Subgroups — C₃₁×#36638 #21493397

Order 7936.

2082 conjugacy classes of subgroups.

The subgroup lattice has 1000 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#2866	C₂	1	2	yes	maximal, complemented
2	C₃₁×#2865	C₂	1	2	yes	maximal, complemented
3	C₃₁×#2864	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#2863	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#2861	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#2860	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#2855	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#2854	C₂	1	1	yes	maximal, characteristic
9	C₃₁×#2853	C₂	1	2	yes	maximal, complemented
10	C₃₁×#2852	C₂	1	2	yes	maximal, complemented
11	C₃₁×#2851	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#2850	C₂	1	1	yes	maximal, characteristic
13	C₄×C₃₁×#125	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×C₃₁×#126	C₂	1	2	yes	maximal, complemented
15	C₄×C₃₁×#124	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×C₃₁×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄×C₃₁×#123	C₂	1	2	yes	maximal, complemented
18	C₄×C₃₁×#121	C₂	1	1	yes	maximal, characteristic
19	C₃₁×#2298	C₂	1	2	yes	maximal, complemented
20	C₃₁×#2295	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃₁×#2293	C₂	1	1	yes	maximal, characteristic, complemented
22	C₃₁×#2290	C₂	1	2	yes	maximal, complemented
23	C₂×C₄³×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₃₁×#126	C₂²	1	2	yes	—
25	C₂×C₃₁×#125	C₂²	1	1	yes	characteristic
26	C₂×C₃₁×#124	C₂²	1	1	yes	characteristic
27	C₂×C₃₁×#123	C₂²	1	2	yes	—
28	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
29	C₂×C₃₁×#121	C₂²	1	1	yes	characteristic
30	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
31	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
32	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
33	C₂×C₃₁×#117	C₂²	1	2	yes	—
34	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
35	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
36	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
37	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
38	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
39	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
40	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
41	C₃₁×#391	C₂²	1	1	yes	characteristic
42	C₃₁×#391	C₂²	1	1	yes	characteristic
43	C₃₁×#391	C₂²	1	1	yes	characteristic
44	C₃₁×#391	C₂²	1	1	yes	characteristic
45	C₃₁×#390	C₂²	1	1	yes	characteristic
46	C₃₁×#390	C₂²	1	1	yes	characteristic
47	C₃₁×#390	C₂²	1	1	yes	characteristic
48	C₃₁×#390	C₂²	1	1	yes	characteristic
49	C₃₁×#389	C₂²	1	1	yes	characteristic
50	C₃₁×#389	C₂²	1	1	yes	characteristic
51	C₃₁×#389	C₂²	1	1	yes	characteristic
52	C₃₁×#389	C₂²	1	1	yes	characteristic
53	C₃₁×#389	C₂²	1	1	yes	characteristic
54	C₃₁×#389	C₂²	1	1	yes	characteristic
55	C₃₁×#389	C₂²	1	1	yes	characteristic
56	C₃₁×#389	C₂²	1	1	yes	characteristic
57	C₃₁×#388	C₂²	1	2	yes	—
58	C₃₁×#388	C₂²	1	2	yes	—
59	C₃₁×#388	C₂²	1	2	yes	—
60	C₃₁×#388	C₂²	1	2	yes	—
61	C₃₁×#388	C₂²	1	2	yes	—
62	C₃₁×#388	C₂²	1	2	yes	—
63	C₃₁×#388	C₂²	1	2	yes	—
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×#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×#387	C₂²	1	2	yes	—
88	C₃₁×#387	C₂²	1	2	yes	—
89	C₃₁×#386	C₂²	1	2	yes	—
90	C₃₁×#386	C₂²	1	2	yes	—
91	C₃₁×#386	C₂²	1	2	yes	—
92	C₃₁×#386	C₂²	1	2	yes	—
93	C₃₁×#385	C₂²	1	2	yes	—
94	C₃₁×#385	C₂²	1	2	yes	—
95	C₃₁×#385	C₂²	1	2	yes	—
96	C₃₁×#385	C₂²	1	2	yes	—
97	C₃₁×#383	C₂²	1	2	yes	—
98	C₃₁×#382	C₂²	1	1	yes	characteristic
99	C₃₁×#382	C₂²	1	1	yes	characteristic
100	C₃₁×#381	C₂²	1	2	yes	—
101	C₃₁×#380	C₂²	1	1	yes	characteristic
102	C₃₁×#380	C₂²	1	1	yes	characteristic
103	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
104	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
105	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
106	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
107	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
108	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
109	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
110	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
111	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
112	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
113	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
114	C₃₁×#376	C₂²	1	2	yes	—
115	C₄³×C₃₁	C₂²	1	1	yes	characteristic
116	C₄³×C₃₁	C₂²	1	1	yes	characteristic
117	C₄³×C₃₁	C₂²	1	1	yes	characteristic
118	C₄³×C₃₁	C₂²	1	1	yes	characteristic
119	C₄³×C₃₁	C₂²	1	1	yes	characteristic
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×D₄×C₃₁	C₂³	1	2	yes	—
125	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
126	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
127	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
128	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
129	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
130	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
131	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
132	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
133	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
134	C₃₁×#126	—	2	8	no	—
135	C₃₁×#125	—	2	4	no	—
136	C₃₁×#124	—	2	4	no	—
137	C₃₁×#123	—	2	8	no	—
138	C₃₁×C₂²⋊Q₈	—	2	4	no	—
139	C₃₁×#121	—	2	4	no	—
140	C₄×Q₈×C₃₁	—	2	4	no	—
141	C₄×D₄×C₃₁	—	2	8	no	—
142	C₄×D₄×C₃₁	—	2	4	no	—
143	C₃₁×#117	—	2	8	no	—
144	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
145	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
146	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
147	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
148	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
149	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
150	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
151	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
152	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
153	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
154	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
155	C₂×C₄⋊C₄×C₃₁	C₂³	1	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	2	yes	—
160	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
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×C₄²×C₃₁	—	2	4	no	—
178	C₂×C₄²×C₃₁	—	2	4	no	—
179	C₂×C₄²×C₃₁	—	2	4	no	—
180	C₂×C₄²×C₃₁	—	2	4	no	—
181	C₂×C₄²×C₃₁	—	2	4	no	—
182	C₂×C₄²×C₃₁	—	2	4	no	—
183	C₂×C₄²×C₃₁	—	2	4	no	—
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	1	yes	characteristic
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	1	yes	characteristic
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	1	yes	characteristic
202	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
203	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
204	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
205	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
206	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
207	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
208	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
209	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
210	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
211	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
212	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
213	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
214	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
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	2	yes	—
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	2	yes	—
230	C₃₁×#95	C₂³	1	2	yes	—
231	C₃₁×#95	C₂³	1	2	yes	—
232	C₃₁×#95	C₂³	1	2	yes	—
233	C₃₁×#95	C₂³	1	2	yes	—
234	C₃₁×#95	C₂³	1	2	yes	—
235	C₃₁×#95	C₂³	1	2	yes	—
236	C₃₁×#95	C₂³	1	2	yes	—
237	C₃₁×#95	C₂³	1	2	yes	—
238	C₃₁×#95	C₂³	1	2	yes	—
239	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
240	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
241	C₂×Q₈×C₃₁	—	2	2	no	—
242	C₂×Q₈×C₃₁	—	2	2	no	—
243	C₂×Q₈×C₃₁	—	2	2	no	—
244	C₂×D₄×C₃₁	—	2	4	no	—
245	C₂×D₄×C₃₁	—	2	4	no	—
246	C₂×D₄×C₃₁	—	2	4	no	—
247	C₂×D₄×C₃₁	—	2	2	no	—
248	C₂×D₄×C₃₁	—	2	2	no	—
249	C₂×D₄×C₃₁	—	2	2	no	—
250	C₂²×C₄×C₃₁	—	2	2	no	—
251	C₂²×C₄×C₃₁	—	2	2	no	—
252	C₂²×C₄×C₃₁	—	2	2	no	—
253	C₂²×C₄×C₃₁	—	2	2	no	—
254	C₂²×C₄×C₃₁	—	2	2	no	—
255	C₂²×C₄×C₃₁	—	2	2	no	—
256	C₂²×C₄×C₃₁	—	2	2	no	—
257	C₂²×C₄×C₃₁	—	2	2	no	—
258	C₂²×C₄×C₃₁	—	2	2	no	—
259	C₂²×C₄×C₃₁	—	2	2	no	—
260	C₂²×C₄×C₃₁	—	2	2	no	—
261	C₂²×C₄×C₃₁	—	2	2	no	—
262	C₂²×C₄×C₃₁	—	2	2	no	—
263	C₂²×C₄×C₃₁	—	2	2	no	—
264	C₂²×C₄×C₃₁	—	2	2	no	—
265	C₂²×C₄×C₃₁	—	2	2	no	—
266	C₂²×C₄×C₃₁	—	2	2	no	—
267	C₂²×C₄×C₃₁	—	2	2	no	—
268	C₂²×C₄×C₃₁	—	2	4	no	—
269	C₂²×C₄×C₃₁	—	2	4	no	—
270	C₂²×C₄×C₃₁	—	2	4	no	—
271	C₂²×C₄×C₃₁	#41	1	4	yes	—
272	C₂²×C₄×C₃₁	#41	1	4	yes	—
273	C₂²×C₄×C₃₁	#41	1	4	yes	—
274	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
275	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
276	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
277	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
278	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
279	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
280	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
281	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
282	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
283	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
284	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
285	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
286	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
287	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
288	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
289	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
290	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
291	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
292	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
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	—	2	4	no	—
297	C₄⋊C₄×C₃₁	—	2	4	no	—
298	C₄⋊C₄×C₃₁	—	2	2	no	—
299	C₄⋊C₄×C₃₁	—	2	2	no	—
300	C₄⋊C₄×C₃₁	—	2	4	no	—
301	C₄⋊C₄×C₃₁	—	2	2	no	—
302	C₄⋊C₄×C₃₁	—	2	2	no	—
303	C₄⋊C₄×C₃₁	—	2	4	no	—
304	C₄⋊C₄×C₃₁	—	2	4	no	—
305	C₄⋊C₄×C₃₁	—	2	4	no	—
306	C₄⋊C₄×C₃₁	—	2	4	no	—
307	C₄⋊C₄×C₃₁	—	2	4	no	—
308	C₄⋊C₄×C₃₁	—	2	2	no	—
309	C₄⋊C₄×C₃₁	—	2	2	no	—
310	C₄⋊C₄×C₃₁	—	2	4	no	—
311	C₄⋊C₄×C₃₁	—	2	4	no	—
312	C₄⋊C₄×C₃₁	—	2	4	no	—
313	C₂²⋊C₄×C₃₁	—	2	4	no	—
314	C₂²⋊C₄×C₃₁	—	2	4	no	—
315	C₂²⋊C₄×C₃₁	—	2	4	no	—
316	C₂²⋊C₄×C₃₁	—	2	4	no	—
317	C₂²⋊C₄×C₃₁	—	2	4	no	—
318	C₂²⋊C₄×C₃₁	—	2	4	no	—
319	C₂²⋊C₄×C₃₁	—	2	4	no	—
320	C₂²⋊C₄×C₃₁	—	2	4	no	—
321	C₂²⋊C₄×C₃₁	—	2	4	no	—
322	C₂²⋊C₄×C₃₁	—	2	4	no	—
323	C₂²⋊C₄×C₃₁	—	2	4	no	—
324	C₂²⋊C₄×C₃₁	—	2	4	no	—
325	C₂²⋊C₄×C₃₁	—	2	4	no	—
326	C₂²⋊C₄×C₃₁	—	2	4	no	—
327	C₂²⋊C₄×C₃₁	—	2	4	no	—
328	C₄²×C₃₁	—	2	2	no	—
329	C₄²×C₃₁	—	2	2	no	—
330	C₄²×C₃₁	—	2	2	no	—
331	C₄²×C₃₁	—	2	2	no	—
332	C₄²×C₃₁	—	2	2	no	—
333	C₄²×C₃₁	—	2	2	no	—
334	C₄²×C₃₁	—	2	2	no	—
335	C₄²×C₃₁	—	2	2	no	—
336	C₄²×C₃₁	—	2	2	no	—
337	C₄²×C₃₁	—	2	2	no	—
338	C₄²×C₃₁	—	2	2	no	—
339	C₄²×C₃₁	—	2	2	no	—
340	C₄²×C₃₁	—	2	2	no	—
341	C₄²×C₃₁	—	2	2	no	—
342	C₄²×C₃₁	—	2	2	no	—
343	C₄²×C₃₁	—	2	2	no	—
344	C₄²×C₃₁	—	2	2	no	—
345	C₄²×C₃₁	—	2	2	no	—
346	C₄²×C₃₁	—	2	2	no	—
347	C₄²×C₃₁	—	2	2	no	—
348	C₄²×C₃₁	—	2	2	no	—
349	C₄²×C₃₁	—	2	2	no	—
350	C₄²×C₃₁	—	2	2	no	—
351	C₄²×C₃₁	—	2	2	no	—
352	C₄²×C₃₁	—	2	4	no	—
353	C₄²×C₃₁	—	2	4	no	—
354	C₄²×C₃₁	—	2	4	no	—
355	C₄²×C₃₁	#41	1	4	yes	—
356	C₄²×C₃₁	#41	1	4	yes	—
357	C₄²×C₃₁	#41	1	4	yes	—
358	C₄²×C₃₁	#41	1	4	yes	—
359	#36638	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
360	C₂³×C₃₁	—	2	1	no	—
361	C₂³×C₃₁	—	2	1	no	—
362	C₂³×C₃₁	—	2	1	no	—
363	C₂³×C₃₁	—	2	1	no	—
364	C₂³×C₃₁	—	2	2	no	—
365	C₂³×C₃₁	—	2	2	no	—
366	C₂³×C₃₁	—	2	2	no	—
367	C₂³×C₃₁	—	2	2	no	—
368	C₂³×C₃₁	—	2	2	no	—
369	C₂³×C₃₁	—	2	2	no	—
370	C₂³×C₃₁	—	2	2	no	—
371	C₂³×C₃₁	C₂×#41	1	2	yes	—
372	C₂³×C₃₁	C₂×#41	1	2	yes	—
373	C₂³×C₃₁	C₂×#41	1	2	yes	—
374	C₂³×C₃₁	C₂⁵	1	1	yes	characteristic
375	Q₈×C₃₁	—	4	4	no	—
376	D₄×C₃₁	—	4	8	no	—
377	D₄×C₃₁	—	4	4	no	—
378	C₂×C₄×C₃₁	—	2	8	no	—
379	C₂×C₄×C₃₁	—	2	8	no	—
380	C₂×C₄×C₃₁	—	2	8	no	—
381	C₂×C₄×C₃₁	—	2	8	no	—
382	C₂×C₄×C₃₁	—	2	8	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	1	no	—
387	C₂×C₄×C₃₁	—	2	1	no	—
388	C₂×C₄×C₃₁	—	2	1	no	—
389	C₂×C₄×C₃₁	—	2	1	no	—
390	C₂×C₄×C₃₁	—	2	1	no	—
391	C₂×C₄×C₃₁	—	2	1	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	1	no	—
397	C₂×C₄×C₃₁	—	2	1	no	—
398	C₂×C₄×C₃₁	—	2	1	no	—
399	C₂×C₄×C₃₁	—	2	1	no	—
400	C₂×C₄×C₃₁	—	2	1	no	—
401	C₂×C₄×C₃₁	—	2	1	no	—
402	C₂×C₄×C₃₁	—	2	1	no	—
403	C₂×C₄×C₃₁	—	2	1	no	—
404	C₂×C₄×C₃₁	—	2	1	no	—
405	C₂×C₄×C₃₁	—	2	1	no	—
406	C₂×C₄×C₃₁	—	2	1	no	—
407	C₂×C₄×C₃₁	—	2	8	no	—
408	C₂×C₄×C₃₁	—	2	8	no	—
409	C₂×C₄×C₃₁	—	2	2	no	—
410	C₂×C₄×C₃₁	—	2	2	no	—
411	C₂×C₄×C₃₁	—	2	2	no	—
412	C₂×C₄×C₃₁	—	2	2	no	—
413	C₂×C₄×C₃₁	—	2	2	no	—
414	C₂×C₄×C₃₁	—	2	2	no	—
415	C₂×C₄×C₃₁	—	2	2	no	—
416	C₂×C₄×C₃₁	—	2	2	no	—
417	C₂×C₄×C₃₁	—	2	2	no	—
418	C₂×C₄×C₃₁	—	2	2	no	—
419	C₂×C₄×C₃₁	—	2	2	no	—
420	C₂×C₄×C₃₁	—	2	2	no	—
421	C₂×C₄×C₃₁	—	2	2	no	—
422	C₂×C₄×C₃₁	—	2	2	no	—
423	C₂×C₄×C₃₁	—	2	2	no	—
424	C₂×C₄×C₃₁	—	2	2	no	—
425	C₂×C₄×C₃₁	—	2	2	no	—
426	C₂×C₄×C₃₁	—	2	2	no	—
427	C₂×C₄×C₃₁	—	2	2	no	—
428	C₂×C₄×C₃₁	—	2	2	no	—
429	C₂×C₄×C₃₁	—	2	2	no	—
430	C₂×C₄×C₃₁	—	4	8	no	—
431	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
432	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
433	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
434	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
435	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
436	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
437	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
438	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
439	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
440	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
441	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
442	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
443	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
444	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
445	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
446	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
447	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
448	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
449	#2866	C₂×C₃₁	1	2	yes	complemented
450	#2865	C₂×C₃₁	1	2	yes	complemented
451	#2864	C₂×C₃₁	1	1	yes	characteristic, complemented
452	#2863	C₂×C₃₁	1	1	yes	characteristic, complemented
453	#2861	C₂×C₃₁	1	1	yes	characteristic, complemented
454	#2860	C₂×C₃₁	1	1	yes	characteristic, complemented
455	#2855	C₂×C₃₁	1	1	yes	characteristic, complemented
456	#2854	C₂×C₃₁	1	1	yes	characteristic
457	#2853	C₂×C₃₁	1	2	yes	complemented
458	#2852	C₂×C₃₁	1	2	yes	complemented
459	#2851	C₂×C₃₁	1	1	yes	characteristic, complemented
460	#2850	C₂×C₃₁	1	1	yes	characteristic
461	C₄×#125	C₂×C₃₁	1	1	yes	characteristic, complemented
462	C₄×#126	C₂×C₃₁	1	2	yes	complemented
463	C₄×#124	C₂×C₃₁	1	1	yes	characteristic, complemented
464	C₄×C₂²⋊Q₈	C₂×C₃₁	1	1	yes	characteristic, complemented
465	C₄×#123	C₂×C₃₁	1	2	yes	complemented
466	C₄×#121	C₂×C₃₁	1	1	yes	characteristic
467	#2298	C₂×C₃₁	1	2	yes	complemented
468	#2295	C₂×C₃₁	1	1	yes	characteristic, complemented
469	#2293	C₂×C₃₁	1	1	yes	characteristic, complemented
470	#2290	C₂×C₃₁	1	2	yes	complemented
471	C₂×C₄³	C₂×C₃₁	1	1	yes	characteristic, complemented
472	C₂²×C₃₁	—	2	2	no	—
473	C₂²×C₃₁	—	2	2	no	—
474	C₂²×C₃₁	—	2	2	no	—
475	C₂²×C₃₁	—	2	2	no	—
476	C₂²×C₃₁	—	2	2	no	—
477	C₂²×C₃₁	—	2	2	no	—
478	C₂²×C₃₁	—	4	2	no	—
479	C₂²×C₃₁	—	4	2	no	—
480	C₂²×C₃₁	—	4	2	no	—
481	C₂²×C₃₁	—	4	2	no	—
482	C₂²×C₃₁	—	4	2	no	—
483	C₂²×C₃₁	—	4	2	no	—
484	C₂²×C₃₁	—	4	2	no	—
485	C₂²×C₃₁	#529	1	4	yes	—
486	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
487	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
488	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
489	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
490	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
491	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
492	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
493	C₄×C₃₁	—	2	2	no	—
494	C₄×C₃₁	—	2	2	no	—
495	C₄×C₃₁	—	2	2	no	—
496	C₄×C₃₁	—	2	2	no	—
497	C₄×C₃₁	—	2	2	no	—
498	C₄×C₃₁	—	2	2	no	—
499	C₄×C₃₁	—	2	2	no	—
500	C₄×C₃₁	—	2	2	no	—
501	C₄×C₃₁	—	2	2	no	—
502	C₄×C₃₁	—	2	2	no	—
503	C₄×C₃₁	—	2	2	no	—
504	C₄×C₃₁	—	2	2	no	—
505	C₄×C₃₁	—	4	2	no	—
506	C₄×C₃₁	—	4	2	no	—
507	C₄×C₃₁	—	4	2	no	—
508	C₄×C₃₁	—	4	2	no	—
509	C₄×C₃₁	—	4	2	no	—
510	C₄×C₃₁	—	4	2	no	—
511	C₄×C₃₁	—	4	2	no	—
512	C₄×C₃₁	#529	1	4	yes	—
513	C₄×C₃₁	#529	1	4	yes	—
514	C₂×#126	C₂²×C₃₁	1	2	yes	—
515	C₂×#125	C₂²×C₃₁	1	1	yes	characteristic
516	C₂×#124	C₂²×C₃₁	1	1	yes	characteristic
517	C₂×#123	C₂²×C₃₁	1	2	yes	—
518	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
519	C₂×#121	C₂²×C₃₁	1	1	yes	characteristic
520	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
521	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
522	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
523	C₂×#117	C₂²×C₃₁	1	2	yes	—
524	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
525	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
526	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
527	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
528	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
529	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
530	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
531	#391	C₂²×C₃₁	1	1	yes	characteristic
532	#391	C₂²×C₃₁	1	1	yes	characteristic
533	#391	C₂²×C₃₁	1	1	yes	characteristic
534	#391	C₂²×C₃₁	1	1	yes	characteristic
535	#390	C₂²×C₃₁	1	1	yes	characteristic
536	#390	C₂²×C₃₁	1	1	yes	characteristic
537	#390	C₂²×C₃₁	1	1	yes	characteristic
538	#390	C₂²×C₃₁	1	1	yes	characteristic
539	#389	C₂²×C₃₁	1	1	yes	characteristic
540	#389	C₂²×C₃₁	1	1	yes	characteristic
541	#389	C₂²×C₃₁	1	1	yes	characteristic
542	#389	C₂²×C₃₁	1	1	yes	characteristic
543	#389	C₂²×C₃₁	1	1	yes	characteristic
544	#389	C₂²×C₃₁	1	1	yes	characteristic
545	#389	C₂²×C₃₁	1	1	yes	characteristic
546	#389	C₂²×C₃₁	1	1	yes	characteristic
547	#388	C₂²×C₃₁	1	2	yes	—
548	#388	C₂²×C₃₁	1	2	yes	—
549	#388	C₂²×C₃₁	1	2	yes	—
550	#388	C₂²×C₃₁	1	2	yes	—
551	#388	C₂²×C₃₁	1	2	yes	—
552	#388	C₂²×C₃₁	1	2	yes	—
553	#388	C₂²×C₃₁	1	2	yes	—
554	#388	C₂²×C₃₁	1	2	yes	—
555	#388	C₂²×C₃₁	1	2	yes	—
556	#388	C₂²×C₃₁	1	2	yes	—
557	#388	C₂²×C₃₁	1	2	yes	—
558	#388	C₂²×C₃₁	1	2	yes	—
559	#388	C₂²×C₃₁	1	2	yes	—
560	#388	C₂²×C₃₁	1	2	yes	—
561	#388	C₂²×C₃₁	1	2	yes	—
562	#388	C₂²×C₃₁	1	2	yes	—
563	#387	C₂²×C₃₁	1	2	yes	—
564	#387	C₂²×C₃₁	1	2	yes	—
565	#387	C₂²×C₃₁	1	2	yes	—
566	#387	C₂²×C₃₁	1	2	yes	—
567	#387	C₂²×C₃₁	1	2	yes	—
568	#387	C₂²×C₃₁	1	2	yes	—
569	#387	C₂²×C₃₁	1	2	yes	—
570	#387	C₂²×C₃₁	1	2	yes	—
571	#387	C₂²×C₃₁	1	2	yes	—
572	#387	C₂²×C₃₁	1	2	yes	—
573	#387	C₂²×C₃₁	1	2	yes	—
574	#387	C₂²×C₃₁	1	2	yes	—
575	#387	C₂²×C₃₁	1	2	yes	—
576	#387	C₂²×C₃₁	1	2	yes	—
577	#387	C₂²×C₃₁	1	2	yes	—
578	#387	C₂²×C₃₁	1	2	yes	—
579	#386	C₂²×C₃₁	1	2	yes	—
580	#386	C₂²×C₃₁	1	2	yes	—
581	#386	C₂²×C₃₁	1	2	yes	—
582	#386	C₂²×C₃₁	1	2	yes	—
583	#385	C₂²×C₃₁	1	2	yes	—
584	#385	C₂²×C₃₁	1	2	yes	—
585	#385	C₂²×C₃₁	1	2	yes	—
586	#385	C₂²×C₃₁	1	2	yes	—
587	#383	C₂²×C₃₁	1	2	yes	—
588	#382	C₂²×C₃₁	1	1	yes	characteristic
589	#382	C₂²×C₃₁	1	1	yes	characteristic
590	#381	C₂²×C₃₁	1	2	yes	—
591	#380	C₂²×C₃₁	1	1	yes	characteristic
592	#380	C₂²×C₃₁	1	1	yes	characteristic
593	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
594	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
595	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
596	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
597	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
598	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
599	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
600	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
601	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
602	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
603	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
604	#376	C₂²×C₃₁	1	2	yes	—
605	C₄³	C₂²×C₃₁	1	1	yes	characteristic
606	C₄³	C₂²×C₃₁	1	1	yes	characteristic
607	C₄³	C₂²×C₃₁	1	1	yes	characteristic
608	C₄³	C₂²×C₃₁	1	1	yes	characteristic
609	C₄³	C₂²×C₃₁	1	1	yes	characteristic
610	C₄³	C₂²×C₃₁	1	1	yes	characteristic
611	C₄³	C₂²×C₃₁	1	1	yes	characteristic
612	C₄³	C₂²×C₃₁	1	1	yes	characteristic
613	C₂×C₃₁	—	2	4	no	—
614	C₂×C₃₁	—	8	2	no	—
615	C₂×C₃₁	C₂×#529	1	1	yes	characteristic
616	C₂×C₃₁	C₂×#529	1	1	yes	characteristic
617	C₂×C₃₁	C₂×#529	1	1	yes	characteristic
618	C₂×C₃₁	#3444	1	1	yes	characteristic
619	C₂×C₃₁	#3444	1	1	yes	characteristic
620	C₂×C₃₁	#3444	1	1	yes	characteristic
621	C₂×C₃₁	#3444	1	1	yes	characteristic
622	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
623	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
624	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
625	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
626	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
627	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
628	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
629	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
630	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
631	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
632	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
633	#126	—	2	8	no	—
634	#125	—	2	4	no	—
635	#124	—	2	4	no	—
636	#123	—	2	8	no	—
637	C₂²⋊Q₈	—	2	4	no	—
638	#121	—	2	4	no	—
639	C₄×Q₈	—	2	4	no	—
640	C₄×D₄	—	2	8	no	—
641	C₄×D₄	—	2	4	no	—
642	#117	—	2	8	no	—
643	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
644	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
645	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
646	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
647	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
648	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
649	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
650	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
651	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
652	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
653	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
654	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
655	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
656	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
657	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
658	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
659	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
660	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
661	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
662	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
663	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
664	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
665	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
666	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
667	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
668	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
669	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
670	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
671	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
672	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
673	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
674	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
675	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
676	C₂×C₄²	—	2	4	no	—
677	C₂×C₄²	—	2	4	no	—
678	C₂×C₄²	—	2	4	no	—
679	C₂×C₄²	—	2	4	no	—
680	C₂×C₄²	—	2	4	no	—
681	C₂×C₄²	—	2	4	no	—
682	C₂×C₄²	—	2	4	no	—
683	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
684	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
685	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
686	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
687	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
688	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
689	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
690	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
691	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
692	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
693	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
694	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
695	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
696	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
697	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
698	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
699	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
700	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
701	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
702	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
703	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
704	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
705	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
706	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
707	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
708	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
709	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
710	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
711	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
712	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
713	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
714	#95	C₂³×C₃₁	1	2	yes	—
715	#95	C₂³×C₃₁	1	2	yes	—
716	#95	C₂³×C₃₁	1	2	yes	—
717	#95	C₂³×C₃₁	1	2	yes	—
718	#95	C₂³×C₃₁	1	2	yes	—
719	#95	C₂³×C₃₁	1	2	yes	—
720	#95	C₂³×C₃₁	1	2	yes	—
721	#95	C₂³×C₃₁	1	2	yes	—
722	#95	C₂³×C₃₁	1	2	yes	—
723	#95	C₂³×C₃₁	1	2	yes	—
724	#95	C₂³×C₃₁	1	2	yes	—
725	#95	C₂³×C₃₁	1	2	yes	—
726	#95	C₂³×C₃₁	1	2	yes	—
727	#95	C₂³×C₃₁	1	2	yes	—
728	#95	C₂³×C₃₁	1	2	yes	—
729	#95	C₂³×C₃₁	1	2	yes	—
730	#95	C₂³×C₃₁	1	2	yes	—
731	#95	C₂³×C₃₁	1	2	yes	—
732	#95	C₂³×C₃₁	1	2	yes	—
733	#95	C₂³×C₃₁	1	2	yes	—
734	#95	C₂³×C₃₁	1	2	yes	—
735	#95	C₂³×C₃₁	1	2	yes	—
736	#95	C₂³×C₃₁	1	2	yes	—
737	#95	C₂³×C₃₁	1	2	yes	—
738	C₃₁	#36638	1	1	yes	characteristic, direct product factor, Sylow
739	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
740	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
741	C₂×Q₈	—	2	2	no	—
742	C₂×Q₈	—	2	2	no	—
743	C₂×Q₈	—	2	2	no	—
744	C₂×D₄	—	2	4	no	—
745	C₂×D₄	—	2	4	no	—
746	C₂×D₄	—	2	4	no	—
747	C₂×D₄	—	2	2	no	—
748	C₂×D₄	—	2	2	no	—
749	C₂×D₄	—	2	2	no	—
750	C₂²×C₄	—	2	2	no	—
751	C₂²×C₄	—	2	2	no	—
752	C₂²×C₄	—	2	2	no	—
753	C₂²×C₄	—	2	2	no	—
754	C₂²×C₄	—	2	2	no	—
755	C₂²×C₄	—	2	2	no	—
756	C₂²×C₄	—	2	2	no	—
757	C₂²×C₄	—	2	2	no	—
758	C₂²×C₄	—	2	2	no	—
759	C₂²×C₄	—	2	2	no	—
760	C₂²×C₄	—	2	2	no	—
761	C₂²×C₄	—	2	2	no	—
762	C₂²×C₄	—	2	2	no	—
763	C₂²×C₄	—	2	2	no	—
764	C₂²×C₄	—	2	2	no	—
765	C₂²×C₄	—	2	2	no	—
766	C₂²×C₄	—	2	2	no	—
767	C₂²×C₄	—	2	2	no	—
768	C₂²×C₄	—	2	4	no	—
769	C₂²×C₄	—	2	4	no	—
770	C₂²×C₄	—	2	4	no	—
771	C₂²×C₄	#41×C₃₁	1	4	yes	—
772	C₂²×C₄	#41×C₃₁	1	4	yes	—
773	C₂²×C₄	#41×C₃₁	1	4	yes	—
774	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
775	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
776	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
777	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
778	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
779	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
780	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
781	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
782	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
783	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
784	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
785	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
786	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
787	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
788	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
789	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
790	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
791	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
792	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
793	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
794	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
795	C₄⋊C₄	—	2	4	no	—
796	C₄⋊C₄	—	2	4	no	—
797	C₄⋊C₄	—	2	4	no	—
798	C₄⋊C₄	—	2	2	no	—
799	C₄⋊C₄	—	2	2	no	—
800	C₄⋊C₄	—	2	4	no	—
801	C₄⋊C₄	—	2	2	no	—
802	C₄⋊C₄	—	2	2	no	—
803	C₄⋊C₄	—	2	4	no	—
804	C₄⋊C₄	—	2	4	no	—
805	C₄⋊C₄	—	2	4	no	—
806	C₄⋊C₄	—	2	4	no	—
807	C₄⋊C₄	—	2	4	no	—
808	C₄⋊C₄	—	2	2	no	—
809	C₄⋊C₄	—	2	2	no	—
810	C₄⋊C₄	—	2	4	no	—
811	C₄⋊C₄	—	2	4	no	—
812	C₄⋊C₄	—	2	4	no	—
813	C₂²⋊C₄	—	2	4	no	—
814	C₂²⋊C₄	—	2	4	no	—
815	C₂²⋊C₄	—	2	4	no	—
816	C₂²⋊C₄	—	2	4	no	—
817	C₂²⋊C₄	—	2	4	no	—
818	C₂²⋊C₄	—	2	4	no	—
819	C₂²⋊C₄	—	2	4	no	—
820	C₂²⋊C₄	—	2	4	no	—
821	C₂²⋊C₄	—	2	4	no	—
822	C₂²⋊C₄	—	2	4	no	—
823	C₂²⋊C₄	—	2	4	no	—
824	C₂²⋊C₄	—	2	4	no	—
825	C₂²⋊C₄	—	2	4	no	—
826	C₂²⋊C₄	—	2	4	no	—
827	C₂²⋊C₄	—	2	4	no	—
828	C₄²	—	2	2	no	—
829	C₄²	—	2	2	no	—
830	C₄²	—	2	2	no	—
831	C₄²	—	2	2	no	—
832	C₄²	—	2	2	no	—
833	C₄²	—	2	2	no	—
834	C₄²	—	2	2	no	—
835	C₄²	—	2	2	no	—
836	C₄²	—	2	2	no	—
837	C₄²	—	2	2	no	—
838	C₄²	—	2	2	no	—
839	C₄²	—	2	2	no	—
840	C₄²	—	2	2	no	—
841	C₄²	—	2	2	no	—
842	C₄²	—	2	2	no	—
843	C₄²	—	2	2	no	—
844	C₄²	—	2	2	no	—
845	C₄²	—	2	2	no	—
846	C₄²	—	2	2	no	—
847	C₄²	—	2	2	no	—
848	C₄²	—	2	2	no	—
849	C₄²	—	2	2	no	—
850	C₄²	—	2	2	no	—
851	C₄²	—	2	2	no	—
852	C₄²	—	2	4	no	—
853	C₄²	—	2	4	no	—
854	C₄²	—	2	4	no	—
855	C₄²	#41×C₃₁	1	4	yes	—
856	C₄²	#41×C₃₁	1	4	yes	—
857	C₄²	#41×C₃₁	1	4	yes	—
858	C₄²	#41×C₃₁	1	4	yes	—
859	C₂³	—	2	1	no	—
860	C₂³	—	2	1	no	—
861	C₂³	—	2	1	no	—
862	C₂³	—	2	1	no	—
863	C₂³	—	2	2	no	—
864	C₂³	—	2	2	no	—
865	C₂³	—	2	2	no	—
866	C₂³	—	2	2	no	—
867	C₂³	—	2	2	no	—
868	C₂³	—	2	2	no	—
869	C₂³	—	2	2	no	—
870	C₂³	C₂×#41×C₃₁	1	2	yes	—
871	C₂³	C₂×#41×C₃₁	1	2	yes	—
872	C₂³	C₂×#41×C₃₁	1	2	yes	—
873	C₂³	C₂⁵×C₃₁	1	1	yes	characteristic
874	Q₈	—	4	4	no	—
875	D₄	—	4	8	no	—
876	D₄	—	4	4	no	—
877	C₂×C₄	—	2	8	no	—
878	C₂×C₄	—	2	8	no	—
879	C₂×C₄	—	2	8	no	—
880	C₂×C₄	—	2	8	no	—
881	C₂×C₄	—	2	8	no	—
882	C₂×C₄	—	2	1	no	—
883	C₂×C₄	—	2	1	no	—
884	C₂×C₄	—	2	1	no	—
885	C₂×C₄	—	2	1	no	—
886	C₂×C₄	—	2	1	no	—
887	C₂×C₄	—	2	1	no	—
888	C₂×C₄	—	2	1	no	—
889	C₂×C₄	—	2	1	no	—
890	C₂×C₄	—	2	1	no	—
891	C₂×C₄	—	2	1	no	—
892	C₂×C₄	—	2	1	no	—
893	C₂×C₄	—	2	1	no	—
894	C₂×C₄	—	2	1	no	—
895	C₂×C₄	—	2	1	no	—
896	C₂×C₄	—	2	1	no	—
897	C₂×C₄	—	2	1	no	—
898	C₂×C₄	—	2	1	no	—
899	C₂×C₄	—	2	1	no	—
900	C₂×C₄	—	2	1	no	—
901	C₂×C₄	—	2	1	no	—
902	C₂×C₄	—	2	1	no	—
903	C₂×C₄	—	2	1	no	—
904	C₂×C₄	—	2	1	no	—
905	C₂×C₄	—	2	1	no	—
906	C₂×C₄	—	2	8	no	—
907	C₂×C₄	—	2	8	no	—
908	C₂×C₄	—	2	2	no	—
909	C₂×C₄	—	2	2	no	—
910	C₂×C₄	—	2	2	no	—
911	C₂×C₄	—	2	2	no	—
912	C₂×C₄	—	2	2	no	—
913	C₂×C₄	—	2	2	no	—
914	C₂×C₄	—	2	2	no	—
915	C₂×C₄	—	2	2	no	—
916	C₂×C₄	—	2	2	no	—
917	C₂×C₄	—	2	2	no	—
918	C₂×C₄	—	2	2	no	—
919	C₂×C₄	—	2	2	no	—
920	C₂×C₄	—	2	2	no	—
921	C₂×C₄	—	2	2	no	—
922	C₂×C₄	—	2	2	no	—
923	C₂×C₄	—	2	2	no	—
924	C₂×C₄	—	2	2	no	—
925	C₂×C₄	—	2	2	no	—
926	C₂×C₄	—	2	2	no	—
927	C₂×C₄	—	2	2	no	—
928	C₂×C₄	—	2	2	no	—
929	C₂×C₄	—	4	8	no	—
930	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
931	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
932	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
933	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
934	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
935	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
936	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
937	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
938	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
939	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
940	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
941	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
942	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
943	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
944	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
945	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
946	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
947	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
948	C₂²	—	2	2	no	—
949	C₂²	—	2	2	no	—
950	C₂²	—	2	2	no	—
951	C₂²	—	2	2	no	—
952	C₂²	—	2	2	no	—
953	C₂²	—	2	2	no	—
954	C₂²	—	4	2	no	—
955	C₂²	—	4	2	no	—
956	C₂²	—	4	2	no	—
957	C₂²	—	4	2	no	—
958	C₂²	—	4	2	no	—
959	C₂²	—	4	2	no	—
960	C₂²	—	4	2	no	—
961	C₂²	C₃₁×#529	1	4	yes	—
962	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
963	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
964	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
965	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
966	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
967	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
968	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
969	C₄	—	2	2	no	—
970	C₄	—	2	2	no	—
971	C₄	—	2	2	no	—
972	C₄	—	2	2	no	—
973	C₄	—	2	2	no	—
974	C₄	—	2	2	no	—
975	C₄	—	2	2	no	—
976	C₄	—	2	2	no	—
977	C₄	—	2	2	no	—
978	C₄	—	2	2	no	—
979	C₄	—	2	2	no	—
980	C₄	—	2	2	no	—
981	C₄	—	4	2	no	—
982	C₄	—	4	2	no	—
983	C₄	—	4	2	no	—
984	C₄	—	4	2	no	—
985	C₄	—	4	2	no	—
986	C₄	—	4	2	no	—
987	C₄	—	4	2	no	—
988	C₄	C₃₁×#529	1	4	yes	—
989	C₄	C₃₁×#529	1	4	yes	—
990	C₂	—	2	4	no	—
991	C₂	—	8	2	no	—
992	C₂	C₂×C₃₁×#529	1	1	yes	characteristic
993	C₂	C₂×C₃₁×#529	1	1	yes	characteristic
994	C₂	C₂×C₃₁×#529	1	1	yes	characteristic
995	C₂	C₃₁×#3444	1	1	yes	characteristic
996	C₂	C₃₁×#3444	1	1	yes	characteristic
997	C₂	C₃₁×#3444	1	1	yes	characteristic
998	C₂	C₃₁×#3444	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₃₁	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₃₁
socle	C₂³×C₃₁	C₂⁵
prime radical	C₂×C₃₁×#121	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#2866	C₂	semidirect
2. C₃₁×#2865	C₂	semidirect
3. C₃₁×#2864	C₂	semidirect
4. C₃₁×#2863	C₂	semidirect
5. C₃₁×#2861	C₂	semidirect
6. C₃₁×#2860	C₂	semidirect
7. C₃₁×#2855	C₂	semidirect
9. C₃₁×#2853	C₂	semidirect
10. C₃₁×#2852	C₂	semidirect
11. C₃₁×#2851	C₂	semidirect
13. C₄×C₃₁×#125	C₂	semidirect
14. C₄×C₃₁×#126	C₂	semidirect
15. C₄×C₃₁×#124	C₂	semidirect
16. C₄×C₃₁×C₂²⋊Q₈	C₂	semidirect
17. C₄×C₃₁×#123	C₂	semidirect
19. C₃₁×#2298	C₂	semidirect
20. C₃₁×#2295	C₂	semidirect
21. C₃₁×#2293	C₂	semidirect
22. C₃₁×#2290	C₂	semidirect
23. C₂×C₄³×C₃₁	C₂	semidirect
359. #36638	C₃₁	direct (N × H)
449. #2866	C₂×C₃₁	semidirect
450. #2865	C₂×C₃₁	semidirect
451. #2864	C₂×C₃₁	semidirect
452. #2863	C₂×C₃₁	semidirect
453. #2861	C₂×C₃₁	semidirect
454. #2860	C₂×C₃₁	semidirect
455. #2855	C₂×C₃₁	semidirect
457. #2853	C₂×C₃₁	semidirect
458. #2852	C₂×C₃₁	semidirect
459. #2851	C₂×C₃₁	semidirect
461. C₄×#125	C₂×C₃₁	semidirect
462. C₄×#126	C₂×C₃₁	semidirect
463. C₄×#124	C₂×C₃₁	semidirect
464. C₄×C₂²⋊Q₈	C₂×C₃₁	semidirect
465. C₄×#123	C₂×C₃₁	semidirect
467. #2298	C₂×C₃₁	semidirect
468. #2295	C₂×C₃₁	semidirect
469. #2293	C₂×C₃₁	semidirect
470. #2290	C₂×C₃₁	semidirect
471. C₂×C₄³	C₂×C₃₁	semidirect
738. C₃₁	#36638	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×#2866	2
C₃₁×#2865	2
C₃₁×#2864	2
C₃₁×#2863	2
C₃₁×#2861	2
C₃₁×#2860	2
C₃₁×#2855	2
C₃₁×#2854	2
C₃₁×#2853	2
C₃₁×#2852	2
C₃₁×#2851	2
C₃₁×#2850	2
C₄×C₃₁×#125	2
C₄×C₃₁×#126	2
C₄×C₃₁×#124	2
C₄×C₃₁×C₂²⋊Q₈	2
C₄×C₃₁×#123	2
C₄×C₃₁×#121	2
C₃₁×#2298	2
C₃₁×#2295	2
C₃₁×#2293	2
C₃₁×#2290	2
C₂×C₄³×C₃₁	2
#36638	31

Subgroups — C31×#36638 #21493397

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#36638 #21493397