Subgroups — C₃₁×#34436 #21491195

Order 7936.

2522 conjugacy classes of subgroups.

The subgroup lattice has 966 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#537	C₂	1	1	yes	maximal, characteristic
2	C₃₁×#2378	C₂	1	2	yes	maximal, complemented
3	C₃₁×#2377	C₂	1	2	yes	maximal, complemented
4	C₃₁×#2368	C₂	1	2	yes	maximal, complemented
5	C₃₁×#2364	C₂	1	2	yes	maximal, complemented
6	C₃₁×#2364	C₂	1	2	yes	maximal, complemented
7	C₃₁×#2361	C₂	1	2	yes	maximal, complemented
8	C₃₁×#2339	C₂	1	2	yes	maximal, complemented
9	C₃₁×#2339	C₂	1	2	yes	maximal, complemented
10	C₃₁×#2333	C₂	1	2	yes	maximal, complemented
11	C₃₁×#2332	C₂	1	2	yes	maximal, complemented
12	C₃₁×#2329	C₂	1	2	yes	maximal, complemented
13	C₃₁×#2325	C₂	1	2	yes	maximal, complemented
14	C₃₁×#2325	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#2325	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#2313	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄×C₃₁×#121	C₂	1	1	yes	maximal, characteristic, complemented
18	C₄×C₃₁×#121	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×C₃₁×#387	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂²×#41×C₃₁	C₂²	1	2	yes	—
21	C₃₁×#537	C₄	1	16	yes	complemented
22	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	—
23	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	—
24	C₂×C₃₁×#121	C₂²	1	2	yes	—
25	C₂×C₃₁×#121	C₂²	1	1	yes	characteristic
26	C₂×C₃₁×#121	C₂²	1	1	yes	characteristic
27	C₂×C₃₁×#121	C₂²	1	2	yes	—
28	C₂×C₃₁×#121	C₂²	1	2	yes	—
29	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
30	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
31	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
32	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
33	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
34	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
35	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
36	C₂²×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
37	C₂²×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
38	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
39	C₃₁×#391	C₂²	1	2	yes	—
40	C₃₁×#391	C₂²	1	2	yes	—
41	C₃₁×#391	C₂²	1	2	yes	—
42	C₃₁×#391	C₂²	1	2	yes	—
43	C₃₁×#390	C₂²	1	1	yes	characteristic
44	C₃₁×#390	C₂²	1	2	yes	—
45	C₃₁×#390	C₂²	1	1	yes	characteristic
46	C₃₁×#389	C₂²	1	1	yes	characteristic
47	C₃₁×#389	C₂²	1	2	yes	—
48	C₃₁×#389	C₂²	1	1	yes	characteristic
49	C₃₁×#388	C₂²	1	2	yes	—
50	C₃₁×#388	C₂²	1	2	yes	—
51	C₃₁×#388	C₂²	1	2	yes	—
52	C₃₁×#388	C₂²	1	2	yes	—
53	C₃₁×#388	C₂²	1	2	yes	—
54	C₃₁×#388	C₂²	1	2	yes	—
55	C₃₁×#388	C₂²	1	2	yes	—
56	C₃₁×#388	C₂²	1	2	yes	—
57	C₃₁×#387	C₂²	1	2	yes	—
58	C₃₁×#387	C₂²	1	2	yes	—
59	C₃₁×#387	C₂²	1	2	yes	—
60	C₃₁×#387	C₂²	1	2	yes	—
61	C₃₁×#387	C₂²	1	2	yes	—
62	C₃₁×#387	C₂²	1	2	yes	—
63	C₃₁×#387	C₂²	1	2	yes	—
64	C₃₁×#387	C₂²	1	2	yes	—
65	C₃₁×#387	C₂²	1	2	yes	—
66	C₃₁×#387	C₂²	1	2	yes	—
67	C₃₁×#387	C₂²	1	2	yes	—
68	C₃₁×#387	C₂²	1	2	yes	—
69	C₃₁×#386	C₂²	1	2	yes	—
70	C₃₁×#386	C₂²	1	2	yes	—
71	C₃₁×#386	C₂²	1	2	yes	—
72	C₃₁×#386	C₂²	1	2	yes	—
73	C₃₁×#386	C₂²	1	2	yes	—
74	C₃₁×#386	C₂²	1	2	yes	—
75	C₃₁×#386	C₂²	1	2	yes	—
76	C₃₁×#386	C₂²	1	2	yes	—
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×#385	C₂²	1	2	yes	—
82	C₃₁×#385	C₂²	1	2	yes	—
83	C₃₁×#385	C₂²	1	2	yes	—
84	C₃₁×#385	C₂²	1	2	yes	—
85	C₃₁×#381	C₂²	1	2	yes	—
86	C₃₁×#381	C₂²	1	2	yes	—
87	C₃₁×#381	C₂²	1	2	yes	—
88	C₃₁×#380	C₂²	1	1	yes	characteristic
89	C₃₁×#380	C₂²	1	1	yes	characteristic
90	C₃₁×#380	C₂²	1	2	yes	—
91	C₃₁×#380	C₂²	1	2	yes	—
92	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
93	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
94	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
95	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
96	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
97	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
98	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
99	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
100	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
101	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
102	C₂×C₃₁×#95	C₂²	1	1	yes	characteristic
103	C₂×C₃₁×#95	C₂²	1	2	yes	—
104	C₂×C₃₁×#95	C₂²	1	2	yes	—
105	C₂×C₃₁×#95	C₂²	1	1	yes	characteristic
106	C₂×C₃₁×#95	C₂²	1	1	yes	characteristic
107	C₂×C₃₁×#95	C₂²	1	1	yes	characteristic
108	C₂×#41×C₃₁	—	4	4	no	—
109	C₂×#41×C₃₁	—	4	4	no	—
110	C₂×#41×C₃₁	C₂×C₄	1	16	yes	complemented
111	C₂²×Q₈×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	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
117	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
118	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
119	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
120	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
121	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
122	C₂³×C₄×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	2	yes	—
126	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
127	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
128	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
129	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
130	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
131	C₃₁×C₂²⋊Q₈	C₂×C₄	1	16	yes	complemented
132	C₃₁×C₂²⋊Q₈	C₂×C₄	1	16	yes	complemented
133	C₃₁×#121	C₂×C₄	1	16	yes	complemented
134	C₃₁×#121	C₂×C₄	1	16	yes	complemented
135	C₃₁×#121	C₂×C₄	1	8	yes	complemented
136	C₃₁×#121	C₂×C₄	1	8	yes	complemented
137	C₃₁×#121	C₂×C₄	1	16	yes	complemented
138	C₄×D₄×C₃₁	—	4	2	no	—
139	C₄×D₄×C₃₁	—	4	2	no	—
140	C₄×D₄×C₃₁	—	4	4	no	—
141	C₄×D₄×C₃₁	—	4	4	no	—
142	C₄×D₄×C₃₁	—	4	4	no	—
143	C₄×D₄×C₃₁	—	4	4	no	—
144	C₄×D₄×C₃₁	—	4	4	no	—
145	C₂×C₄⋊C₄×C₃₁	—	4	2	no	—
146	C₂×C₄⋊C₄×C₃₁	C₂×C₄	1	8	yes	complemented
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	1	yes	characteristic
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	1	yes	characteristic
154	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
155	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
156	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
157	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
158	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
159	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
160	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
161	C₂×C₄⋊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×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×C₄²×C₃₁	—	4	2	no	—
181	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
182	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
183	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
184	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
185	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
186	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
187	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
188	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
189	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
190	C₂×C₄²×C₃₁	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	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	C₃₁×#95	C₂³	1	2	yes	—
214	C₃₁×#95	C₂³	1	2	yes	—
215	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
216	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
217	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
218	#41×C₃₁	—	4	32	no	—
219	C₂×Q₈×C₃₁	—	4	2	no	—
220	C₂×Q₈×C₃₁	—	4	2	no	—
221	C₂×Q₈×C₃₁	C₂²×C₄	1	8	yes	—
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	—	2	4	no	—
226	C₂×D₄×C₃₁	—	4	1	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	1	no	—
231	C₂×D₄×C₃₁	—	4	1	no	—
232	C₂×D₄×C₃₁	—	4	2	no	—
233	C₂×D₄×C₃₁	—	4	2	no	—
234	C₂×D₄×C₃₁	C₂²×C₄	1	8	yes	—
235	C₂×D₄×C₃₁	C₂²×C₄	1	8	yes	—
236	C₂×D₄×C₃₁	C₂²×C₄	1	4	yes	—
237	C₂×D₄×C₃₁	C₂²×C₄	1	8	yes	—
238	C₂×D₄×C₃₁	C₂²×C₄	1	4	yes	—
239	C₂×D₄×C₃₁	C₂²×C₄	1	8	yes	—
240	C₂²×C₄×C₃₁	—	2	2	no	—
241	C₂²×C₄×C₃₁	—	2	2	no	—
242	C₂²×C₄×C₃₁	—	2	2	no	—
243	C₂²×C₄×C₃₁	—	2	2	no	—
244	C₂²×C₄×C₃₁	—	2	2	no	—
245	C₂²×C₄×C₃₁	—	2	2	no	—
246	C₂²×C₄×C₃₁	—	2	2	no	—
247	C₂²×C₄×C₃₁	—	2	2	no	—
248	C₂²×C₄×C₃₁	—	2	4	no	—
249	C₂²×C₄×C₃₁	—	2	4	no	—
250	C₂²×C₄×C₃₁	—	4	1	no	—
251	C₂²×C₄×C₃₁	—	4	1	no	—
252	C₂²×C₄×C₃₁	—	4	1	no	—
253	C₂²×C₄×C₃₁	—	4	1	no	—
254	C₂²×C₄×C₃₁	—	4	1	no	—
255	C₂²×C₄×C₃₁	—	4	1	no	—
256	C₂²×C₄×C₃₁	—	4	2	no	—
257	C₂²×C₄×C₃₁	—	4	2	no	—
258	C₂²×C₄×C₃₁	—	4	2	no	—
259	C₂²×C₄×C₃₁	—	4	2	no	—
260	C₂²×C₄×C₃₁	—	4	1	no	—
261	C₂²×C₄×C₃₁	—	4	2	no	—
262	C₂²×C₄×C₃₁	—	4	2	no	—
263	C₂²×C₄×C₃₁	—	4	2	no	—
264	C₂²×C₄×C₃₁	—	4	2	no	—
265	C₂²×C₄×C₃₁	—	4	2	no	—
266	C₂²×C₄×C₃₁	—	4	2	no	—
267	C₂²×C₄×C₃₁	—	4	2	no	—
268	C₂²×C₄×C₃₁	—	4	2	no	—
269	C₂²×C₄×C₃₁	—	4	2	no	—
270	C₂²×C₄×C₃₁	—	4	1	no	—
271	C₂²×C₄×C₃₁	—	4	1	no	—
272	C₂²×C₄×C₃₁	—	4	1	no	—
273	C₂²×C₄×C₃₁	—	4	2	no	—
274	C₂²×C₄×C₃₁	C₂²×C₄	1	4	yes	—
275	C₂²×C₄×C₃₁	C₂²×C₄	1	4	yes	—
276	C₂²×C₄×C₃₁	C₂²×C₄	1	4	yes	—
277	C₂²×C₄×C₃₁	C₂²×C₄	1	8	yes	—
278	C₂²×C₄×C₃₁	C₂²×C₄	1	8	yes	—
279	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
280	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
281	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
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	1	yes	characteristic
287	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
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	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
292	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
293	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
294	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
295	C₄⋊C₄×C₃₁	—	2	4	no	—
296	C₄⋊C₄×C₃₁	—	4	2	no	—
297	C₄⋊C₄×C₃₁	—	4	1	no	—
298	C₄⋊C₄×C₃₁	—	4	1	no	—
299	C₄⋊C₄×C₃₁	—	4	1	no	—
300	C₄⋊C₄×C₃₁	—	4	1	no	—
301	C₄⋊C₄×C₃₁	—	4	2	no	—
302	C₄⋊C₄×C₃₁	—	4	2	no	—
303	C₄⋊C₄×C₃₁	—	4	2	no	—
304	C₄⋊C₄×C₃₁	—	4	2	no	—
305	C₄⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
306	C₄⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
307	C₄⋊C₄×C₃₁	C₂²×C₄	1	4	yes	—
308	C₄⋊C₄×C₃₁	C₂²×C₄	1	4	yes	—
309	C₄⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
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	—	2	4	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	2	no	—
320	C₂²⋊C₄×C₃₁	—	4	2	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	C₂²×C₄	1	8	yes	—
325	C₂²⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
326	C₂²⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
327	C₂²⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
328	C₄²×C₃₁	—	2	2	no	—
329	C₄²×C₃₁	—	2	2	no	—
330	C₄²×C₃₁	—	4	1	no	—
331	C₄²×C₃₁	—	4	1	no	—
332	C₄²×C₃₁	—	4	2	no	—
333	C₄²×C₃₁	—	4	2	no	—
334	C₄²×C₃₁	—	4	2	no	—
335	C₄²×C₃₁	—	4	2	no	—
336	C₄²×C₃₁	—	4	2	no	—
337	C₄²×C₃₁	—	4	2	no	—
338	#34436	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
339	C₂³×C₃₁	—	2	1	no	—
340	C₂³×C₃₁	—	2	1	no	—
341	C₂³×C₃₁	—	2	1	no	—
342	C₂³×C₃₁	—	2	1	no	—
343	C₂³×C₃₁	—	2	2	no	—
344	C₂³×C₃₁	—	2	2	no	—
345	C₂³×C₃₁	—	2	2	no	—
346	C₂³×C₃₁	—	2	2	no	—
347	C₂³×C₃₁	—	2	2	no	—
348	C₂³×C₃₁	—	2	2	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	2	no	—
354	C₂³×C₃₁	—	2	2	no	—
355	C₂³×C₃₁	C₂³×C₄	1	4	yes	—
356	C₂³×C₃₁	C₂³×C₄	1	4	yes	—
357	C₂³×C₃₁	C₂³×C₄	1	2	yes	—
358	C₂³×C₃₁	H(5,𝔽₂)	1	2	yes	—
359	C₂³×C₃₁	H(5,𝔽₂)	1	2	yes	—
360	C₂³×C₃₁	C₂⁵	1	1	yes	characteristic
361	Q₈×C₃₁	—	4	8	no	—
362	D₄×C₃₁	—	2	16	no	—
363	D₄×C₃₁	—	2	16	no	—
364	D₄×C₃₁	—	4	4	no	—
365	D₄×C₃₁	—	4	4	no	—
366	D₄×C₃₁	—	4	8	no	—
367	D₄×C₃₁	—	4	8	no	—
368	C₂×C₄×C₃₁	—	2	8	no	—
369	C₂×C₄×C₃₁	—	2	1	no	—
370	C₂×C₄×C₃₁	—	2	1	no	—
371	C₂×C₄×C₃₁	—	2	1	no	—
372	C₂×C₄×C₃₁	—	2	1	no	—
373	C₂×C₄×C₃₁	—	2	1	no	—
374	C₂×C₄×C₃₁	—	2	2	no	—
375	C₂×C₄×C₃₁	—	2	2	no	—
376	C₂×C₄×C₃₁	—	2	2	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	1	no	—
383	C₂×C₄×C₃₁	—	2	1	no	—
384	C₂×C₄×C₃₁	—	2	1	no	—
385	C₂×C₄×C₃₁	—	2	1	no	—
386	C₂×C₄×C₃₁	—	2	2	no	—
387	C₂×C₄×C₃₁	—	2	1	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	1	no	—
396	C₂×C₄×C₃₁	—	2	1	no	—
397	C₂×C₄×C₃₁	—	2	2	no	—
398	C₂×C₄×C₃₁	—	2	2	no	—
399	C₂×C₄×C₃₁	—	2	1	no	—
400	C₂×C₄×C₃₁	—	2	2	no	—
401	C₂×C₄×C₃₁	—	2	2	no	—
402	C₂×C₄×C₃₁	—	2	2	no	—
403	C₂×C₄×C₃₁	—	2	1	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	—	4	4	no	—
410	C₂×C₄×C₃₁	—	4	4	no	—
411	C₂×C₄×C₃₁	—	4	8	no	—
412	C₂×C₄×C₃₁	—	4	8	no	—
413	C₂×C₄×C₃₁	—	4	4	no	—
414	C₂×C₄×C₃₁	—	4	4	no	—
415	C₂×C₄×C₃₁	—	8	4	no	—
416	C₂×C₄×C₃₁	—	8	4	no	—
417	C₂×C₄×C₃₁	—	8	2	no	—
418	C₂×C₄×C₃₁	—	8	2	no	—
419	C₂×C₄×C₃₁	—	8	4	no	—
420	C₂×C₄×C₃₁	—	8	4	no	—
421	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
422	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
423	C₂×C₄×C₃₁	C₂³×C₄	1	4	yes	—
424	C₂×C₄×C₃₁	C₂³×C₄	1	4	yes	—
425	C₂×C₄×C₃₁	C₂³×C₄	1	4	yes	—
426	C₂×C₄×C₃₁	C₂³×C₄	1	4	yes	—
427	C₂×C₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
428	C₂×C₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
429	C₂×#537	C₂×C₃₁	1	1	yes	characteristic
430	#2378	C₂×C₃₁	1	2	yes	complemented
431	#2377	C₂×C₃₁	1	2	yes	complemented
432	#2368	C₂×C₃₁	1	2	yes	complemented
433	#2364	C₂×C₃₁	1	2	yes	complemented
434	#2364	C₂×C₃₁	1	2	yes	complemented
435	#2361	C₂×C₃₁	1	2	yes	complemented
436	#2339	C₂×C₃₁	1	2	yes	complemented
437	#2339	C₂×C₃₁	1	2	yes	complemented
438	#2333	C₂×C₃₁	1	2	yes	complemented
439	#2332	C₂×C₃₁	1	2	yes	complemented
440	#2329	C₂×C₃₁	1	2	yes	complemented
441	#2325	C₂×C₃₁	1	2	yes	complemented
442	#2325	C₂×C₃₁	1	1	yes	characteristic, complemented
443	#2325	C₂×C₃₁	1	1	yes	characteristic, complemented
444	#2313	C₂×C₃₁	1	1	yes	characteristic, complemented
445	C₄×#121	C₂×C₃₁	1	1	yes	characteristic, complemented
446	C₄×#121	C₂×C₃₁	1	1	yes	characteristic, complemented
447	C₂×#387	C₂×C₃₁	1	1	yes	characteristic, complemented
448	C₂²×C₃₁	—	2	2	no	—
449	C₂²×C₃₁	—	2	2	no	—
450	C₂²×C₃₁	—	2	2	no	—
451	C₂²×C₃₁	—	2	2	no	—
452	C₂²×C₃₁	—	2	2	no	—
453	C₂²×C₃₁	—	2	2	no	—
454	C₂²×C₃₁	—	2	4	no	—
455	C₂²×C₃₁	—	2	4	no	—
456	C₂²×C₃₁	—	2	4	no	—
457	C₂²×C₃₁	—	2	4	no	—
458	C₂²×C₃₁	—	2	4	no	—
459	C₂²×C₃₁	—	2	4	no	—
460	C₂²×C₃₁	—	4	2	no	—
461	C₂²×C₃₁	—	4	2	no	—
462	C₂²×C₃₁	—	4	2	no	—
463	C₂²×C₃₁	—	4	2	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	#518	1	4	yes	—
469	C₂²×C₃₁	C₂⁴×C₄	1	1	yes	characteristic
470	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
471	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
472	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
473	C₂²×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
474	C₂²×C₃₁	#585	1	1	yes	characteristic
475	C₂²×C₃₁	#585	1	1	yes	characteristic
476	C₄×C₃₁	—	2	4	no	—
477	C₄×C₃₁	—	2	4	no	—
478	C₄×C₃₁	—	2	4	no	—
479	C₄×C₃₁	—	2	2	no	—
480	C₄×C₃₁	—	2	2	no	—
481	C₄×C₃₁	—	2	4	no	—
482	C₄×C₃₁	—	2	2	no	—
483	C₄×C₃₁	—	2	2	no	—
484	C₄×C₃₁	—	4	1	no	—
485	C₄×C₃₁	—	4	2	no	—
486	C₄×C₃₁	—	4	2	no	—
487	C₄×C₃₁	—	4	1	no	—
488	C₄×C₃₁	—	4	2	no	—
489	C₄×C₃₁	—	4	2	no	—
490	C₄×C₃₁	—	4	2	no	—
491	C₄×C₃₁	—	4	2	no	—
492	C₂²×#41	C₂²×C₃₁	1	2	yes	—
493	#537	C₄×C₃₁	1	16	yes	complemented
494	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	—
495	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	—
496	C₂×#121	C₂²×C₃₁	1	2	yes	—
497	C₂×#121	C₂²×C₃₁	1	1	yes	characteristic
498	C₂×#121	C₂²×C₃₁	1	1	yes	characteristic
499	C₂×#121	C₂²×C₃₁	1	2	yes	—
500	C₂×#121	C₂²×C₃₁	1	2	yes	—
501	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
502	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
503	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
504	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
505	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
506	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
507	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
508	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
509	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
510	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
511	#391	C₂²×C₃₁	1	2	yes	—
512	#391	C₂²×C₃₁	1	2	yes	—
513	#391	C₂²×C₃₁	1	2	yes	—
514	#391	C₂²×C₃₁	1	2	yes	—
515	#390	C₂²×C₃₁	1	1	yes	characteristic
516	#390	C₂²×C₃₁	1	2	yes	—
517	#390	C₂²×C₃₁	1	1	yes	characteristic
518	#389	C₂²×C₃₁	1	1	yes	characteristic
519	#389	C₂²×C₃₁	1	2	yes	—
520	#389	C₂²×C₃₁	1	1	yes	characteristic
521	#388	C₂²×C₃₁	1	2	yes	—
522	#388	C₂²×C₃₁	1	2	yes	—
523	#388	C₂²×C₃₁	1	2	yes	—
524	#388	C₂²×C₃₁	1	2	yes	—
525	#388	C₂²×C₃₁	1	2	yes	—
526	#388	C₂²×C₃₁	1	2	yes	—
527	#388	C₂²×C₃₁	1	2	yes	—
528	#388	C₂²×C₃₁	1	2	yes	—
529	#387	C₂²×C₃₁	1	2	yes	—
530	#387	C₂²×C₃₁	1	2	yes	—
531	#387	C₂²×C₃₁	1	2	yes	—
532	#387	C₂²×C₃₁	1	2	yes	—
533	#387	C₂²×C₃₁	1	2	yes	—
534	#387	C₂²×C₃₁	1	2	yes	—
535	#387	C₂²×C₃₁	1	2	yes	—
536	#387	C₂²×C₃₁	1	2	yes	—
537	#387	C₂²×C₃₁	1	2	yes	—
538	#387	C₂²×C₃₁	1	2	yes	—
539	#387	C₂²×C₃₁	1	2	yes	—
540	#387	C₂²×C₃₁	1	2	yes	—
541	#386	C₂²×C₃₁	1	2	yes	—
542	#386	C₂²×C₃₁	1	2	yes	—
543	#386	C₂²×C₃₁	1	2	yes	—
544	#386	C₂²×C₃₁	1	2	yes	—
545	#386	C₂²×C₃₁	1	2	yes	—
546	#386	C₂²×C₃₁	1	2	yes	—
547	#386	C₂²×C₃₁	1	2	yes	—
548	#386	C₂²×C₃₁	1	2	yes	—
549	#386	C₂²×C₃₁	1	2	yes	—
550	#386	C₂²×C₃₁	1	2	yes	—
551	#386	C₂²×C₃₁	1	2	yes	—
552	#386	C₂²×C₃₁	1	2	yes	—
553	#385	C₂²×C₃₁	1	2	yes	—
554	#385	C₂²×C₃₁	1	2	yes	—
555	#385	C₂²×C₃₁	1	2	yes	—
556	#385	C₂²×C₃₁	1	2	yes	—
557	#381	C₂²×C₃₁	1	2	yes	—
558	#381	C₂²×C₃₁	1	2	yes	—
559	#381	C₂²×C₃₁	1	2	yes	—
560	#380	C₂²×C₃₁	1	1	yes	characteristic
561	#380	C₂²×C₃₁	1	1	yes	characteristic
562	#380	C₂²×C₃₁	1	2	yes	—
563	#380	C₂²×C₃₁	1	2	yes	—
564	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
565	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
566	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
567	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
568	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
569	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
570	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
571	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
572	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
573	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
574	C₂×#95	C₂²×C₃₁	1	1	yes	characteristic
575	C₂×#95	C₂²×C₃₁	1	2	yes	—
576	C₂×#95	C₂²×C₃₁	1	2	yes	—
577	C₂×#95	C₂²×C₃₁	1	1	yes	characteristic
578	C₂×#95	C₂²×C₃₁	1	1	yes	characteristic
579	C₂×#95	C₂²×C₃₁	1	1	yes	characteristic
580	C₂×C₃₁	—	2	4	no	—
581	C₂×C₃₁	—	4	4	no	—
582	C₂×C₃₁	—	4	4	no	—
583	C₂×C₃₁	C₂×#518	1	1	yes	characteristic
584	C₂×C₃₁	C₄×H(5,𝔽₂)	1	1	yes	characteristic
585	C₂×C₃₁	C₄×2₋¹⁺⁴	1	1	yes	characteristic
586	C₂×C₃₁	#3534	1	1	yes	characteristic
587	C₂×C₃₁	#3536	1	1	yes	characteristic
588	C₂×C₃₁	#3559	1	1	yes	characteristic
589	C₂×C₃₁	#3560	1	1	yes	characteristic
590	C₂×#41	—	4	4	no	—
591	C₂×#41	—	4	4	no	—
592	C₂×#41	C₂×C₄×C₃₁	1	16	yes	complemented
593	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
594	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
595	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
596	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
597	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
598	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
599	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
600	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
601	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
602	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
603	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
604	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
605	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
606	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
607	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
608	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
609	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
610	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
611	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
612	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
613	C₂²⋊Q₈	C₂×C₄×C₃₁	1	16	yes	complemented
614	C₂²⋊Q₈	C₂×C₄×C₃₁	1	16	yes	complemented
615	#121	C₂×C₄×C₃₁	1	16	yes	complemented
616	#121	C₂×C₄×C₃₁	1	16	yes	complemented
617	#121	C₂×C₄×C₃₁	1	8	yes	complemented
618	#121	C₂×C₄×C₃₁	1	8	yes	complemented
619	#121	C₂×C₄×C₃₁	1	16	yes	complemented
620	C₄×D₄	—	4	2	no	—
621	C₄×D₄	—	4	2	no	—
622	C₄×D₄	—	4	4	no	—
623	C₄×D₄	—	4	4	no	—
624	C₄×D₄	—	4	4	no	—
625	C₄×D₄	—	4	4	no	—
626	C₄×D₄	—	4	4	no	—
627	C₂×C₄⋊C₄	—	4	2	no	—
628	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	8	yes	complemented
629	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
630	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
631	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
632	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
633	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
634	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
635	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
636	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
637	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
638	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
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	1	yes	characteristic
643	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
644	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
645	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
646	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
647	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
648	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
649	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
650	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
651	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
652	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
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×C₄²	—	4	2	no	—
663	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
664	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
665	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
666	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
667	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
668	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
669	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
670	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
671	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
672	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
673	#95	C₂³×C₃₁	1	2	yes	—
674	#95	C₂³×C₃₁	1	2	yes	—
675	#95	C₂³×C₃₁	1	2	yes	—
676	#95	C₂³×C₃₁	1	2	yes	—
677	#95	C₂³×C₃₁	1	2	yes	—
678	#95	C₂³×C₃₁	1	2	yes	—
679	#95	C₂³×C₃₁	1	2	yes	—
680	#95	C₂³×C₃₁	1	2	yes	—
681	#95	C₂³×C₃₁	1	2	yes	—
682	#95	C₂³×C₃₁	1	2	yes	—
683	#95	C₂³×C₃₁	1	2	yes	—
684	#95	C₂³×C₃₁	1	2	yes	—
685	#95	C₂³×C₃₁	1	2	yes	—
686	#95	C₂³×C₃₁	1	2	yes	—
687	#95	C₂³×C₃₁	1	2	yes	—
688	#95	C₂³×C₃₁	1	2	yes	—
689	#95	C₂³×C₃₁	1	2	yes	—
690	#95	C₂³×C₃₁	1	2	yes	—
691	#95	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	C₃₁	#34436	1	1	yes	characteristic, direct product factor, Sylow
698	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
699	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
700	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
701	#41	—	4	32	no	—
702	C₂×Q₈	—	4	2	no	—
703	C₂×Q₈	—	4	2	no	—
704	C₂×Q₈	C₂²×C₄×C₃₁	1	8	yes	—
705	C₂×D₄	—	2	4	no	—
706	C₂×D₄	—	2	4	no	—
707	C₂×D₄	—	2	4	no	—
708	C₂×D₄	—	2	4	no	—
709	C₂×D₄	—	4	1	no	—
710	C₂×D₄	—	4	1	no	—
711	C₂×D₄	—	4	2	no	—
712	C₂×D₄	—	4	2	no	—
713	C₂×D₄	—	4	1	no	—
714	C₂×D₄	—	4	1	no	—
715	C₂×D₄	—	4	2	no	—
716	C₂×D₄	—	4	2	no	—
717	C₂×D₄	C₂²×C₄×C₃₁	1	8	yes	—
718	C₂×D₄	C₂²×C₄×C₃₁	1	8	yes	—
719	C₂×D₄	C₂²×C₄×C₃₁	1	4	yes	—
720	C₂×D₄	C₂²×C₄×C₃₁	1	8	yes	—
721	C₂×D₄	C₂²×C₄×C₃₁	1	4	yes	—
722	C₂×D₄	C₂²×C₄×C₃₁	1	8	yes	—
723	C₂²×C₄	—	2	2	no	—
724	C₂²×C₄	—	2	2	no	—
725	C₂²×C₄	—	2	2	no	—
726	C₂²×C₄	—	2	2	no	—
727	C₂²×C₄	—	2	2	no	—
728	C₂²×C₄	—	2	2	no	—
729	C₂²×C₄	—	2	2	no	—
730	C₂²×C₄	—	2	2	no	—
731	C₂²×C₄	—	2	4	no	—
732	C₂²×C₄	—	2	4	no	—
733	C₂²×C₄	—	4	1	no	—
734	C₂²×C₄	—	4	1	no	—
735	C₂²×C₄	—	4	1	no	—
736	C₂²×C₄	—	4	1	no	—
737	C₂²×C₄	—	4	1	no	—
738	C₂²×C₄	—	4	1	no	—
739	C₂²×C₄	—	4	2	no	—
740	C₂²×C₄	—	4	2	no	—
741	C₂²×C₄	—	4	2	no	—
742	C₂²×C₄	—	4	2	no	—
743	C₂²×C₄	—	4	1	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	1	no	—
754	C₂²×C₄	—	4	1	no	—
755	C₂²×C₄	—	4	1	no	—
756	C₂²×C₄	—	4	2	no	—
757	C₂²×C₄	C₂²×C₄×C₃₁	1	4	yes	—
758	C₂²×C₄	C₂²×C₄×C₃₁	1	4	yes	—
759	C₂²×C₄	C₂²×C₄×C₃₁	1	4	yes	—
760	C₂²×C₄	C₂²×C₄×C₃₁	1	8	yes	—
761	C₂²×C₄	C₂²×C₄×C₃₁	1	8	yes	—
762	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
763	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
764	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
765	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
766	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
767	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
768	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
769	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
770	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
771	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
772	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
773	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
774	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
775	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
776	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
777	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
778	C₄⋊C₄	—	2	4	no	—
779	C₄⋊C₄	—	4	2	no	—
780	C₄⋊C₄	—	4	1	no	—
781	C₄⋊C₄	—	4	1	no	—
782	C₄⋊C₄	—	4	1	no	—
783	C₄⋊C₄	—	4	1	no	—
784	C₄⋊C₄	—	4	2	no	—
785	C₄⋊C₄	—	4	2	no	—
786	C₄⋊C₄	—	4	2	no	—
787	C₄⋊C₄	—	4	2	no	—
788	C₄⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
789	C₄⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
790	C₄⋊C₄	C₂²×C₄×C₃₁	1	4	yes	—
791	C₄⋊C₄	C₂²×C₄×C₃₁	1	4	yes	—
792	C₄⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
793	C₂²⋊C₄	—	2	4	no	—
794	C₂²⋊C₄	—	2	4	no	—
795	C₂²⋊C₄	—	2	4	no	—
796	C₂²⋊C₄	—	2	4	no	—
797	C₂²⋊C₄	—	4	2	no	—
798	C₂²⋊C₄	—	4	2	no	—
799	C₂²⋊C₄	—	4	2	no	—
800	C₂²⋊C₄	—	4	2	no	—
801	C₂²⋊C₄	—	4	2	no	—
802	C₂²⋊C₄	—	4	2	no	—
803	C₂²⋊C₄	—	4	2	no	—
804	C₂²⋊C₄	—	4	2	no	—
805	C₂²⋊C₄	—	4	2	no	—
806	C₂²⋊C₄	—	4	2	no	—
807	C₂²⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
808	C₂²⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
809	C₂²⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
810	C₂²⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
811	C₄²	—	2	2	no	—
812	C₄²	—	2	2	no	—
813	C₄²	—	4	1	no	—
814	C₄²	—	4	1	no	—
815	C₄²	—	4	2	no	—
816	C₄²	—	4	2	no	—
817	C₄²	—	4	2	no	—
818	C₄²	—	4	2	no	—
819	C₄²	—	4	2	no	—
820	C₄²	—	4	2	no	—
821	C₂³	—	2	1	no	—
822	C₂³	—	2	1	no	—
823	C₂³	—	2	1	no	—
824	C₂³	—	2	1	no	—
825	C₂³	—	2	2	no	—
826	C₂³	—	2	2	no	—
827	C₂³	—	2	2	no	—
828	C₂³	—	2	2	no	—
829	C₂³	—	2	2	no	—
830	C₂³	—	2	2	no	—
831	C₂³	—	2	2	no	—
832	C₂³	—	2	2	no	—
833	C₂³	—	2	2	no	—
834	C₂³	—	2	2	no	—
835	C₂³	—	2	2	no	—
836	C₂³	—	2	2	no	—
837	C₂³	C₂³×C₄×C₃₁	1	4	yes	—
838	C₂³	C₂³×C₄×C₃₁	1	4	yes	—
839	C₂³	C₂³×C₄×C₃₁	1	2	yes	—
840	C₂³	C₃₁×H(5,𝔽₂)	1	2	yes	—
841	C₂³	C₃₁×H(5,𝔽₂)	1	2	yes	—
842	C₂³	C₂⁵×C₃₁	1	1	yes	characteristic
843	Q₈	—	4	8	no	—
844	D₄	—	2	16	no	—
845	D₄	—	2	16	no	—
846	D₄	—	4	4	no	—
847	D₄	—	4	4	no	—
848	D₄	—	4	8	no	—
849	D₄	—	4	8	no	—
850	C₂×C₄	—	2	8	no	—
851	C₂×C₄	—	2	1	no	—
852	C₂×C₄	—	2	1	no	—
853	C₂×C₄	—	2	1	no	—
854	C₂×C₄	—	2	1	no	—
855	C₂×C₄	—	2	1	no	—
856	C₂×C₄	—	2	2	no	—
857	C₂×C₄	—	2	2	no	—
858	C₂×C₄	—	2	2	no	—
859	C₂×C₄	—	2	2	no	—
860	C₂×C₄	—	2	2	no	—
861	C₂×C₄	—	2	2	no	—
862	C₂×C₄	—	2	2	no	—
863	C₂×C₄	—	2	2	no	—
864	C₂×C₄	—	2	1	no	—
865	C₂×C₄	—	2	1	no	—
866	C₂×C₄	—	2	1	no	—
867	C₂×C₄	—	2	1	no	—
868	C₂×C₄	—	2	2	no	—
869	C₂×C₄	—	2	1	no	—
870	C₂×C₄	—	2	2	no	—
871	C₂×C₄	—	2	2	no	—
872	C₂×C₄	—	2	2	no	—
873	C₂×C₄	—	2	2	no	—
874	C₂×C₄	—	2	2	no	—
875	C₂×C₄	—	2	2	no	—
876	C₂×C₄	—	2	2	no	—
877	C₂×C₄	—	2	1	no	—
878	C₂×C₄	—	2	1	no	—
879	C₂×C₄	—	2	2	no	—
880	C₂×C₄	—	2	2	no	—
881	C₂×C₄	—	2	1	no	—
882	C₂×C₄	—	2	2	no	—
883	C₂×C₄	—	2	2	no	—
884	C₂×C₄	—	2	2	no	—
885	C₂×C₄	—	2	1	no	—
886	C₂×C₄	—	2	2	no	—
887	C₂×C₄	—	2	2	no	—
888	C₂×C₄	—	2	2	no	—
889	C₂×C₄	—	2	2	no	—
890	C₂×C₄	—	2	2	no	—
891	C₂×C₄	—	4	4	no	—
892	C₂×C₄	—	4	4	no	—
893	C₂×C₄	—	4	8	no	—
894	C₂×C₄	—	4	8	no	—
895	C₂×C₄	—	4	4	no	—
896	C₂×C₄	—	4	4	no	—
897	C₂×C₄	—	8	4	no	—
898	C₂×C₄	—	8	4	no	—
899	C₂×C₄	—	8	2	no	—
900	C₂×C₄	—	8	2	no	—
901	C₂×C₄	—	8	4	no	—
902	C₂×C₄	—	8	4	no	—
903	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
904	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
905	C₂×C₄	C₂³×C₄×C₃₁	1	4	yes	—
906	C₂×C₄	C₂³×C₄×C₃₁	1	4	yes	—
907	C₂×C₄	C₂³×C₄×C₃₁	1	4	yes	—
908	C₂×C₄	C₂³×C₄×C₃₁	1	4	yes	—
909	C₂×C₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
910	C₂×C₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
911	C₂²	—	2	2	no	—
912	C₂²	—	2	2	no	—
913	C₂²	—	2	2	no	—
914	C₂²	—	2	2	no	—
915	C₂²	—	2	2	no	—
916	C₂²	—	2	2	no	—
917	C₂²	—	2	4	no	—
918	C₂²	—	2	4	no	—
919	C₂²	—	2	4	no	—
920	C₂²	—	2	4	no	—
921	C₂²	—	2	4	no	—
922	C₂²	—	2	4	no	—
923	C₂²	—	4	2	no	—
924	C₂²	—	4	2	no	—
925	C₂²	—	4	2	no	—
926	C₂²	—	4	2	no	—
927	C₂²	—	4	2	no	—
928	C₂²	—	4	2	no	—
929	C₂²	—	4	2	no	—
930	C₂²	—	4	2	no	—
931	C₂²	C₃₁×#518	1	4	yes	—
932	C₂²	C₂⁴×C₄×C₃₁	1	1	yes	characteristic
933	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
934	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
935	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
936	C₂²	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
937	C₂²	C₃₁×#585	1	1	yes	characteristic
938	C₂²	C₃₁×#585	1	1	yes	characteristic
939	C₄	—	2	4	no	—
940	C₄	—	2	4	no	—
941	C₄	—	2	4	no	—
942	C₄	—	2	2	no	—
943	C₄	—	2	2	no	—
944	C₄	—	2	4	no	—
945	C₄	—	2	2	no	—
946	C₄	—	2	2	no	—
947	C₄	—	4	1	no	—
948	C₄	—	4	2	no	—
949	C₄	—	4	2	no	—
950	C₄	—	4	1	no	—
951	C₄	—	4	2	no	—
952	C₄	—	4	2	no	—
953	C₄	—	4	2	no	—
954	C₄	—	4	2	no	—
955	C₂	—	2	4	no	—
956	C₂	—	4	4	no	—
957	C₂	—	4	4	no	—
958	C₂	C₂×C₃₁×#518	1	1	yes	characteristic
959	C₂	C₄×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
960	C₂	C₄×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
961	C₂	C₃₁×#3534	1	1	yes	characteristic
962	C₂	C₃₁×#3536	1	1	yes	characteristic
963	C₂	C₃₁×#3559	1	1	yes	characteristic
964	C₂	C₃₁×#3560	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃₁	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₃₁
Frattini, cosocle	C₂³	C₂⁵×C₃₁
prime radical	C₂×C₃₁×#537	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₃₁ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₃₁×#2378	C₂	semidirect
3. C₃₁×#2377	C₂	semidirect
4. C₃₁×#2368	C₂	semidirect
5. C₃₁×#2364	C₂	semidirect
6. C₃₁×#2364	C₂	semidirect
7. C₃₁×#2361	C₂	semidirect
8. C₃₁×#2339	C₂	semidirect
9. C₃₁×#2339	C₂	semidirect
10. C₃₁×#2333	C₂	semidirect
11. C₃₁×#2332	C₂	semidirect
12. C₃₁×#2329	C₂	semidirect
13. C₃₁×#2325	C₂	semidirect
14. C₃₁×#2325	C₂	semidirect
15. C₃₁×#2325	C₂	semidirect
16. C₃₁×#2313	C₂	semidirect
17. C₄×C₃₁×#121	C₂	semidirect
18. C₄×C₃₁×#121	C₂	semidirect
19. C₂×C₃₁×#387	C₂	semidirect
21. C₃₁×#537	C₄	semidirect
110. C₂×#41×C₃₁	C₂×C₄	semidirect
131. C₃₁×C₂²⋊Q₈	C₂×C₄	semidirect
132. C₃₁×C₂²⋊Q₈	C₂×C₄	semidirect
133. C₃₁×#121	C₂×C₄	semidirect
134. C₃₁×#121	C₂×C₄	semidirect
135. C₃₁×#121	C₂×C₄	semidirect
136. C₃₁×#121	C₂×C₄	semidirect
137. C₃₁×#121	C₂×C₄	semidirect
146. C₂×C₄⋊C₄×C₃₁	C₂×C₄	semidirect
338. #34436	C₃₁	direct (N × H)
430. #2378	C₂×C₃₁	semidirect
431. #2377	C₂×C₃₁	semidirect
432. #2368	C₂×C₃₁	semidirect
433. #2364	C₂×C₃₁	semidirect
434. #2364	C₂×C₃₁	semidirect
435. #2361	C₂×C₃₁	semidirect
436. #2339	C₂×C₃₁	semidirect
437. #2339	C₂×C₃₁	semidirect
438. #2333	C₂×C₃₁	semidirect
439. #2332	C₂×C₃₁	semidirect
440. #2329	C₂×C₃₁	semidirect
441. #2325	C₂×C₃₁	semidirect
442. #2325	C₂×C₃₁	semidirect
443. #2325	C₂×C₃₁	semidirect
444. #2313	C₂×C₃₁	semidirect
445. C₄×#121	C₂×C₃₁	semidirect
446. C₄×#121	C₂×C₃₁	semidirect
447. C₂×#387	C₂×C₃₁	semidirect
493. #537	C₄×C₃₁	semidirect
592. C₂×#41	C₂×C₄×C₃₁	semidirect
613. C₂²⋊Q₈	C₂×C₄×C₃₁	semidirect
614. C₂²⋊Q₈	C₂×C₄×C₃₁	semidirect
615. #121	C₂×C₄×C₃₁	semidirect
616. #121	C₂×C₄×C₃₁	semidirect
617. #121	C₂×C₄×C₃₁	semidirect
618. #121	C₂×C₄×C₃₁	semidirect
619. #121	C₂×C₄×C₃₁	semidirect
628. C₂×C₄⋊C₄	C₂×C₄×C₃₁	semidirect
697. C₃₁	#34436	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃₁×#537	2
C₃₁×#2378	2
C₃₁×#2377	2
C₃₁×#2368	2
C₃₁×#2364	2
C₃₁×#2361	2
C₃₁×#2339	2
C₃₁×#2333	2
C₃₁×#2332	2
C₃₁×#2329	2
C₃₁×#2325	2
C₃₁×#2313	2
C₄×C₃₁×#121	2
C₂×C₃₁×#387	2
#34436	31

Subgroups — C31×#34436 #21491195

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#34436 #21491195