Subgroups — C₃₁×#35117 #21491876

Order 7936.

1664 conjugacy classes of subgroups.

The subgroup lattice has 926 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#2863	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#2862	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#2861	C₂	1	1	yes	maximal, characteristic
4	C₃₁×#2860	C₂	1	1	yes	maximal, characteristic
5	C₃₁×#2650	C₂	1	2	yes	maximal, complemented
6	C₃₁×#2637	C₂	1	2	yes	maximal, complemented
7	C₃₁×#2592	C₂	1	1	yes	maximal, characteristic
8	C₃₁×#2581	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#2550	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#2545	C₂	1	1	yes	maximal, characteristic
11	C₃₁×#2532	C₂	1	2	yes	maximal, complemented
12	C₃₁×#2529	C₂	1	2	yes	maximal, complemented
13	C₃₁×#2515	C₂	1	2	yes	maximal, complemented
14	C₃₁×#2465	C₂	1	2	yes	maximal, complemented
15	C₃₁×#2453	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#2452	C₂	1	1	yes	maximal, characteristic
17	C₃₁×#2447	C₂	1	1	yes	maximal, characteristic
18	C₃₁×#2446	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#2334	C₂	1	2	yes	maximal, complemented
20	C₃₁×#2332	C₂	1	2	yes	maximal, complemented
21	C₄×C₃₁×#124	C₂	1	1	yes	maximal, characteristic
22	C₃₁×#2295	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄²×Q₈×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
25	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
26	C₂×C₃₁×#126	C₂²	1	2	yes	—
27	C₂×C₃₁×#125	C₂²	1	1	yes	characteristic
28	C₂×C₃₁×#124	C₂²	1	1	yes	characteristic
29	C₂×C₃₁×#124	C₂²	1	1	yes	characteristic
30	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	—
31	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
32	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
33	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
34	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
35	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
36	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
37	C₃₁×#400	C₂²	1	2	yes	—
38	C₃₁×#400	C₂²	1	2	yes	—
39	C₃₁×#400	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×#397	C₂²	1	2	yes	—
44	C₃₁×#397	C₂²	1	2	yes	—
45	C₃₁×#397	C₂²	1	2	yes	—
46	C₃₁×#396	C₂²	1	2	yes	—
47	C₃₁×#396	C₂²	1	2	yes	—
48	C₃₁×#396	C₂²	1	2	yes	—
49	C₃₁×#395	C₂²	1	2	yes	—
50	C₃₁×#395	C₂²	1	2	yes	—
51	C₃₁×#393	C₂²	1	2	yes	—
52	C₃₁×#393	C₂²	1	2	yes	—
53	C₃₁×#391	C₂²	1	1	yes	characteristic
54	C₃₁×#391	C₂²	1	1	yes	characteristic
55	C₃₁×#391	C₂²	1	2	yes	—
56	C₃₁×#391	C₂²	1	2	yes	—
57	C₃₁×#391	C₂²	1	1	yes	characteristic
58	C₃₁×#391	C₂²	1	1	yes	characteristic
59	C₃₁×#391	C₂²	1	1	yes	characteristic
60	C₃₁×#391	C₂²	1	1	yes	characteristic
61	C₃₁×#391	C₂²	1	2	yes	—
62	C₃₁×#391	C₂²	1	1	yes	characteristic
63	C₃₁×#391	C₂²	1	1	yes	characteristic
64	C₃₁×#390	C₂²	1	1	yes	characteristic
65	C₃₁×#390	C₂²	1	1	yes	characteristic
66	C₃₁×#390	C₂²	1	1	yes	characteristic
67	C₃₁×#390	C₂²	1	1	yes	characteristic
68	C₃₁×#389	C₂²	1	1	yes	characteristic
69	C₃₁×#389	C₂²	1	1	yes	characteristic
70	C₃₁×#389	C₂²	1	2	yes	—
71	C₃₁×#389	C₂²	1	2	yes	—
72	C₃₁×#389	C₂²	1	1	yes	characteristic
73	C₃₁×#389	C₂²	1	1	yes	characteristic
74	C₃₁×#389	C₂²	1	1	yes	characteristic
75	C₃₁×#389	C₂²	1	1	yes	characteristic
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	—
80	C₃₁×#388	C₂²	1	2	yes	—
81	C₃₁×#388	C₂²	1	2	yes	—
82	C₃₁×#388	C₂²	1	2	yes	—
83	C₃₁×#388	C₂²	1	2	yes	—
84	C₃₁×#388	C₂²	1	2	yes	—
85	C₃₁×#388	C₂²	1	2	yes	—
86	C₃₁×#388	C₂²	1	2	yes	—
87	C₃₁×#388	C₂²	1	2	yes	—
88	C₃₁×#388	C₂²	1	2	yes	—
89	C₃₁×#387	C₂²	1	2	yes	—
90	C₃₁×#387	C₂²	1	2	yes	—
91	C₃₁×#387	C₂²	1	2	yes	—
92	C₃₁×#387	C₂²	1	2	yes	—
93	C₃₁×#387	C₂²	1	2	yes	—
94	C₃₁×#387	C₂²	1	2	yes	—
95	C₃₁×#387	C₂²	1	2	yes	—
96	C₃₁×#387	C₂²	1	2	yes	—
97	C₃₁×#387	C₂²	1	2	yes	—
98	C₃₁×#387	C₂²	1	2	yes	—
99	C₃₁×#385	C₂²	1	2	yes	—
100	C₃₁×#385	C₂²	1	2	yes	—
101	C₃₁×#383	C₂²	1	2	yes	—
102	C₃₁×#382	C₂²	1	1	yes	characteristic
103	C₃₁×#382	C₂²	1	2	yes	—
104	C₃₁×#382	C₂²	1	2	yes	—
105	C₃₁×#381	C₂²	1	2	yes	—
106	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
107	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
108	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
109	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
110	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
111	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
112	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
113	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
114	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
115	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
116	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
117	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
118	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
119	C₃₁×#376	C₂²	1	2	yes	—
120	C₄³×C₃₁	C₂²	1	1	yes	characteristic
121	C₄³×C₃₁	C₂²	1	1	yes	characteristic
122	C₄³×C₃₁	C₂²	1	1	yes	characteristic
123	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
124	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
125	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
126	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
127	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
128	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
129	C₃₁×C₄⋊Q₈	—	4	2	no	—
130	C₃₁×C₄⋊Q₈	—	4	2	no	—
131	C₃₁×#126	—	2	8	no	—
132	C₃₁×#125	—	4	2	no	—
133	C₃₁×#124	—	2	4	no	—
134	C₃₁×#124	—	4	2	no	—
135	C₃₁×C₂²⋊Q₈	—	2	8	no	—
136	C₄×Q₈×C₃₁	—	2	4	no	—
137	C₄×Q₈×C₃₁	—	2	4	no	—
138	C₄×Q₈×C₃₁	—	2	4	no	—
139	C₄×Q₈×C₃₁	—	2	4	no	—
140	C₄×Q₈×C₃₁	—	4	2	no	—
141	C₄×D₄×C₃₁	—	4	2	no	—
142	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
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	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	2	yes	—
151	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
152	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
153	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
157	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
158	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
159	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
160	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
161	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
162	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
163	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
164	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
165	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
166	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
167	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
168	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
169	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
170	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
171	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
172	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
173	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
174	C₂×C₂²⋊C₄×C₃₁	C₂³	1	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×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	1	yes	characteristic
186	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
187	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
195	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
196	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
197	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
198	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
199	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
200	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
201	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
202	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
203	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
214	C₃₁×#95	C₂³	1	2	yes	—
215	C₃₁×#95	C₂³	1	2	yes	—
216	C₃₁×#95	C₂³	1	2	yes	—
217	C₃₁×#95	C₂³	1	2	yes	—
218	C₃₁×#95	C₂³	1	2	yes	—
219	C₃₁×#95	C₂³	1	2	yes	—
220	C₃₁×#95	C₂³	1	1	yes	characteristic
221	C₃₁×#95	C₂³	1	2	yes	—
222	C₃₁×#95	C₂³	1	2	yes	—
223	C₃₁×#95	C₂³	1	2	yes	—
224	C₃₁×#95	C₂³	1	2	yes	—
225	C₃₁×#95	C₂³	1	2	yes	—
226	C₃₁×#95	C₂³	1	2	yes	—
227	C₃₁×#95	C₂³	1	2	yes	—
228	C₃₁×#95	C₂³	1	2	yes	—
229	C₃₁×#95	C₂³	1	1	yes	characteristic
230	C₃₁×#95	C₂³	1	1	yes	characteristic
231	C₃₁×#95	C₂³	1	1	yes	characteristic
232	C₃₁×#95	C₂³	1	1	yes	characteristic
233	C₃₁×#95	C₂³	1	2	yes	—
234	C₃₁×#95	C₂³	1	2	yes	—
235	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
236	C₂×Q₈×C₃₁	—	2	2	no	—
237	C₂×Q₈×C₃₁	—	2	2	no	—
238	C₂×Q₈×C₃₁	—	2	2	no	—
239	C₂×Q₈×C₃₁	—	2	2	no	—
240	C₂×Q₈×C₃₁	—	2	2	no	—
241	C₂×Q₈×C₃₁	—	2	4	no	—
242	C₂×Q₈×C₃₁	—	2	2	no	—
243	C₂×Q₈×C₃₁	—	2	2	no	—
244	C₂×Q₈×C₃₁	—	2	2	no	—
245	C₂×Q₈×C₃₁	—	2	2	no	—
246	C₂×Q₈×C₃₁	—	4	2	no	—
247	C₂×Q₈×C₃₁	—	4	2	no	—
248	C₂×D₄×C₃₁	—	2	2	no	—
249	C₂×D₄×C₃₁	—	2	2	no	—
250	C₂×D₄×C₃₁	—	2	2	no	—
251	C₂²×C₄×C₃₁	—	2	4	no	—
252	C₂²×C₄×C₃₁	—	4	2	no	—
253	C₂²×C₄×C₃₁	—	4	2	no	—
254	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
255	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
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	1	yes	characteristic
261	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
262	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
263	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
264	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
265	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
266	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
267	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
268	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
269	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
270	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
271	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
272	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
273	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
274	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
275	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
276	C₄⋊C₄×C₃₁	—	2	2	no	—
277	C₄⋊C₄×C₃₁	—	2	2	no	—
278	C₄⋊C₄×C₃₁	—	2	2	no	—
279	C₄⋊C₄×C₃₁	—	2	2	no	—
280	C₄⋊C₄×C₃₁	—	2	2	no	—
281	C₄⋊C₄×C₃₁	—	2	2	no	—
282	C₄⋊C₄×C₃₁	—	2	2	no	—
283	C₄⋊C₄×C₃₁	—	2	2	no	—
284	C₄⋊C₄×C₃₁	—	2	2	no	—
285	C₄⋊C₄×C₃₁	—	2	4	no	—
286	C₄⋊C₄×C₃₁	—	2	4	no	—
287	C₄⋊C₄×C₃₁	—	2	4	no	—
288	C₄⋊C₄×C₃₁	—	2	4	no	—
289	C₄⋊C₄×C₃₁	—	2	4	no	—
290	C₄⋊C₄×C₃₁	—	2	4	no	—
291	C₄⋊C₄×C₃₁	—	2	2	no	—
292	C₄⋊C₄×C₃₁	—	2	2	no	—
293	C₄⋊C₄×C₃₁	—	2	2	no	—
294	C₄⋊C₄×C₃₁	—	2	2	no	—
295	C₄⋊C₄×C₃₁	—	4	2	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	#41	1	4	yes	—
303	C₂²⋊C₄×C₃₁	—	2	4	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	—	4	2	no	—
312	C₂²⋊C₄×C₃₁	—	4	2	no	—
313	C₂²⋊C₄×C₃₁	—	4	2	no	—
314	C₂²⋊C₄×C₃₁	—	4	2	no	—
315	C₂²⋊C₄×C₃₁	—	4	2	no	—
316	C₄²×C₃₁	—	2	2	no	—
317	C₄²×C₃₁	—	2	2	no	—
318	C₄²×C₃₁	—	2	2	no	—
319	C₄²×C₃₁	—	2	2	no	—
320	C₄²×C₃₁	—	2	2	no	—
321	C₄²×C₃₁	—	2	2	no	—
322	C₄²×C₃₁	—	2	2	no	—
323	C₄²×C₃₁	—	2	4	no	—
324	C₄²×C₃₁	—	2	2	no	—
325	C₄²×C₃₁	—	2	2	no	—
326	C₄²×C₃₁	—	2	2	no	—
327	C₄²×C₃₁	—	2	2	no	—
328	C₄²×C₃₁	—	2	2	no	—
329	C₄²×C₃₁	—	2	2	no	—
330	C₄²×C₃₁	—	2	2	no	—
331	C₄²×C₃₁	—	4	1	no	—
332	C₄²×C₃₁	—	4	1	no	—
333	C₄²×C₃₁	—	4	1	no	—
334	C₄²×C₃₁	—	4	2	no	—
335	C₄²×C₃₁	—	4	2	no	—
336	C₄²×C₃₁	#41	1	4	yes	—
337	C₄²×C₃₁	#41	1	4	yes	—
338	#35117	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
339	C₂³×C₃₁	—	2	2	no	—
340	C₂³×C₃₁	—	2	2	no	—
341	C₂³×C₃₁	—	2	2	no	—
342	C₂³×C₃₁	—	2	2	no	—
343	C₂³×C₃₁	—	2	2	no	—
344	C₂³×C₃₁	—	2	2	no	—
345	C₂³×C₃₁	—	2	2	no	—
346	C₂³×C₃₁	C₂⁵	1	1	yes	characteristic
347	Q₈×C₃₁	—	2	8	no	—
348	Q₈×C₃₁	—	4	4	no	—
349	Q₈×C₃₁	—	4	4	no	—
350	Q₈×C₃₁	—	8	4	no	—
351	D₄×C₃₁	—	4	4	no	—
352	C₂×C₄×C₃₁	—	2	1	no	—
353	C₂×C₄×C₃₁	—	2	1	no	—
354	C₂×C₄×C₃₁	—	2	1	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	1	no	—
362	C₂×C₄×C₃₁	—	2	1	no	—
363	C₂×C₄×C₃₁	—	2	1	no	—
364	C₂×C₄×C₃₁	—	2	1	no	—
365	C₂×C₄×C₃₁	—	2	1	no	—
366	C₂×C₄×C₃₁	—	2	1	no	—
367	C₂×C₄×C₃₁	—	2	1	no	—
368	C₂×C₄×C₃₁	—	2	1	no	—
369	C₂×C₄×C₃₁	—	2	1	no	—
370	C₂×C₄×C₃₁	—	2	2	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	1	no	—
375	C₂×C₄×C₃₁	—	2	1	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	2	no	—
383	C₂×C₄×C₃₁	—	2	2	no	—
384	C₂×C₄×C₃₁	—	2	1	no	—
385	C₂×C₄×C₃₁	—	2	1	no	—
386	C₂×C₄×C₃₁	—	2	1	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	1	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	2	no	—
397	C₂×C₄×C₃₁	—	2	2	no	—
398	C₂×C₄×C₃₁	—	2	2	no	—
399	C₂×C₄×C₃₁	—	2	2	no	—
400	C₂×C₄×C₃₁	—	2	1	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	1	no	—
405	C₂×C₄×C₃₁	—	2	2	no	—
406	C₂×C₄×C₃₁	—	8	4	no	—
407	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
408	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
409	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
410	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
411	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
412	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
413	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
414	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
415	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
416	C₂×C₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
417	C₂×C₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
418	C₂×C₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
419	#2863	C₂×C₃₁	1	1	yes	characteristic, complemented
420	#2862	C₂×C₃₁	1	1	yes	characteristic, complemented
421	#2861	C₂×C₃₁	1	1	yes	characteristic
422	#2860	C₂×C₃₁	1	1	yes	characteristic
423	#2650	C₂×C₃₁	1	2	yes	complemented
424	#2637	C₂×C₃₁	1	2	yes	complemented
425	#2592	C₂×C₃₁	1	1	yes	characteristic
426	#2581	C₂×C₃₁	1	1	yes	characteristic, complemented
427	#2550	C₂×C₃₁	1	1	yes	characteristic, complemented
428	#2545	C₂×C₃₁	1	1	yes	characteristic
429	#2532	C₂×C₃₁	1	2	yes	complemented
430	#2529	C₂×C₃₁	1	2	yes	complemented
431	#2515	C₂×C₃₁	1	2	yes	complemented
432	#2465	C₂×C₃₁	1	2	yes	complemented
433	#2453	C₂×C₃₁	1	1	yes	characteristic, complemented
434	#2452	C₂×C₃₁	1	1	yes	characteristic
435	#2447	C₂×C₃₁	1	1	yes	characteristic
436	#2446	C₂×C₃₁	1	1	yes	characteristic, complemented
437	#2334	C₂×C₃₁	1	2	yes	complemented
438	#2332	C₂×C₃₁	1	2	yes	complemented
439	C₄×#124	C₂×C₃₁	1	1	yes	characteristic
440	#2295	C₂×C₃₁	1	1	yes	characteristic, complemented
441	C₄²×Q₈	C₂×C₃₁	1	1	yes	characteristic, complemented
442	C₂²×C₃₁	—	4	2	no	—
443	C₂²×C₃₁	—	4	2	no	—
444	C₂²×C₃₁	—	4	2	no	—
445	C₂²×C₃₁	—	4	2	no	—
446	C₂²×C₃₁	—	4	2	no	—
447	C₂²×C₃₁	—	4	2	no	—
448	C₂²×C₃₁	—	4	2	no	—
449	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
450	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
451	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
452	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
453	C₂²×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
454	C₂²×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
455	C₂²×C₃₁	#585	1	1	yes	characteristic
456	C₄×C₃₁	—	2	2	no	—
457	C₄×C₃₁	—	2	2	no	—
458	C₄×C₃₁	—	2	2	no	—
459	C₄×C₃₁	—	2	2	no	—
460	C₄×C₃₁	—	2	2	no	—
461	C₄×C₃₁	—	2	2	no	—
462	C₄×C₃₁	—	2	2	no	—
463	C₄×C₃₁	—	2	2	no	—
464	C₄×C₃₁	—	2	2	no	—
465	C₄×C₃₁	—	4	2	no	—
466	C₄×C₃₁	—	4	2	no	—
467	C₄×C₃₁	—	4	2	no	—
468	C₄×C₃₁	—	4	1	no	—
469	C₄×C₃₁	—	4	1	no	—
470	C₄×C₃₁	—	4	2	no	—
471	C₄×C₃₁	—	4	1	no	—
472	C₄×C₃₁	—	4	1	no	—
473	C₄×C₃₁	—	4	2	no	—
474	C₄×C₃₁	—	4	1	no	—
475	C₄×C₃₁	—	4	2	no	—
476	C₄×C₃₁	—	4	2	no	—
477	C₄×C₃₁	#542	1	4	yes	—
478	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
479	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
480	C₂×#126	C₂²×C₃₁	1	2	yes	—
481	C₂×#125	C₂²×C₃₁	1	1	yes	characteristic
482	C₂×#124	C₂²×C₃₁	1	1	yes	characteristic
483	C₂×#124	C₂²×C₃₁	1	1	yes	characteristic
484	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	—
485	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
486	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
487	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
488	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
489	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
490	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
491	#400	C₂²×C₃₁	1	2	yes	—
492	#400	C₂²×C₃₁	1	2	yes	—
493	#400	C₂²×C₃₁	1	2	yes	—
494	#398	C₂²×C₃₁	1	2	yes	—
495	#398	C₂²×C₃₁	1	2	yes	—
496	#398	C₂²×C₃₁	1	2	yes	—
497	#397	C₂²×C₃₁	1	2	yes	—
498	#397	C₂²×C₃₁	1	2	yes	—
499	#397	C₂²×C₃₁	1	2	yes	—
500	#396	C₂²×C₃₁	1	2	yes	—
501	#396	C₂²×C₃₁	1	2	yes	—
502	#396	C₂²×C₃₁	1	2	yes	—
503	#395	C₂²×C₃₁	1	2	yes	—
504	#395	C₂²×C₃₁	1	2	yes	—
505	#393	C₂²×C₃₁	1	2	yes	—
506	#393	C₂²×C₃₁	1	2	yes	—
507	#391	C₂²×C₃₁	1	1	yes	characteristic
508	#391	C₂²×C₃₁	1	1	yes	characteristic
509	#391	C₂²×C₃₁	1	2	yes	—
510	#391	C₂²×C₃₁	1	2	yes	—
511	#391	C₂²×C₃₁	1	1	yes	characteristic
512	#391	C₂²×C₃₁	1	1	yes	characteristic
513	#391	C₂²×C₃₁	1	1	yes	characteristic
514	#391	C₂²×C₃₁	1	1	yes	characteristic
515	#391	C₂²×C₃₁	1	2	yes	—
516	#391	C₂²×C₃₁	1	1	yes	characteristic
517	#391	C₂²×C₃₁	1	1	yes	characteristic
518	#390	C₂²×C₃₁	1	1	yes	characteristic
519	#390	C₂²×C₃₁	1	1	yes	characteristic
520	#390	C₂²×C₃₁	1	1	yes	characteristic
521	#390	C₂²×C₃₁	1	1	yes	characteristic
522	#389	C₂²×C₃₁	1	1	yes	characteristic
523	#389	C₂²×C₃₁	1	1	yes	characteristic
524	#389	C₂²×C₃₁	1	2	yes	—
525	#389	C₂²×C₃₁	1	2	yes	—
526	#389	C₂²×C₃₁	1	1	yes	characteristic
527	#389	C₂²×C₃₁	1	1	yes	characteristic
528	#389	C₂²×C₃₁	1	1	yes	characteristic
529	#389	C₂²×C₃₁	1	1	yes	characteristic
530	#388	C₂²×C₃₁	1	2	yes	—
531	#388	C₂²×C₃₁	1	2	yes	—
532	#388	C₂²×C₃₁	1	2	yes	—
533	#388	C₂²×C₃₁	1	2	yes	—
534	#388	C₂²×C₃₁	1	2	yes	—
535	#388	C₂²×C₃₁	1	2	yes	—
536	#388	C₂²×C₃₁	1	2	yes	—
537	#388	C₂²×C₃₁	1	2	yes	—
538	#388	C₂²×C₃₁	1	2	yes	—
539	#388	C₂²×C₃₁	1	2	yes	—
540	#388	C₂²×C₃₁	1	2	yes	—
541	#388	C₂²×C₃₁	1	2	yes	—
542	#388	C₂²×C₃₁	1	2	yes	—
543	#387	C₂²×C₃₁	1	2	yes	—
544	#387	C₂²×C₃₁	1	2	yes	—
545	#387	C₂²×C₃₁	1	2	yes	—
546	#387	C₂²×C₃₁	1	2	yes	—
547	#387	C₂²×C₃₁	1	2	yes	—
548	#387	C₂²×C₃₁	1	2	yes	—
549	#387	C₂²×C₃₁	1	2	yes	—
550	#387	C₂²×C₃₁	1	2	yes	—
551	#387	C₂²×C₃₁	1	2	yes	—
552	#387	C₂²×C₃₁	1	2	yes	—
553	#385	C₂²×C₃₁	1	2	yes	—
554	#385	C₂²×C₃₁	1	2	yes	—
555	#383	C₂²×C₃₁	1	2	yes	—
556	#382	C₂²×C₃₁	1	1	yes	characteristic
557	#382	C₂²×C₃₁	1	2	yes	—
558	#382	C₂²×C₃₁	1	2	yes	—
559	#381	C₂²×C₃₁	1	2	yes	—
560	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
561	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
562	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
563	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
564	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
565	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
566	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
567	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
568	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
569	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
570	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
571	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
572	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
573	#376	C₂²×C₃₁	1	2	yes	—
574	C₄³	C₂²×C₃₁	1	1	yes	characteristic
575	C₄³	C₂²×C₃₁	1	1	yes	characteristic
576	C₄³	C₂²×C₃₁	1	1	yes	characteristic
577	C₂×C₃₁	—	8	2	no	—
578	C₂×C₃₁	#3444	1	1	yes	characteristic
579	C₂×C₃₁	C₂×#542	1	1	yes	characteristic
580	C₂×C₃₁	#3461	1	1	yes	characteristic
581	C₂×C₃₁	#3507	1	1	yes	characteristic
582	C₂×C₃₁	#3511	1	1	yes	characteristic
583	C₂×C₃₁	#3514	1	1	yes	characteristic
584	C₂×C₃₁	#3523	1	1	yes	characteristic
585	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
586	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
587	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
588	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
589	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
590	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
591	C₄⋊Q₈	—	4	2	no	—
592	C₄⋊Q₈	—	4	2	no	—
593	#126	—	2	8	no	—
594	#125	—	4	2	no	—
595	#124	—	2	4	no	—
596	#124	—	4	2	no	—
597	C₂²⋊Q₈	—	2	8	no	—
598	C₄×Q₈	—	2	4	no	—
599	C₄×Q₈	—	2	4	no	—
600	C₄×Q₈	—	2	4	no	—
601	C₄×Q₈	—	2	4	no	—
602	C₄×Q₈	—	4	2	no	—
603	C₄×D₄	—	4	2	no	—
604	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
605	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
606	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
607	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
608	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
609	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
610	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
611	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
612	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
613	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
614	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
615	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
616	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
617	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
618	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
619	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
620	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
621	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
622	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
623	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
624	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
625	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
626	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
627	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
628	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
629	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
630	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
631	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
632	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
633	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
634	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
635	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
636	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
637	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
638	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
639	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
640	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
641	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
642	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
643	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
644	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
645	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
646	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
647	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
648	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
649	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
650	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
651	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
652	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
653	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
654	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
655	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
656	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
657	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
658	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
659	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
660	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
661	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
662	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
663	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
664	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
665	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
666	#95	C₂³×C₃₁	1	2	yes	—
667	#95	C₂³×C₃₁	1	2	yes	—
668	#95	C₂³×C₃₁	1	2	yes	—
669	#95	C₂³×C₃₁	1	2	yes	—
670	#95	C₂³×C₃₁	1	2	yes	—
671	#95	C₂³×C₃₁	1	2	yes	—
672	#95	C₂³×C₃₁	1	2	yes	—
673	#95	C₂³×C₃₁	1	2	yes	—
674	#95	C₂³×C₃₁	1	1	yes	characteristic
675	#95	C₂³×C₃₁	1	1	yes	characteristic
676	#95	C₂³×C₃₁	1	1	yes	characteristic
677	#95	C₂³×C₃₁	1	1	yes	characteristic
678	#95	C₂³×C₃₁	1	1	yes	characteristic
679	#95	C₂³×C₃₁	1	1	yes	characteristic
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	#35117	1	1	yes	characteristic, direct product factor, Sylow
698	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
699	C₂×Q₈	—	2	2	no	—
700	C₂×Q₈	—	2	2	no	—
701	C₂×Q₈	—	2	2	no	—
702	C₂×Q₈	—	2	2	no	—
703	C₂×Q₈	—	2	2	no	—
704	C₂×Q₈	—	2	4	no	—
705	C₂×Q₈	—	2	2	no	—
706	C₂×Q₈	—	2	2	no	—
707	C₂×Q₈	—	2	2	no	—
708	C₂×Q₈	—	2	2	no	—
709	C₂×Q₈	—	4	2	no	—
710	C₂×Q₈	—	4	2	no	—
711	C₂×D₄	—	2	2	no	—
712	C₂×D₄	—	2	2	no	—
713	C₂×D₄	—	2	2	no	—
714	C₂²×C₄	—	2	4	no	—
715	C₂²×C₄	—	4	2	no	—
716	C₂²×C₄	—	4	2	no	—
717	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
718	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
719	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
720	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
721	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
722	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
723	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
724	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
725	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
726	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
727	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
728	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
729	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
730	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
731	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
732	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
733	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
734	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
735	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
736	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
737	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
738	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
739	C₄⋊C₄	—	2	2	no	—
740	C₄⋊C₄	—	2	2	no	—
741	C₄⋊C₄	—	2	2	no	—
742	C₄⋊C₄	—	2	2	no	—
743	C₄⋊C₄	—	2	2	no	—
744	C₄⋊C₄	—	2	2	no	—
745	C₄⋊C₄	—	2	2	no	—
746	C₄⋊C₄	—	2	2	no	—
747	C₄⋊C₄	—	2	2	no	—
748	C₄⋊C₄	—	2	4	no	—
749	C₄⋊C₄	—	2	4	no	—
750	C₄⋊C₄	—	2	4	no	—
751	C₄⋊C₄	—	2	4	no	—
752	C₄⋊C₄	—	2	4	no	—
753	C₄⋊C₄	—	2	4	no	—
754	C₄⋊C₄	—	2	2	no	—
755	C₄⋊C₄	—	2	2	no	—
756	C₄⋊C₄	—	2	2	no	—
757	C₄⋊C₄	—	2	2	no	—
758	C₄⋊C₄	—	4	2	no	—
759	C₄⋊C₄	—	4	2	no	—
760	C₄⋊C₄	—	4	2	no	—
761	C₄⋊C₄	—	4	2	no	—
762	C₄⋊C₄	—	4	2	no	—
763	C₄⋊C₄	—	4	2	no	—
764	C₄⋊C₄	—	4	2	no	—
765	C₄⋊C₄	#41×C₃₁	1	4	yes	—
766	C₂²⋊C₄	—	2	4	no	—
767	C₂²⋊C₄	—	2	4	no	—
768	C₂²⋊C₄	—	2	4	no	—
769	C₂²⋊C₄	—	2	4	no	—
770	C₂²⋊C₄	—	2	4	no	—
771	C₂²⋊C₄	—	2	4	no	—
772	C₂²⋊C₄	—	2	4	no	—
773	C₂²⋊C₄	—	2	4	no	—
774	C₂²⋊C₄	—	4	2	no	—
775	C₂²⋊C₄	—	4	2	no	—
776	C₂²⋊C₄	—	4	2	no	—
777	C₂²⋊C₄	—	4	2	no	—
778	C₂²⋊C₄	—	4	2	no	—
779	C₄²	—	2	2	no	—
780	C₄²	—	2	2	no	—
781	C₄²	—	2	2	no	—
782	C₄²	—	2	2	no	—
783	C₄²	—	2	2	no	—
784	C₄²	—	2	2	no	—
785	C₄²	—	2	2	no	—
786	C₄²	—	2	4	no	—
787	C₄²	—	2	2	no	—
788	C₄²	—	2	2	no	—
789	C₄²	—	2	2	no	—
790	C₄²	—	2	2	no	—
791	C₄²	—	2	2	no	—
792	C₄²	—	2	2	no	—
793	C₄²	—	2	2	no	—
794	C₄²	—	4	1	no	—
795	C₄²	—	4	1	no	—
796	C₄²	—	4	1	no	—
797	C₄²	—	4	2	no	—
798	C₄²	—	4	2	no	—
799	C₄²	#41×C₃₁	1	4	yes	—
800	C₄²	#41×C₃₁	1	4	yes	—
801	C₂³	—	2	2	no	—
802	C₂³	—	2	2	no	—
803	C₂³	—	2	2	no	—
804	C₂³	—	2	2	no	—
805	C₂³	—	2	2	no	—
806	C₂³	—	2	2	no	—
807	C₂³	—	2	2	no	—
808	C₂³	C₂⁵×C₃₁	1	1	yes	characteristic
809	Q₈	—	2	8	no	—
810	Q₈	—	4	4	no	—
811	Q₈	—	4	4	no	—
812	Q₈	—	8	4	no	—
813	D₄	—	4	4	no	—
814	C₂×C₄	—	2	1	no	—
815	C₂×C₄	—	2	1	no	—
816	C₂×C₄	—	2	1	no	—
817	C₂×C₄	—	2	1	no	—
818	C₂×C₄	—	2	1	no	—
819	C₂×C₄	—	2	1	no	—
820	C₂×C₄	—	2	1	no	—
821	C₂×C₄	—	2	1	no	—
822	C₂×C₄	—	2	1	no	—
823	C₂×C₄	—	2	1	no	—
824	C₂×C₄	—	2	1	no	—
825	C₂×C₄	—	2	1	no	—
826	C₂×C₄	—	2	1	no	—
827	C₂×C₄	—	2	1	no	—
828	C₂×C₄	—	2	1	no	—
829	C₂×C₄	—	2	1	no	—
830	C₂×C₄	—	2	1	no	—
831	C₂×C₄	—	2	1	no	—
832	C₂×C₄	—	2	2	no	—
833	C₂×C₄	—	2	1	no	—
834	C₂×C₄	—	2	1	no	—
835	C₂×C₄	—	2	1	no	—
836	C₂×C₄	—	2	1	no	—
837	C₂×C₄	—	2	1	no	—
838	C₂×C₄	—	2	2	no	—
839	C₂×C₄	—	2	2	no	—
840	C₂×C₄	—	2	2	no	—
841	C₂×C₄	—	2	2	no	—
842	C₂×C₄	—	2	2	no	—
843	C₂×C₄	—	2	2	no	—
844	C₂×C₄	—	2	2	no	—
845	C₂×C₄	—	2	2	no	—
846	C₂×C₄	—	2	1	no	—
847	C₂×C₄	—	2	1	no	—
848	C₂×C₄	—	2	1	no	—
849	C₂×C₄	—	2	2	no	—
850	C₂×C₄	—	2	2	no	—
851	C₂×C₄	—	2	2	no	—
852	C₂×C₄	—	2	2	no	—
853	C₂×C₄	—	2	2	no	—
854	C₂×C₄	—	2	1	no	—
855	C₂×C₄	—	2	1	no	—
856	C₂×C₄	—	2	1	no	—
857	C₂×C₄	—	2	1	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	1	no	—
863	C₂×C₄	—	2	1	no	—
864	C₂×C₄	—	2	2	no	—
865	C₂×C₄	—	2	2	no	—
866	C₂×C₄	—	2	1	no	—
867	C₂×C₄	—	2	2	no	—
868	C₂×C₄	—	8	4	no	—
869	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
870	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
871	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
872	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
873	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
874	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
875	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
876	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
877	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
878	C₂×C₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
879	C₂×C₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
880	C₂×C₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
881	C₂²	—	4	2	no	—
882	C₂²	—	4	2	no	—
883	C₂²	—	4	2	no	—
884	C₂²	—	4	2	no	—
885	C₂²	—	4	2	no	—
886	C₂²	—	4	2	no	—
887	C₂²	—	4	2	no	—
888	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
889	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
890	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
891	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
892	C₂²	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
893	C₂²	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
894	C₂²	C₃₁×#585	1	1	yes	characteristic
895	C₄	—	2	2	no	—
896	C₄	—	2	2	no	—
897	C₄	—	2	2	no	—
898	C₄	—	2	2	no	—
899	C₄	—	2	2	no	—
900	C₄	—	2	2	no	—
901	C₄	—	2	2	no	—
902	C₄	—	2	2	no	—
903	C₄	—	2	2	no	—
904	C₄	—	4	2	no	—
905	C₄	—	4	2	no	—
906	C₄	—	4	2	no	—
907	C₄	—	4	1	no	—
908	C₄	—	4	1	no	—
909	C₄	—	4	2	no	—
910	C₄	—	4	1	no	—
911	C₄	—	4	1	no	—
912	C₄	—	4	2	no	—
913	C₄	—	4	2	no	—
914	C₄	—	4	2	no	—
915	C₄	—	4	1	no	—
916	C₄	C₃₁×#542	1	4	yes	—
917	C₂	—	8	2	no	—
918	C₂	C₃₁×#3444	1	1	yes	characteristic
919	C₂	C₂×C₃₁×#542	1	1	yes	characteristic
920	C₂	C₃₁×#3461	1	1	yes	characteristic
921	C₂	C₃₁×#3507	1	1	yes	characteristic
922	C₂	C₃₁×#3511	1	1	yes	characteristic
923	C₂	C₃₁×#3514	1	1	yes	characteristic
924	C₂	C₃₁×#3523	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃₁	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₃₁
prime radical	C₂²×D₄×C₃₁	C₂³
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×#2863	C₂	semidirect
2. C₃₁×#2862	C₂	semidirect
5. C₃₁×#2650	C₂	semidirect
6. C₃₁×#2637	C₂	semidirect
8. C₃₁×#2581	C₂	semidirect
9. C₃₁×#2550	C₂	semidirect
11. C₃₁×#2532	C₂	semidirect
12. C₃₁×#2529	C₂	semidirect
13. C₃₁×#2515	C₂	semidirect
14. C₃₁×#2465	C₂	semidirect
15. C₃₁×#2453	C₂	semidirect
18. C₃₁×#2446	C₂	semidirect
19. C₃₁×#2334	C₂	semidirect
20. C₃₁×#2332	C₂	semidirect
22. C₃₁×#2295	C₂	semidirect
23. C₄²×Q₈×C₃₁	C₂	semidirect
338. #35117	C₃₁	direct (N × H)
419. #2863	C₂×C₃₁	semidirect
420. #2862	C₂×C₃₁	semidirect
423. #2650	C₂×C₃₁	semidirect
424. #2637	C₂×C₃₁	semidirect
426. #2581	C₂×C₃₁	semidirect
427. #2550	C₂×C₃₁	semidirect
429. #2532	C₂×C₃₁	semidirect
430. #2529	C₂×C₃₁	semidirect
431. #2515	C₂×C₃₁	semidirect
432. #2465	C₂×C₃₁	semidirect
433. #2453	C₂×C₃₁	semidirect
436. #2446	C₂×C₃₁	semidirect
437. #2334	C₂×C₃₁	semidirect
438. #2332	C₂×C₃₁	semidirect
440. #2295	C₂×C₃₁	semidirect
441. C₄²×Q₈	C₂×C₃₁	semidirect
697. C₃₁	#35117	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×#2863	2
C₃₁×#2862	2
C₃₁×#2861	2
C₃₁×#2860	2
C₃₁×#2650	2
C₃₁×#2637	2
C₃₁×#2592	2
C₃₁×#2581	2
C₃₁×#2550	2
C₃₁×#2545	2
C₃₁×#2532	2
C₃₁×#2529	2
C₃₁×#2515	2
C₃₁×#2465	2
C₃₁×#2453	2
C₃₁×#2452	2
C₃₁×#2447	2
C₃₁×#2446	2
C₃₁×#2334	2
C₃₁×#2332	2
C₄×C₃₁×#124	2
C₃₁×#2295	2
C₄²×Q₈×C₃₁	2
#35117	31

Subgroups — C31×#35117 #21491876

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#35117 #21491876