃₁	1	2	yes	—
455	#389	C₂²×C₃₁	1	2	yes	—
456	#389	C₂²×C₃₁	1	2	yes	—
457	#389	C₂²×C₃₁	1	2	yes	—
458	#389	C₂²×C₃₁	1	1	yes	characteristic
459	#389	C₂²×C₃₁	1	1	yes	characteristic
460	#389	C₂²×C₃₁	1	1	yes	characteristic
461	#389	C₂²×C₃₁	1	2	yes	—
462	#389	C₂²×C₃₁	1	1	yes	characteristic
463	#389	C₂²×C₃₁	1	2	yes	—
464	#389	C₂²×C₃₁	1	2	yes	—
465	#389	C₂²×C₃₁	1	2	yes	—
466	#389	C₂²×C₃₁	1	2	yes	—
467	#387	C₂²×C₃₁	1	2	yes	—
468	#387	C₂²×C₃₁	1	2	yes	—
469	#387	C₂²×C₃₁	1	2	yes	—
470	#387	C₂²×C₃₁	1	2	yes	—
471	#387	C₂²×C₃₁	1	2	yes	—
472	#387	C₂²×C₃₁	1	2	yes	—
473	#387	C₂²×C₃₁	1	2	yes	—
474	#387	C₂²×C₃₁	1	2	yes	—
475	#387	C₂²×C₃₁	1	2	yes	—
476	#387	C₂²×C₃₁	1	2	yes	—
477	#387	C₂²×C₃₁	1	2	yes	—
478	#387	C₂²×C₃₁	1	2	yes	—
479	#387	C₂²×C₃₁	1	2	yes	—
480	#387	C₂²×C₃₁	1	2	yes	—
481	#387	C₂²×C₃₁	1	2	yes	—
482	#387	C₂²×C₃₁	1	2	yes	—
483	#387	C₂²×C₃₁	1	2	yes	—
484	#387	C₂²×C₃₁	1	2	yes	—
485	#385	C₂²×C₃₁	1	2	yes	—
486	#385	C₂²×C₃₁	1	2	yes	—
487	#385	C₂²×C₃₁	1	2	yes	—
488	#385	C₂²×C₃₁	1	2	yes	—
489	#384	C₂²×C₃₁	1	1	yes	characteristic
490	#384	C₂²×C₃₁	1	2	yes	—
491	#382	C₂²×C₃₁	1	1	yes	characteristic
492	#381	C₂²×C₃₁	1	2	yes	—
493	#380	C₂²×C₃₁	1	1	yes	characteristic
494	#380	C₂²×C₃₁	1	1	yes	characteristic
495	#380	C₂²×C₃₁	1	2	yes	—
496	#380	C₂²×C₃₁	1	2	yes	—
497	#380	C₂²×C₃₁	1	2	yes	—
498	#380	C₂²×C₃₁	1	1	yes	characteristic
499	#380	C₂²×C₃₁	1	1	yes	characteristic
500	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
501	C₂×#95	C₂²×C₃₁	1	1	yes	characteristic
502	C₂×#95	C₂²×C₃₁	1	1	yes	characteristic
503	C₂×#95	C₂²×C₃₁	1	1	yes	characteristic
504	C₂×#95	C₂²×C₃₁	1	1	yes	characteristic
505	C₂×C₃₁	—	2	4	no	—
506	C₂×C₃₁	C₂×#544	1	1	yes	characteristic
507	C₂×C₃₁	#3501	1	1	yes	characteristic
508	C₂×C₃₁	#3502	1	1	yes	characteristic
509	C₂×C₃₁	#3534	1	1	yes	characteristic
510	C₂×C₃₁	#3538	1	1	yes	characteristic
511	C₂×C₃₁	#3559	1	1	yes	characteristic
512	C₂×C₃₁	#3564	1	1	yes	characteristic
513	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
514	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
515	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
516	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
517	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
518	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
519	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
520	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
521	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
522	C₄⋊Q₈	—	4	2	no	—
523	C₄⋊Q₈	—	4	4	no	—
524	#125	—	4	2	no	—
525	C₂²⋊Q₈	—	4	4	no	—
526	C₂²⋊Q₈	—	4	4	no	—
527	#117	—	4	4	no	—
528	C₂×C₄⋊C₄	—	4	2	no	—
529	C₂×C₄⋊C₄	Q₈×C₃₁	1	8	yes	complemented
530	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
531	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
532	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
533	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
534	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
535	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
536	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
537	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
538	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
539	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
540	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
541	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
542	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
543	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
544	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
545	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
546	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
547	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
548	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
549	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
550	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
551	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
552	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
553	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
554	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
555	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
556	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
557	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
558	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
559	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
560	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
561	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
562	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
563	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
564	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
565	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
566	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
567	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
568	C₂×C₄²	—	4	2	no	—
569	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
570	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
571	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
572	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
573	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
574	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
575	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
576	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
577	#95	C₂³×C₃₁	1	2	yes	—
578	#95	C₂³×C₃₁	1	2	yes	—
579	#95	C₂³×C₃₁	1	2	yes	—
580	#95	C₂³×C₃₁	1	2	yes	—
581	#95	C₂³×C₃₁	1	2	yes	—
582	#95	C₂³×C₃₁	1	2	yes	—
583	#95	C₂³×C₃₁	1	2	yes	—
584	#95	C₂³×C₃₁	1	2	yes	—
585	#95	C₂³×C₃₁	1	2	yes	—
586	#95	C₂³×C₃₁	1	2	yes	—
587	#95	C₂³×C₃₁	1	2	yes	—
588	#95	C₂³×C₃₁	1	2	yes	—
589	#95	C₂³×C₃₁	1	2	yes	—
590	#95	C₂³×C₃₁	1	2	yes	—
591	#95	C₂³×C₃₁	1	2	yes	—
592	#95	C₂³×C₃₁	1	2	yes	—
593	#95	C₂³×C₃₁	1	2	yes	—
594	#95	C₂³×C₃₁	1	2	yes	—
595	#95	C₂³×C₃₁	1	2	yes	—
596	#95	C₂³×C₃₁	1	2	yes	—
597	#95	C₂³×C₃₁	1	2	yes	—
598	#95	C₂³×C₃₁	1	2	yes	—
599	#95	C₂³×C₃₁	1	2	yes	—
600	#95	C₂³×C₃₁	1	2	yes	—
601	#95	C₂³×C₃₁	1	2	yes	—
602	#95	C₂³×C₃₁	1	2	yes	—
603	#95	C₂³×C₃₁	1	2	yes	—
604	#95	C₂³×C₃₁	1	2	yes	—
605	#95	C₂³×C₃₁	1	2	yes	—
606	#95	C₂³×C₃₁	1	2	yes	—
607	#95	C₂³×C₃₁	1	2	yes	—
608	#95	C₂³×C₃₁	1	2	yes	—
609	C₃₁	#36752	1	1	yes	characteristic, direct product factor, Sylow
610	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
611	C₂×Q₈	—	2	4	no	—
612	C₂×Q₈	—	4	2	no	—
613	C₂×Q₈	—	4	2	no	—
614	C₂×Q₈	—	4	2	no	—
615	C₂×Q₈	—	4	2	no	—
616	C₂×Q₈	—	4	2	no	—
617	C₂²×C₄	—	2	2	no	—
618	C₂²×C₄	—	2	2	no	—
619	C₂²×C₄	—	2	2	no	—
620	C₂²×C₄	—	2	2	no	—
621	C₂²×C₄	—	2	2	no	—
622	C₂²×C₄	—	2	2	no	—
623	C₂²×C₄	—	2	2	no	—
624	C₂²×C₄	—	2	2	no	—
625	C₂²×C₄	—	4	1	no	—
626	C₂²×C₄	—	4	1	no	—
627	C₂²×C₄	—	4	1	no	—
628	C₂²×C₄	—	4	1	no	—
629	C₂²×C₄	—	4	1	no	—
630	C₂²×C₄	—	4	1	no	—
631	C₂²×C₄	—	4	1	no	—
632	C₂²×C₄	—	4	1	no	—
633	C₂²×C₄	—	4	1	no	—
634	C₂²×C₄	—	4	1	no	—
635	C₂²×C₄	C₂×Q₈×C₃₁	1	4	yes	—
636	C₂²×C₄	C₂×Q₈×C₃₁	1	4	yes	—
637	C₂²×C₄	C₂×Q₈×C₃₁	1	4	yes	—
638	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
639	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
640	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
641	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
642	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
643	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
644	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
645	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
646	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
647	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
648	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
649	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
650	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
651	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
652	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
653	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
654	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
655	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
656	C₄⋊C₄	—	2	4	no	—
657	C₄⋊C₄	—	2	4	no	—
658	C₄⋊C₄	—	2	4	no	—
659	C₄⋊C₄	—	2	4	no	—
660	C₄⋊C₄	—	4	2	no	—
661	C₄⋊C₄	—	4	2	no	—
662	C₄⋊C₄	—	4	1	no	—
663	C₄⋊C₄	—	4	1	no	—
664	C₄⋊C₄	—	4	1	no	—
665	C₄⋊C₄	—	4	1	no	—
666	C₄⋊C₄	—	4	2	no	—
667	C₄⋊C₄	—	4	2	no	—
668	C₄⋊C₄	—	4	2	no	—
669	C₄⋊C₄	—	4	2	no	—
670	C₄⋊C₄	—	4	2	no	—
671	C₄⋊C₄	—	4	2	no	—
672	C₄⋊C₄	—	4	2	no	—
673	C₄⋊C₄	—	4	2	no	—
674	C₄⋊C₄	—	4	2	no	—
675	C₄⋊C₄	—	4	2	no	—
676	C₄⋊C₄	—	4	2	no	—
677	C₄⋊C₄	—	4	2	no	—
678	C₄⋊C₄	—	4	2	no	—
679	C₄⋊C₄	—	4	2	no	—
680	C₄⋊C₄	—	4	1	no	—
681	C₄⋊C₄	—	4	1	no	—
682	C₄⋊C₄	—	4	2	no	—
683	C₄⋊C₄	—	4	1	no	—
684	C₄⋊C₄	—	4	2	no	—
685	C₄⋊C₄	—	4	1	no	—
686	C₄⋊C₄	—	4	2	no	—
687	C₄⋊C₄	—	4	2	no	—
688	C₄⋊C₄	C₂×Q₈×C₃₁	1	8	yes	—
689	C₄⋊C₄	C₂×Q₈×C₃₁	1	8	yes	—
690	C₂²⋊C₄	—	2	4	no	—
691	C₂²⋊C₄	—	2	4	no	—
692	C₂²⋊C₄	—	2	4	no	—
693	C₂²⋊C₄	—	2	4	no	—
694	C₄²	—	2	2	no	—
695	C₄²	—	2	2	no	—
696	C₄²	—	4	1	no	—
697	C₄²	—	4	1	no	—
698	C₄²	—	4	2	no	—
699	C₄²	—	4	2	no	—
700	C₄²	—	4	2	no	—
701	C₄²	—	4	2	no	—
702	C₂³	—	2	1	no	—
703	C₂³	—	2	1	no	—
704	C₂³	—	2	1	no	—
705	C₂³	—	2	1	no	—
706	C₂³	C₂²×Q₈×C₃₁	1	2	yes	—
707	C₂³	C₃₁×H(5,𝔽₂)	1	2	yes	—
708	C₂³	C₃₁×2₋¹⁺⁴	1	2	yes	—
709	C₂³	C₂⁵×C₃₁	1	1	yes	characteristic
710	Q₈	—	8	4	no	—
711	Q₈	—	8	4	no	—
712	C₂×C₄	—	2	8	no	—
713	C₂×C₄	—	2	1	no	—
714	C₂×C₄	—	2	1	no	—
715	C₂×C₄	—	2	1	no	—
716	C₂×C₄	—	2	2	no	—
717	C₂×C₄	—	2	2	no	—
718	C₂×C₄	—	2	1	no	—
719	C₂×C₄	—	2	2	no	—
720	C₂×C₄	—	2	1	no	—
721	C₂×C₄	—	2	2	no	—
722	C₂×C₄	—	2	1	no	—
723	C₂×C₄	—	2	1	no	—
724	C₂×C₄	—	2	1	no	—
725	C₂×C₄	—	2	1	no	—
726	C₂×C₄	—	2	1	no	—
727	C₂×C₄	—	2	2	no	—
728	C₂×C₄	—	2	2	no	—
729	C₂×C₄	—	2	2	no	—
730	C₂×C₄	—	2	2	no	—
731	C₂×C₄	—	2	2	no	—
732	C₂×C₄	—	2	2	no	—
733	C₂×C₄	—	2	2	no	—
734	C₂×C₄	—	2	2	no	—
735	C₂×C₄	—	2	2	no	—
736	C₂×C₄	—	2	2	no	—
737	C₂×C₄	—	2	1	no	—
738	C₂×C₄	—	2	2	no	—
739	C₂×C₄	—	2	2	no	—
740	C₂×C₄	—	2	2	no	—
741	C₂×C₄	—	2	2	no	—
742	C₂×C₄	—	2	2	no	—
743	C₂×C₄	—	2	2	no	—
744	C₂×C₄	—	2	2	no	—
745	C₂×C₄	—	2	2	no	—
746	C₂×C₄	—	2	1	no	—
747	C₂×C₄	—	2	1	no	—
748	C₂×C₄	—	2	2	no	—
749	C₂×C₄	—	2	2	no	—
750	C₂×C₄	—	2	2	no	—
751	C₂×C₄	—	2	2	no	—
752	C₂×C₄	—	2	2	no	—
753	C₂×C₄	—	2	2	no	—
754	C₂×C₄	—	2	1	no	—
755	C₂×C₄	—	2	2	no	—
756	C₂×C₄	—	2	2	no	—
757	C₂×C₄	—	2	2	no	—
758	C₂×C₄	—	2	2	no	—
759	C₂×C₄	—	2	2	no	—
760	C₂×C₄	—	2	2	no	—
761	C₂×C₄	—	4	4	no	—
762	C₂×C₄	—	4	4	no	—
763	C₂×C₄	—	4	4	no	—
764	C₂×C₄	—	4	4	no	—
765	C₂×C₄	—	8	2	no	—
766	C₂×C₄	—	8	2	no	—
767	C₂×C₄	C₂²×Q₈×C₃₁	1	4	yes	—
768	C₂×C₄	C₂²×Q₈×C₃₁	1	2	yes	—
769	C₂×C₄	C₂²×Q₈×C₃₁	1	2	yes	—
770	C₂×C₄	C₂²×Q₈×C₃₁	1	4	yes	—
771	C₂×C₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
772	C₂×C₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
773	C₂²	—	2	2	no	—
774	C₂²	—	2	2	no	—
775	C₂²	—	2	2	no	—
776	C₂²	—	2	2	no	—
777	C₂²	—	2	2	no	—
778	C₂²	—	2	2	no	—
779	C₂²	C₃₁×#544	1	4	yes	—
780	C₂²	C₂³×Q₈×C₃₁	1	1	yes	characteristic
781	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
782	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
783	C₂²	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
784	C₂²	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
785	C₂²	C₃₁×#585	1	1	yes	characteristic
786	C₂²	C₃₁×#585	1	1	yes	characteristic
787	C₄	—	2	4	no	—
788	C₄	—	2	2	no	—
789	C₄	—	2	2	no	—
790	C₄	—	2	4	no	—
791	C₄	—	2	2	no	—
792	C₄	—	2	2	no	—
793	C₄	—	4	1	no	—
794	C₄	—	4	2	no	—
795	C₄	—	4	2	no	—
796	C₄	—	4	2	no	—
797	C₄	—	4	2	no	—
798	C₄	—	4	1	no	—
799	C₄	—	4	2	no	—
800	C₄	—	4	2	no	—
801	C₄	—	4	2	no	—
802	C₄	—	4	2	no	—
803	C₄	—	4	2	no	—
804	C₄	—	4	2	no	—
805	C₂	—	2	4	no	—
806	C₂	C₂×C₃₁×#544	1	1	yes	characteristic
807	C₂	C₃₁×#3501	1	1	yes	characteristic
808	C₂	C₃₁×#3502	1	1	yes	characteristic
809	C₂	C₃₁×#3534	1	1	yes	characteristic
810	C₂	C₃₁×#3538	1	1	yes	characteristic
811	C₂	C₃₁×#3559	1	1	yes	characteristic
812	C₂	C₃₁×#3564	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃₁	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₃₁
prime radical	C₂⁴×C₃₁	C₂⁴
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
3. C₃₁×#2805	C₂	semidirect
4. C₃₁×#2802	C₂	semidirect
5. C₃₁×#2792	C₂	semidirect
6. C₃₁×#2791	C₂	semidirect
7. C₃₁×#2791	C₂	semidirect
8. C₃₁×#2755	C₂	semidirect
9. C₃₁×#2734	C₂	semidirect
10. C₃₁×#2713	C₂	semidirect
123. C₂×C₄⋊C₄×C₃₁	Q₈	semidirect
295. #36752	C₃₁	direct (N × H)
369. #2805	C₂×C₃₁	semidirect
370. #2802	C₂×C₃₁	semidirect
371. #2792	C₂×C₃₁	semidirect
372. #2791	C₂×C₃₁	semidirect
373. #2791	C₂×C₃₁	semidirect
374. #2755	C₂×C₃₁	semidirect
375. #2734	C₂×C₃₁	semidirect
376. #2713	C₂×C₃₁	semidirect
529. C₂×C₄⋊C₄	Q₈×C₃₁	semidirect
609. C₃₁	#36752	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×#2857	2
C₃₁×#2851	2
C₃₁×#2805	2
C₃₁×#2802	2
C₃₁×#2792	2
C₃₁×#2791	2
C₃₁×#2755	2
C₃₁×#2734	2
C₃₁×#2713	2
C₃₁×#2659	2
C₃₁×#2646	2
C₃₁×#2569	2
C₃₁×#2440	2
C₃₁×#2438	2
C₃₁×#2316	2
C₃₁×#2313	2
C₂×C₃₁×#387	2
#36752	31

Subgroups — C31×#36752 #21493511

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#36752 #21493511