Subgroups — C₃₁×#34261 #21491020

Order 7936.

2718 conjugacy classes of subgroups.

The subgroup lattice has 1068 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#518	C₂	1	1	yes	maximal, characteristic
2	C₃₁×#2357	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#2354	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#2353	C₂	1	2	yes	maximal, complemented
5	C₃₁×#2352	C₂	1	2	yes	maximal, complemented
6	C₃₁×#2349	C₂	1	1	yes	maximal, characteristic, complemented
7	D₄×C₄⋊C₄×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#2347	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#2346	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#2342	C₂	1	2	yes	maximal, complemented
11	C₃₁×#2342	C₂	1	2	yes	maximal, complemented
12	D₄×C₂²⋊C₄×C₃₁	C₂	1	1	yes	maximal, characteristic
13	D₄×C₂²⋊C₄×C₃₁	C₂	1	1	yes	maximal, characteristic
14	C₃₁×#2319	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#2318	C₂	1	2	yes	maximal, complemented
16	C₃₁×#2314	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#2312	C₂	1	2	yes	maximal, complemented
18	C₃₁×#2298	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#2293	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃₁×#2290	C₂	1	2	yes	maximal, complemented
21	C₂×C₃₁×#388	C₂	1	2	yes	maximal, complemented
22	C₃₁×#2275	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄²×D₄×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂³×D₄×C₃₁	C₂²	1	1	yes	characteristic
25	C₃₁×#518	C₄	1	16	yes	complemented
26	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
27	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
28	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
29	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
30	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
31	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
32	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
33	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
34	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
35	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
36	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
37	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
38	C₂×C₃₁×#117	C₂²	1	2	yes	complemented
39	C₂×C₃₁×#117	C₂²	1	2	yes	complemented
40	C₂²×C₄⋊C₄×C₃₁	C₂²	1	2	yes	complemented
41	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
42	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
43	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
44	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
45	C₂²×C₄²×C₃₁	C₂²	1	2	yes	complemented
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×#390	C₂²	1	1	yes	characteristic
50	C₃₁×#389	C₂²	1	1	yes	characteristic, complemented
51	C₃₁×#389	C₂²	1	1	yes	characteristic, complemented
52	C₃₁×#389	C₂²	1	1	yes	characteristic, complemented
53	C₃₁×#389	C₂²	1	1	yes	characteristic, complemented
54	C₃₁×#388	C₂²	1	1	yes	characteristic
55	C₃₁×#388	C₂²	1	2	yes	—
56	C₃₁×#388	C₂²	1	2	yes	—
57	C₃₁×#388	C₂²	1	2	yes	—
58	C₃₁×#388	C₂²	1	2	yes	—
59	C₃₁×#388	C₂²	1	1	yes	characteristic
60	C₃₁×#388	C₂²	1	1	yes	characteristic
61	C₃₁×#388	C₂²	1	2	yes	—
62	C₃₁×#388	C₂²	1	2	yes	—
63	C₃₁×#388	C₂²	1	1	yes	characteristic
64	C₃₁×#388	C₂²	1	2	yes	complemented
65	C₃₁×#388	C₂²	1	2	yes	complemented
66	C₃₁×#388	C₂²	1	2	yes	complemented
67	C₃₁×#388	C₂²	1	2	yes	complemented
68	C₃₁×#388	C₂²	1	2	yes	complemented
69	C₃₁×#388	C₂²	1	2	yes	complemented
70	C₃₁×#388	C₂²	1	2	yes	complemented
71	C₃₁×#388	C₂²	1	2	yes	complemented
72	C₃₁×#387	C₂²	1	2	yes	complemented
73	C₃₁×#387	C₂²	1	2	yes	complemented
74	C₃₁×#387	C₂²	1	1	yes	characteristic, complemented
75	C₃₁×#387	C₂²	1	1	yes	characteristic, complemented
76	C₃₁×#387	C₂²	1	1	yes	characteristic, complemented
77	C₃₁×#387	C₂²	1	1	yes	characteristic, complemented
78	C₃₁×#386	C₂²	1	2	yes	—
79	C₃₁×#386	C₂²	1	2	yes	—
80	C₃₁×#386	C₂²	1	2	yes	—
81	C₃₁×#386	C₂²	1	2	yes	—
82	C₃₁×#385	C₂²	1	2	yes	complemented
83	C₃₁×#385	C₂²	1	2	yes	complemented
84	C₃₁×#385	C₂²	1	2	yes	complemented
85	C₃₁×#385	C₂²	1	2	yes	complemented
86	C₃₁×#384	C₂²	1	1	yes	characteristic, complemented
87	C₃₁×#383	C₂²	1	2	yes	complemented
88	C₃₁×#382	C₂²	1	1	yes	characteristic, complemented
89	C₃₁×#382	C₂²	1	2	yes	complemented
90	C₃₁×#381	C₂²	1	2	yes	complemented
91	C₃₁×#381	C₂²	1	2	yes	complemented
92	C₃₁×#380	C₂²	1	1	yes	characteristic
93	C₃₁×#380	C₂²	1	1	yes	characteristic
94	C₃₁×#380	C₂²	1	2	yes	complemented
95	C₃₁×#380	C₂²	1	2	yes	complemented
96	C₃₁×#380	C₂²	1	2	yes	complemented
97	C₃₁×#380	C₂²	1	2	yes	complemented
98	C₃₁×#379	C₂²	1	2	yes	—
99	C₃₁×#379	C₂²	1	2	yes	—
100	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
101	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
102	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
103	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
104	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	complemented
105	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
106	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
107	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
108	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
109	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
110	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
111	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	complemented
112	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	complemented
113	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	complemented
114	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	complemented
115	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	complemented
116	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	complemented
117	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	complemented
118	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	complemented
119	C₃₁×#376	C₂²	1	1	yes	characteristic, complemented
120	C₃₁×#376	C₂²	1	2	yes	complemented
121	C₂×C₃₁×#95	C₂²	1	2	yes	complemented
122	C₂×C₃₁×#95	C₂²	1	2	yes	complemented
123	C₄³×C₃₁	C₂²	1	1	yes	characteristic, complemented
124	C₂⁵×C₃₁	C₂³	1	2	yes	—
125	C₂²×D₄×C₃₁	—	2	4	no	—
126	C₂²×D₄×C₃₁	—	2	4	no	—
127	C₂²×D₄×C₃₁	C₂×C₄	1	8	yes	—
128	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
129	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
130	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
131	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
132	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
133	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
134	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
135	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
136	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
137	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
138	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
139	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
140	C₄×D₄×C₃₁	—	2	4	no	—
141	C₄×D₄×C₃₁	—	2	4	no	—
142	C₄×D₄×C₃₁	—	2	4	no	—
143	C₄×D₄×C₃₁	—	2	4	no	—
144	C₄×D₄×C₃₁	C₂×C₄	1	8	yes	—
145	C₄×D₄×C₃₁	C₂×C₄	1	8	yes	—
146	C₄×D₄×C₃₁	C₂×C₄	1	8	yes	complemented
147	C₄×D₄×C₃₁	C₂×C₄	1	8	yes	complemented
148	C₄×D₄×C₃₁	C₂×C₄	1	16	yes	complemented
149	C₄×D₄×C₃₁	C₂×C₄	1	16	yes	complemented
150	C₃₁×#117	—	4	4	no	—
151	C₃₁×#117	—	4	4	no	—
152	C₃₁×#117	C₂×C₄	1	8	yes	complemented
153	C₃₁×#117	C₂×C₄	1	8	yes	complemented
154	C₂×C₄⋊C₄×C₃₁	—	4	4	no	—
155	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
156	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
157	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
158	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
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	1	yes	characteristic
167	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
168	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
169	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
170	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
171	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
172	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
173	C₂×C₂²⋊C₄×C₃₁	—	4	4	no	—
174	C₂×C₂²⋊C₄×C₃₁	—	4	4	no	—
175	C₂×C₂²⋊C₄×C₃₁	C₂×C₄	1	16	yes	complemented
176	C₂×C₂²⋊C₄×C₃₁	C₂×C₄	1	16	yes	complemented
177	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
178	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
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×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
183	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
184	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
185	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
186	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
187	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
188	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
189	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
190	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
191	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
192	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
193	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
194	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
195	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
196	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
197	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
198	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
199	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
200	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
201	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
202	C₂×C₄²×C₃₁	—	4	4	no	—
203	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
204	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
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	1	yes	characteristic
209	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
210	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
211	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
212	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
213	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
214	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
215	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
216	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
217	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
218	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
219	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
220	C₃₁×#95	C₂³	1	1	yes	characteristic
221	C₃₁×#95	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
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	2	yes	—
233	C₃₁×#95	C₂³	1	2	yes	—
234	C₃₁×#95	C₂³	1	1	yes	characteristic
235	C₃₁×#95	C₂³	1	1	yes	characteristic
236	C₃₁×#95	C₂³	1	1	yes	characteristic
237	C₃₁×#95	C₂³	1	2	yes	—
238	C₃₁×#95	C₂³	1	2	yes	—
239	C₃₁×#95	C₂³	1	2	yes	—
240	C₃₁×#95	C₂³	1	1	yes	characteristic
241	C₃₁×#95	C₂³	1	2	yes	—
242	C₃₁×#95	C₂³	1	2	yes	—
243	C₃₁×#95	C₂³	1	2	yes	—
244	C₃₁×#95	C₂³	1	1	yes	characteristic
245	C₃₁×#95	C₂³	1	1	yes	characteristic
246	C₂⁴×C₃₁	—	2	4	no	—
247	C₂⁴×C₃₁	—	2	4	no	—
248	C₂⁴×C₃₁	—	4	2	no	—
249	C₂⁴×C₃₁	—	4	2	no	—
250	C₂⁴×C₃₁	—	4	2	no	—
251	C₂⁴×C₃₁	—	4	2	no	—
252	C₂⁴×C₃₁	C₂²×C₄	1	8	yes	—
253	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
254	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
255	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
256	C₂×D₄×C₃₁	—	2	4	no	—
257	C₂×D₄×C₃₁	—	2	4	no	—
258	C₂×D₄×C₃₁	—	2	32	no	—
259	C₂×D₄×C₃₁	—	2	2	no	—
260	C₂×D₄×C₃₁	—	2	2	no	—
261	C₂×D₄×C₃₁	C₂²×C₄	1	8	yes	—
262	C₂×D₄×C₃₁	C₂²×C₄	1	4	yes	—
263	C₂×D₄×C₃₁	C₂²×C₄	1	4	yes	—
264	C₂×D₄×C₃₁	#41	1	4	yes	—
265	C₂×D₄×C₃₁	#41	1	4	yes	—
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	—	2	4	no	—
272	C₂²×C₄×C₃₁	—	2	4	no	—
273	C₂²×C₄×C₃₁	—	2	4	no	—
274	C₂²×C₄×C₃₁	—	4	2	no	—
275	C₂²×C₄×C₃₁	—	4	2	no	—
276	C₂²×C₄×C₃₁	—	4	2	no	—
277	C₂²×C₄×C₃₁	—	4	2	no	—
278	C₂²×C₄×C₃₁	—	4	2	no	—
279	C₂²×C₄×C₃₁	—	4	2	no	—
280	C₂²×C₄×C₃₁	—	4	2	no	—
281	C₂²×C₄×C₃₁	—	4	2	no	—
282	C₂²×C₄×C₃₁	—	4	2	no	—
283	C₂²×C₄×C₃₁	—	4	2	no	—
284	C₂²×C₄×C₃₁	—	4	2	no	—
285	C₂²×C₄×C₃₁	—	4	2	no	—
286	C₂²×C₄×C₃₁	—	4	2	no	—
287	C₂²×C₄×C₃₁	—	4	2	no	—
288	C₂²×C₄×C₃₁	C₂²×C₄	1	4	yes	—
289	C₂²×C₄×C₃₁	C₂²×C₄	1	8	yes	—
290	C₂²×C₄×C₃₁	C₂²×C₄	1	8	yes	—
291	C₂²×C₄×C₃₁	C₂²×C₄	1	8	yes	—
292	C₂²×C₄×C₃₁	C₂²×C₄	1	8	yes	—
293	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
294	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
295	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
296	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
297	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
298	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
299	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
300	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
301	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
302	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
303	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
304	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
305	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
306	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
307	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
308	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
309	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
310	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
311	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
312	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
313	C₄⋊C₄×C₃₁	—	2	2	no	—
314	C₄⋊C₄×C₃₁	—	2	2	no	—
315	C₄⋊C₄×C₃₁	—	2	2	no	—
316	C₄⋊C₄×C₃₁	—	2	2	no	—
317	C₄⋊C₄×C₃₁	—	2	2	no	—
318	C₄⋊C₄×C₃₁	—	2	4	no	—
319	C₄⋊C₄×C₃₁	—	2	2	no	—
320	C₄⋊C₄×C₃₁	—	4	2	no	—
321	C₄⋊C₄×C₃₁	—	4	2	no	—
322	C₄⋊C₄×C₃₁	—	4	1	no	—
323	C₄⋊C₄×C₃₁	—	4	1	no	—
324	C₄⋊C₄×C₃₁	—	4	2	no	—
325	C₄⋊C₄×C₃₁	—	4	2	no	—
326	C₄⋊C₄×C₃₁	—	4	2	no	—
327	C₄⋊C₄×C₃₁	C₂²×C₄	1	4	yes	—
328	C₄⋊C₄×C₃₁	C₂²×C₄	1	4	yes	—
329	C₄⋊C₄×C₃₁	C₂²×C₄	1	4	yes	—
330	C₄⋊C₄×C₃₁	C₂²×C₄	1	4	yes	—
331	C₂²⋊C₄×C₃₁	—	2	4	no	—
332	C₂²⋊C₄×C₃₁	—	2	4	no	—
333	C₂²⋊C₄×C₃₁	—	2	4	no	—
334	C₂²⋊C₄×C₃₁	—	2	4	no	—
335	C₂²⋊C₄×C₃₁	—	2	2	no	—
336	C₂²⋊C₄×C₃₁	—	2	2	no	—
337	C₂²⋊C₄×C₃₁	—	2	4	no	—
338	C₂²⋊C₄×C₃₁	—	2	4	no	—
339	C₂²⋊C₄×C₃₁	—	4	2	no	—
340	C₂²⋊C₄×C₃₁	—	4	2	no	—
341	C₂²⋊C₄×C₃₁	—	4	2	no	—
342	C₂²⋊C₄×C₃₁	—	4	2	no	—
343	C₂²⋊C₄×C₃₁	—	4	1	no	—
344	C₂²⋊C₄×C₃₁	—	4	2	no	—
345	C₂²⋊C₄×C₃₁	—	4	1	no	—
346	C₂²⋊C₄×C₃₁	—	4	2	no	—
347	C₂²⋊C₄×C₃₁	—	4	2	no	—
348	C₂²⋊C₄×C₃₁	—	4	2	no	—
349	C₂²⋊C₄×C₃₁	C₂²×C₄	1	4	yes	—
350	C₂²⋊C₄×C₃₁	C₂²×C₄	1	4	yes	—
351	C₂²⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
352	C₂²⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
353	C₂²⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
354	C₂²⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
355	C₂²⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
356	C₄²×C₃₁	—	2	2	no	—
357	C₄²×C₃₁	—	2	2	no	—
358	C₄²×C₃₁	—	2	2	no	—
359	C₄²×C₃₁	—	2	2	no	—
360	C₄²×C₃₁	—	2	2	no	—
361	C₄²×C₃₁	—	2	4	no	—
362	C₄²×C₃₁	—	2	2	no	—
363	C₄²×C₃₁	—	4	2	no	—
364	C₄²×C₃₁	—	4	2	no	—
365	C₄²×C₃₁	—	4	1	no	—
366	C₄²×C₃₁	—	4	2	no	—
367	C₄²×C₃₁	—	4	1	no	—
368	C₄²×C₃₁	—	4	2	no	—
369	C₄²×C₃₁	—	4	2	no	—
370	C₄²×C₃₁	C₂²×C₄	1	4	yes	—
371	C₄²×C₃₁	C₂²×C₄	1	4	yes	—
372	C₄²×C₃₁	C₂²×C₄	1	8	yes	—
373	#34261	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
374	C₂³×C₃₁	—	2	2	no	—
375	C₂³×C₃₁	—	2	2	no	—
376	C₂³×C₃₁	—	2	2	no	—
377	C₂³×C₃₁	—	2	2	no	—
378	C₂³×C₃₁	—	2	1	no	—
379	C₂³×C₃₁	—	2	1	no	—
380	C₂³×C₃₁	—	2	2	no	—
381	C₂³×C₃₁	—	2	2	no	—
382	C₂³×C₃₁	—	2	2	no	—
383	C₂³×C₃₁	—	2	2	no	—
384	C₂³×C₃₁	—	2	1	no	—
385	C₂³×C₃₁	—	2	1	no	—
386	C₂³×C₃₁	—	2	2	no	—
387	C₂³×C₃₁	—	2	2	no	—
388	C₂³×C₃₁	—	2	1	no	—
389	C₂³×C₃₁	—	2	1	no	—
390	C₂³×C₃₁	—	2	16	no	—
391	C₂³×C₃₁	—	4	8	no	—
392	C₂³×C₃₁	—	4	8	no	—
393	C₂³×C₃₁	—	8	4	no	—
394	C₂³×C₃₁	—	8	4	no	—
395	C₂³×C₃₁	—	8	4	no	—
396	C₂³×C₃₁	—	8	4	no	—
397	C₂³×C₃₁	C₂³×C₄	1	2	yes	—
398	C₂³×C₃₁	C₂³×C₄	1	4	yes	—
399	C₂³×C₃₁	C₂³×C₄	1	4	yes	—
400	C₂³×C₃₁	C₂×#41	1	4	yes	—
401	C₂³×C₃₁	C₂×#41	1	4	yes	—
402	C₂³×C₃₁	C₂⁵	1	1	yes	characteristic
403	D₄×C₃₁	—	2	16	no	—
404	D₄×C₃₁	—	2	8	no	—
405	D₄×C₃₁	#117	1	16	yes	complemented
406	C₂×C₄×C₃₁	—	2	1	no	—
407	C₂×C₄×C₃₁	—	2	1	no	—
408	C₂×C₄×C₃₁	—	2	1	no	—
409	C₂×C₄×C₃₁	—	2	1	no	—
410	C₂×C₄×C₃₁	—	2	1	no	—
411	C₂×C₄×C₃₁	—	2	2	no	—
412	C₂×C₄×C₃₁	—	2	1	no	—
413	C₂×C₄×C₃₁	—	2	1	no	—
414	C₂×C₄×C₃₁	—	2	1	no	—
415	C₂×C₄×C₃₁	—	2	1	no	—
416	C₂×C₄×C₃₁	—	2	2	no	—
417	C₂×C₄×C₃₁	—	2	1	no	—
418	C₂×C₄×C₃₁	—	2	2	no	—
419	C₂×C₄×C₃₁	—	2	1	no	—
420	C₂×C₄×C₃₁	—	2	1	no	—
421	C₂×C₄×C₃₁	—	2	1	no	—
422	C₂×C₄×C₃₁	—	2	2	no	—
423	C₂×C₄×C₃₁	—	2	1	no	—
424	C₂×C₄×C₃₁	—	2	8	no	—
425	C₂×C₄×C₃₁	—	2	1	no	—
426	C₂×C₄×C₃₁	—	2	1	no	—
427	C₂×C₄×C₃₁	—	2	1	no	—
428	C₂×C₄×C₃₁	—	2	1	no	—
429	C₂×C₄×C₃₁	—	2	1	no	—
430	C₂×C₄×C₃₁	—	2	1	no	—
431	C₂×C₄×C₃₁	—	2	2	no	—
432	C₂×C₄×C₃₁	—	2	2	no	—
433	C₂×C₄×C₃₁	—	2	2	no	—
434	C₂×C₄×C₃₁	—	2	2	no	—
435	C₂×C₄×C₃₁	—	2	2	no	—
436	C₂×C₄×C₃₁	—	2	1	no	—
437	C₂×C₄×C₃₁	—	2	1	no	—
438	C₂×C₄×C₃₁	—	2	2	no	—
439	C₂×C₄×C₃₁	—	2	2	no	—
440	C₂×C₄×C₃₁	—	2	2	no	—
441	C₂×C₄×C₃₁	—	2	2	no	—
442	C₂×C₄×C₃₁	—	2	1	no	—
443	C₂×C₄×C₃₁	—	2	1	no	—
444	C₂×C₄×C₃₁	—	2	2	no	—
445	C₂×C₄×C₃₁	—	2	1	no	—
446	C₂×C₄×C₃₁	—	2	1	no	—
447	C₂×C₄×C₃₁	—	2	1	no	—
448	C₂×C₄×C₃₁	—	2	1	no	—
449	C₂×C₄×C₃₁	—	2	1	no	—
450	C₂×C₄×C₃₁	—	2	2	no	—
451	C₂×C₄×C₃₁	—	2	1	no	—
452	C₂×C₄×C₃₁	—	2	1	no	—
453	C₂×C₄×C₃₁	—	2	2	no	—
454	C₂×C₄×C₃₁	—	2	1	no	—
455	C₂×C₄×C₃₁	—	4	8	no	—
456	C₂×C₄×C₃₁	—	4	8	no	—
457	C₂×C₄×C₃₁	—	4	8	no	—
458	C₂×C₄×C₃₁	—	4	8	no	—
459	C₂×C₄×C₃₁	—	4	8	no	—
460	C₂×C₄×C₃₁	—	4	8	no	—
461	C₂×C₄×C₃₁	—	8	4	no	—
462	C₂×C₄×C₃₁	—	8	4	no	—
463	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
464	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
465	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
466	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
467	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
468	C₂×C₄×C₃₁	C₂³×C₄	1	4	yes	—
469	C₂×C₄×C₃₁	C₂³×C₄	1	4	yes	—
470	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
471	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
472	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
473	C₂×C₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
474	C₂×C₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
475	C₂×#518	C₂×C₃₁	1	1	yes	characteristic
476	#2357	C₂×C₃₁	1	1	yes	characteristic, complemented
477	#2354	C₂×C₃₁	1	1	yes	characteristic, complemented
478	#2353	C₂×C₃₁	1	2	yes	complemented
479	#2352	C₂×C₃₁	1	2	yes	complemented
480	#2349	C₂×C₃₁	1	1	yes	characteristic, complemented
481	D₄×C₄⋊C₄	C₂×C₃₁	1	1	yes	characteristic, complemented
482	#2347	C₂×C₃₁	1	1	yes	characteristic, complemented
483	#2346	C₂×C₃₁	1	1	yes	characteristic, complemented
484	#2342	C₂×C₃₁	1	2	yes	complemented
485	#2342	C₂×C₃₁	1	2	yes	complemented
486	D₄×C₂²⋊C₄	C₂×C₃₁	1	1	yes	characteristic
487	D₄×C₂²⋊C₄	C₂×C₃₁	1	1	yes	characteristic
488	#2319	C₂×C₃₁	1	1	yes	characteristic, complemented
489	#2318	C₂×C₃₁	1	2	yes	complemented
490	#2314	C₂×C₃₁	1	1	yes	characteristic, complemented
491	#2312	C₂×C₃₁	1	2	yes	complemented
492	#2298	C₂×C₃₁	1	1	yes	characteristic, complemented
493	#2293	C₂×C₃₁	1	1	yes	characteristic, complemented
494	#2290	C₂×C₃₁	1	2	yes	complemented
495	C₂×#388	C₂×C₃₁	1	2	yes	complemented
496	#2275	C₂×C₃₁	1	1	yes	characteristic, complemented
497	C₄²×D₄	C₂×C₃₁	1	1	yes	characteristic, complemented
498	C₂²×C₃₁	—	2	4	no	—
499	C₂²×C₃₁	—	2	4	no	—
500	C₂²×C₃₁	—	2	4	no	—
501	C₂²×C₃₁	—	2	4	no	—
502	C₂²×C₃₁	—	2	4	no	—
503	C₂²×C₃₁	—	2	4	no	—
504	C₂²×C₃₁	—	2	2	no	—
505	C₂²×C₃₁	—	2	4	no	—
506	C₂²×C₃₁	—	2	4	no	—
507	C₂²×C₃₁	—	2	4	no	—
508	C₂²×C₃₁	—	2	2	no	—
509	C₂²×C₃₁	—	2	2	no	—
510	C₂²×C₃₁	—	4	2	no	—
511	C₂²×C₃₁	—	4	1	no	—
512	C₂²×C₃₁	—	4	2	no	—
513	C₂²×C₃₁	—	4	1	no	—
514	C₂²×C₃₁	—	4	2	no	—
515	C₂²×C₃₁	—	4	1	no	—
516	C₂²×C₃₁	—	4	2	no	—
517	C₂²×C₃₁	—	4	1	no	—
518	C₂²×C₃₁	—	8	16	no	—
519	C₂²×C₃₁	C₂×#117	1	8	yes	—
520	C₂²×C₃₁	C₂⁴×C₄	1	1	yes	characteristic
521	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
522	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
523	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
524	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
525	C₂²×C₃₁	#585	1	1	yes	characteristic
526	C₂²×C₃₁	#585	1	1	yes	characteristic
527	C₄×C₃₁	—	2	2	no	—
528	C₄×C₃₁	—	2	2	no	—
529	C₄×C₃₁	—	2	4	no	—
530	C₄×C₃₁	—	2	2	no	—
531	C₄×C₃₁	—	2	2	no	—
532	C₄×C₃₁	—	2	2	no	—
533	C₄×C₃₁	—	2	4	no	—
534	C₄×C₃₁	—	2	2	no	—
535	C₄×C₃₁	—	2	2	no	—
536	C₄×C₃₁	—	4	1	no	—
537	C₄×C₃₁	—	4	2	no	—
538	C₄×C₃₁	—	4	1	no	—
539	C₄×C₃₁	—	4	2	no	—
540	C₄×C₃₁	—	4	1	no	—
541	C₄×C₃₁	—	4	2	no	—
542	C₄×C₃₁	—	4	2	no	—
543	C₄×C₃₁	—	4	1	no	—
544	C₄×C₃₁	—	4	1	no	—
545	C₄×C₃₁	—	4	1	no	—
546	C₄×C₃₁	C₂×#117	1	4	yes	—
547	C₂³×D₄	C₂²×C₃₁	1	1	yes	characteristic
548	#518	C₄×C₃₁	1	16	yes	complemented
549	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
550	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
551	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
552	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
553	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
554	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
555	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
556	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
557	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
558	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
559	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
560	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
561	C₂×#117	C₂²×C₃₁	1	2	yes	complemented
562	C₂×#117	C₂²×C₃₁	1	2	yes	complemented
563	C₂²×C₄⋊C₄	C₂²×C₃₁	1	2	yes	complemented
564	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
565	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
566	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
567	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
568	C₂²×C₄²	C₂²×C₃₁	1	2	yes	complemented
569	#390	C₂²×C₃₁	1	1	yes	characteristic
570	#390	C₂²×C₃₁	1	1	yes	characteristic
571	#390	C₂²×C₃₁	1	1	yes	characteristic
572	#390	C₂²×C₃₁	1	1	yes	characteristic
573	#389	C₂²×C₃₁	1	1	yes	characteristic, complemented
574	#389	C₂²×C₃₁	1	1	yes	characteristic, complemented
575	#389	C₂²×C₃₁	1	1	yes	characteristic, complemented
576	#389	C₂²×C₃₁	1	1	yes	characteristic, complemented
577	#388	C₂²×C₃₁	1	1	yes	characteristic
578	#388	C₂²×C₃₁	1	2	yes	—
579	#388	C₂²×C₃₁	1	2	yes	—
580	#388	C₂²×C₃₁	1	2	yes	—
581	#388	C₂²×C₃₁	1	2	yes	—
582	#388	C₂²×C₃₁	1	1	yes	characteristic
583	#388	C₂²×C₃₁	1	1	yes	characteristic
584	#388	C₂²×C₃₁	1	2	yes	—
585	#388	C₂²×C₃₁	1	2	yes	—
586	#388	C₂²×C₃₁	1	1	yes	characteristic
587	#388	C₂²×C₃₁	1	2	yes	complemented
588	#388	C₂²×C₃₁	1	2	yes	complemented
589	#388	C₂²×C₃₁	1	2	yes	complemented
590	#388	C₂²×C₃₁	1	2	yes	complemented
591	#388	C₂²×C₃₁	1	2	yes	complemented
592	#388	C₂²×C₃₁	1	2	yes	complemented
593	#388	C₂²×C₃₁	1	2	yes	complemented
594	#388	C₂²×C₃₁	1	2	yes	complemented
595	#387	C₂²×C₃₁	1	2	yes	complemented
596	#387	C₂²×C₃₁	1	2	yes	complemented
597	#387	C₂²×C₃₁	1	1	yes	characteristic, complemented
598	#387	C₂²×C₃₁	1	1	yes	characteristic, complemented
599	#387	C₂²×C₃₁	1	1	yes	characteristic, complemented
600	#387	C₂²×C₃₁	1	1	yes	characteristic, complemented
601	#386	C₂²×C₃₁	1	2	yes	—
602	#386	C₂²×C₃₁	1	2	yes	—
603	#386	C₂²×C₃₁	1	2	yes	—
604	#386	C₂²×C₃₁	1	2	yes	—
605	#385	C₂²×C₃₁	1	2	yes	complemented
606	#385	C₂²×C₃₁	1	2	yes	complemented
607	#385	C₂²×C₃₁	1	2	yes	complemented
608	#385	C₂²×C₃₁	1	2	yes	complemented
609	#384	C₂²×C₃₁	1	1	yes	characteristic, complemented
610	#383	C₂²×C₃₁	1	2	yes	complemented
611	#382	C₂²×C₃₁	1	1	yes	characteristic, complemented
612	#382	C₂²×C₃₁	1	2	yes	complemented
613	#381	C₂²×C₃₁	1	2	yes	complemented
614	#381	C₂²×C₃₁	1	2	yes	complemented
615	#380	C₂²×C₃₁	1	1	yes	characteristic
616	#380	C₂²×C₃₁	1	1	yes	characteristic
617	#380	C₂²×C₃₁	1	2	yes	complemented
618	#380	C₂²×C₃₁	1	2	yes	complemented
619	#380	C₂²×C₃₁	1	2	yes	complemented
620	#380	C₂²×C₃₁	1	2	yes	complemented
621	#379	C₂²×C₃₁	1	2	yes	—
622	#379	C₂²×C₃₁	1	2	yes	—
623	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
624	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
625	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
626	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
627	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	complemented
628	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
629	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
630	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
631	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
632	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
633	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
634	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	complemented
635	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	complemented
636	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	complemented
637	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	complemented
638	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	complemented
639	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	complemented
640	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	complemented
641	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	complemented
642	#376	C₂²×C₃₁	1	1	yes	characteristic, complemented
643	#376	C₂²×C₃₁	1	2	yes	complemented
644	C₂×#95	C₂²×C₃₁	1	2	yes	complemented
645	C₂×#95	C₂²×C₃₁	1	2	yes	complemented
646	C₄³	C₂²×C₃₁	1	1	yes	characteristic, complemented
647	C₂×C₃₁	—	2	8	no	—
648	C₂×C₃₁	—	4	4	no	—
649	C₂×C₃₁	—	4	2	no	—
650	C₂×C₃₁	C₂²×#117	1	1	yes	characteristic
651	C₂×C₃₁	C₄×H(5,𝔽₂)	1	1	yes	characteristic
652	C₂×C₃₁	C₄×H(5,𝔽₂)	1	1	yes	characteristic
653	C₂×C₃₁	#3513	1	1	yes	characteristic
654	C₂×C₃₁	#3514	1	1	yes	characteristic
655	C₂×C₃₁	#3519	1	1	yes	characteristic
656	C₂×C₃₁	#3521	1	1	yes	characteristic
657	C₂⁵	C₂³×C₃₁	1	2	yes	—
658	C₂²×D₄	—	2	4	no	—
659	C₂²×D₄	—	2	4	no	—
660	C₂²×D₄	C₂×C₄×C₃₁	1	8	yes	—
661	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
662	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
663	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
664	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
665	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
666	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
667	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
668	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
669	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
670	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
671	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
672	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
673	C₄×D₄	—	2	4	no	—
674	C₄×D₄	—	2	4	no	—
675	C₄×D₄	—	2	4	no	—
676	C₄×D₄	—	2	4	no	—
677	C₄×D₄	C₂×C₄×C₃₁	1	8	yes	—
678	C₄×D₄	C₂×C₄×C₃₁	1	8	yes	—
679	C₄×D₄	C₂×C₄×C₃₁	1	8	yes	complemented
680	C₄×D₄	C₂×C₄×C₃₁	1	8	yes	complemented
681	C₄×D₄	C₂×C₄×C₃₁	1	16	yes	complemented
682	C₄×D₄	C₂×C₄×C₃₁	1	16	yes	complemented
683	#117	—	4	4	no	—
684	#117	—	4	4	no	—
685	#117	C₂×C₄×C₃₁	1	8	yes	complemented
686	#117	C₂×C₄×C₃₁	1	8	yes	complemented
687	C₂×C₄⋊C₄	—	4	4	no	—
688	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
689	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
690	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
691	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
692	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
693	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
694	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
695	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
696	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
697	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
698	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
699	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
700	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
701	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
702	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
703	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
704	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
705	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
706	C₂×C₂²⋊C₄	—	4	4	no	—
707	C₂×C₂²⋊C₄	—	4	4	no	—
708	C₂×C₂²⋊C₄	C₂×C₄×C₃₁	1	16	yes	complemented
709	C₂×C₂²⋊C₄	C₂×C₄×C₃₁	1	16	yes	complemented
710	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
711	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
712	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
713	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
714	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
715	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
716	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
717	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
718	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
719	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
720	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
721	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
722	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
723	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
724	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
725	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
726	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
727	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
728	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
729	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
730	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
731	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
732	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
733	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
734	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
735	C₂×C₄²	—	4	4	no	—
736	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
737	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
738	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
739	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
740	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
741	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
742	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
743	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
744	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
745	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
746	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
747	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
748	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
749	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
750	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
751	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
752	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
753	#95	C₂³×C₃₁	1	1	yes	characteristic
754	#95	C₂³×C₃₁	1	1	yes	characteristic
755	#95	C₂³×C₃₁	1	2	yes	—
756	#95	C₂³×C₃₁	1	2	yes	—
757	#95	C₂³×C₃₁	1	2	yes	—
758	#95	C₂³×C₃₁	1	2	yes	—
759	#95	C₂³×C₃₁	1	2	yes	—
760	#95	C₂³×C₃₁	1	2	yes	—
761	#95	C₂³×C₃₁	1	1	yes	characteristic
762	#95	C₂³×C₃₁	1	1	yes	characteristic
763	#95	C₂³×C₃₁	1	1	yes	characteristic
764	#95	C₂³×C₃₁	1	1	yes	characteristic
765	#95	C₂³×C₃₁	1	2	yes	—
766	#95	C₂³×C₃₁	1	2	yes	—
767	#95	C₂³×C₃₁	1	1	yes	characteristic
768	#95	C₂³×C₃₁	1	1	yes	characteristic
769	#95	C₂³×C₃₁	1	1	yes	characteristic
770	#95	C₂³×C₃₁	1	2	yes	—
771	#95	C₂³×C₃₁	1	2	yes	—
772	#95	C₂³×C₃₁	1	2	yes	—
773	#95	C₂³×C₃₁	1	1	yes	characteristic
774	#95	C₂³×C₃₁	1	2	yes	—
775	#95	C₂³×C₃₁	1	2	yes	—
776	#95	C₂³×C₃₁	1	2	yes	—
777	#95	C₂³×C₃₁	1	1	yes	characteristic
778	#95	C₂³×C₃₁	1	1	yes	characteristic
779	C₃₁	#34261	1	1	yes	characteristic, direct product factor, Sylow
780	C₂⁴	—	2	4	no	—
781	C₂⁴	—	2	4	no	—
782	C₂⁴	—	4	2	no	—
783	C₂⁴	—	4	2	no	—
784	C₂⁴	—	4	2	no	—
785	C₂⁴	—	4	2	no	—
786	C₂⁴	C₂²×C₄×C₃₁	1	8	yes	—
787	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
788	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
789	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
790	C₂×D₄	—	2	4	no	—
791	C₂×D₄	—	2	4	no	—
792	C₂×D₄	—	2	32	no	—
793	C₂×D₄	—	2	2	no	—
794	C₂×D₄	—	2	2	no	—
795	C₂×D₄	C₂²×C₄×C₃₁	1	8	yes	—
796	C₂×D₄	C₂²×C₄×C₃₁	1	4	yes	—
797	C₂×D₄	C₂²×C₄×C₃₁	1	4	yes	—
798	C₂×D₄	#41×C₃₁	1	4	yes	—
799	C₂×D₄	#41×C₃₁	1	4	yes	—
800	C₂²×C₄	—	2	2	no	—
801	C₂²×C₄	—	2	2	no	—
802	C₂²×C₄	—	2	4	no	—
803	C₂²×C₄	—	2	4	no	—
804	C₂²×C₄	—	2	4	no	—
805	C₂²×C₄	—	2	4	no	—
806	C₂²×C₄	—	2	4	no	—
807	C₂²×C₄	—	2	4	no	—
808	C₂²×C₄	—	4	2	no	—
809	C₂²×C₄	—	4	2	no	—
810	C₂²×C₄	—	4	2	no	—
811	C₂²×C₄	—	4	2	no	—
812	C₂²×C₄	—	4	2	no	—
813	C₂²×C₄	—	4	2	no	—
814	C₂²×C₄	—	4	2	no	—
815	C₂²×C₄	—	4	2	no	—
816	C₂²×C₄	—	4	2	no	—
817	C₂²×C₄	—	4	2	no	—
818	C₂²×C₄	—	4	2	no	—
819	C₂²×C₄	—	4	2	no	—
820	C₂²×C₄	—	4	2	no	—
821	C₂²×C₄	—	4	2	no	—
822	C₂²×C₄	C₂²×C₄×C₃₁	1	4	yes	—
823	C₂²×C₄	C₂²×C₄×C₃₁	1	8	yes	—
824	C₂²×C₄	C₂²×C₄×C₃₁	1	8	yes	—
825	C₂²×C₄	C₂²×C₄×C₃₁	1	8	yes	—
826	C₂²×C₄	C₂²×C₄×C₃₁	1	8	yes	—
827	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
828	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
829	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
830	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
831	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
832	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
833	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
834	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
835	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
836	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
837	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
838	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
839	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
840	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
841	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
842	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
843	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
844	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
845	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
846	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
847	C₄⋊C₄	—	2	2	no	—
848	C₄⋊C₄	—	2	2	no	—
849	C₄⋊C₄	—	2	2	no	—
850	C₄⋊C₄	—	2	2	no	—
851	C₄⋊C₄	—	2	2	no	—
852	C₄⋊C₄	—	2	4	no	—
853	C₄⋊C₄	—	2	2	no	—
854	C₄⋊C₄	—	4	2	no	—
855	C₄⋊C₄	—	4	2	no	—
856	C₄⋊C₄	—	4	1	no	—
857	C₄⋊C₄	—	4	1	no	—
858	C₄⋊C₄	—	4	2	no	—
859	C₄⋊C₄	—	4	2	no	—
860	C₄⋊C₄	—	4	2	no	—
861	C₄⋊C₄	C₂²×C₄×C₃₁	1	4	yes	—
862	C₄⋊C₄	C₂²×C₄×C₃₁	1	4	yes	—
863	C₄⋊C₄	C₂²×C₄×C₃₁	1	4	yes	—
864	C₄⋊C₄	C₂²×C₄×C₃₁	1	4	yes	—
865	C₂²⋊C₄	—	2	4	no	—
866	C₂²⋊C₄	—	2	4	no	—
867	C₂²⋊C₄	—	2	4	no	—
868	C₂²⋊C₄	—	2	4	no	—
869	C₂²⋊C₄	—	2	2	no	—
870	C₂²⋊C₄	—	2	2	no	—
871	C₂²⋊C₄	—	2	4	no	—
872	C₂²⋊C₄	—	2	4	no	—
873	C₂²⋊C₄	—	4	2	no	—
874	C₂²⋊C₄	—	4	2	no	—
875	C₂²⋊C₄	—	4	2	no	—
876	C₂²⋊C₄	—	4	2	no	—
877	C₂²⋊C₄	—	4	1	no	—
878	C₂²⋊C₄	—	4	2	no	—
879	C₂²⋊C₄	—	4	1	no	—
880	C₂²⋊C₄	—	4	2	no	—
881	C₂²⋊C₄	—	4	2	no	—
882	C₂²⋊C₄	—	4	2	no	—
883	C₂²⋊C₄	C₂²×C₄×C₃₁	1	4	yes	—
884	C₂²⋊C₄	C₂²×C₄×C₃₁	1	4	yes	—
885	C₂²⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
886	C₂²⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
887	C₂²⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
888	C₂²⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
889	C₂²⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
890	C₄²	—	2	2	no	—
891	C₄²	—	2	2	no	—
892	C₄²	—	2	2	no	—
893	C₄²	—	2	2	no	—
894	C₄²	—	2	2	no	—
895	C₄²	—	2	4	no	—
896	C₄²	—	2	2	no	—
897	C₄²	—	4	2	no	—
898	C₄²	—	4	2	no	—
899	C₄²	—	4	1	no	—
900	C₄²	—	4	2	no	—
901	C₄²	—	4	1	no	—
902	C₄²	—	4	2	no	—
903	C₄²	—	4	2	no	—
904	C₄²	C₂²×C₄×C₃₁	1	4	yes	—
905	C₄²	C₂²×C₄×C₃₁	1	4	yes	—
906	C₄²	C₂²×C₄×C₃₁	1	8	yes	—
907	C₂³	—	2	2	no	—
908	C₂³	—	2	2	no	—
909	C₂³	—	2	2	no	—
910	C₂³	—	2	2	no	—
911	C₂³	—	2	1	no	—
912	C₂³	—	2	1	no	—
913	C₂³	—	2	2	no	—
914	C₂³	—	2	2	no	—
915	C₂³	—	2	2	no	—
916	C₂³	—	2	2	no	—
917	C₂³	—	2	1	no	—
918	C₂³	—	2	1	no	—
919	C₂³	—	2	2	no	—
920	C₂³	—	2	2	no	—
921	C₂³	—	2	1	no	—
922	C₂³	—	2	1	no	—
923	C₂³	—	2	16	no	—
924	C₂³	—	4	8	no	—
925	C₂³	—	4	8	no	—
926	C₂³	—	8	4	no	—
927	C₂³	—	8	4	no	—
928	C₂³	—	8	4	no	—
929	C₂³	—	8	4	no	—
930	C₂³	C₂³×C₄×C₃₁	1	2	yes	—
931	C₂³	C₂³×C₄×C₃₁	1	4	yes	—
932	C₂³	C₂³×C₄×C₃₁	1	4	yes	—
933	C₂³	C₂×#41×C₃₁	1	4	yes	—
934	C₂³	C₂×#41×C₃₁	1	4	yes	—
935	C₂³	C₂⁵×C₃₁	1	1	yes	characteristic
936	D₄	—	2	16	no	—
937	D₄	—	2	8	no	—
938	D₄	C₃₁×#117	1	16	yes	complemented
939	C₂×C₄	—	2	1	no	—
940	C₂×C₄	—	2	1	no	—
941	C₂×C₄	—	2	1	no	—
942	C₂×C₄	—	2	1	no	—
943	C₂×C₄	—	2	1	no	—
944	C₂×C₄	—	2	2	no	—
945	C₂×C₄	—	2	1	no	—
946	C₂×C₄	—	2	1	no	—
947	C₂×C₄	—	2	1	no	—
948	C₂×C₄	—	2	1	no	—
949	C₂×C₄	—	2	2	no	—
950	C₂×C₄	—	2	1	no	—
951	C₂×C₄	—	2	2	no	—
952	C₂×C₄	—	2	1	no	—
953	C₂×C₄	—	2	1	no	—
954	C₂×C₄	—	2	1	no	—
955	C₂×C₄	—	2	2	no	—
956	C₂×C₄	—	2	1	no	—
957	C₂×C₄	—	2	8	no	—
958	C₂×C₄	—	2	1	no	—
959	C₂×C₄	—	2	1	no	—
960	C₂×C₄	—	2	1	no	—
961	C₂×C₄	—	2	1	no	—
962	C₂×C₄	—	2	1	no	—
963	C₂×C₄	—	2	1	no	—
964	C₂×C₄	—	2	2	no	—
965	C₂×C₄	—	2	2	no	—
966	C₂×C₄	—	2	2	no	—
967	C₂×C₄	—	2	2	no	—
968	C₂×C₄	—	2	2	no	—
969	C₂×C₄	—	2	1	no	—
970	C₂×C₄	—	2	1	no	—
971	C₂×C₄	—	2	2	no	—
972	C₂×C₄	—	2	2	no	—
973	C₂×C₄	—	2	2	no	—
974	C₂×C₄	—	2	2	no	—
975	C₂×C₄	—	2	1	no	—
976	C₂×C₄	—	2	1	no	—
977	C₂×C₄	—	2	2	no	—
978	C₂×C₄	—	2	1	no	—
979	C₂×C₄	—	2	1	no	—
980	C₂×C₄	—	2	1	no	—
981	C₂×C₄	—	2	1	no	—
982	C₂×C₄	—	2	1	no	—
983	C₂×C₄	—	2	2	no	—
984	C₂×C₄	—	2	1	no	—
985	C₂×C₄	—	2	1	no	—
986	C₂×C₄	—	2	2	no	—
987	C₂×C₄	—	2	1	no	—
988	C₂×C₄	—	4	8	no	—
989	C₂×C₄	—	4	8	no	—
990	C₂×C₄	—	4	8	no	—
991	C₂×C₄	—	4	8	no	—
992	C₂×C₄	—	4	8	no	—
993	C₂×C₄	—	4	8	no	—
994	C₂×C₄	—	8	4	no	—
995	C₂×C₄	—	8	4	no	—
996	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
997	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
998	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
999	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
1000	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
1001	C₂×C₄	C₂³×C₄×C₃₁	1	4	yes	—
1002	C₂×C₄	C₂³×C₄×C₃₁	1	4	yes	—
1003	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
1004	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
1005	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
1006	C₂×C₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
1007	C₂×C₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
1008	C₂²	—	2	4	no	—
1009	C₂²	—	2	4	no	—
1010	C₂²	—	2	4	no	—
1011	C₂²	—	2	4	no	—
1012	C₂²	—	2	4	no	—
1013	C₂²	—	2	4	no	—
1014	C₂²	—	2	2	no	—
1015	C₂²	—	2	4	no	—
1016	C₂²	—	2	4	no	—
1017	C₂²	—	2	4	no	—
1018	C₂²	—	2	2	no	—
1019	C₂²	—	2	2	no	—
1020	C₂²	—	4	1	no	—
1021	C₂²	—	4	2	no	—
1022	C₂²	—	4	1	no	—
1023	C₂²	—	4	2	no	—
1024	C₂²	—	4	1	no	—
1025	C₂²	—	4	2	no	—
1026	C₂²	—	4	1	no	—
1027	C₂²	—	4	2	no	—
1028	C₂²	—	8	16	no	—
1029	C₂²	C₂×C₃₁×#117	1	8	yes	—
1030	C₂²	C₂⁴×C₄×C₃₁	1	1	yes	characteristic
1031	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
1032	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
1033	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
1034	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
1035	C₂²	C₃₁×#585	1	1	yes	characteristic
1036	C₂²	C₃₁×#585	1	1	yes	characteristic
1037	C₄	—	2	2	no	—
1038	C₄	—	2	2	no	—
1039	C₄	—	2	4	no	—
1040	C₄	—	2	2	no	—
1041	C₄	—	2	2	no	—
1042	C₄	—	2	2	no	—
1043	C₄	—	2	4	no	—
1044	C₄	—	2	2	no	—
1045	C₄	—	2	2	no	—
1046	C₄	—	4	2	no	—
1047	C₄	—	4	1	no	—
1048	C₄	—	4	1	no	—
1049	C₄	—	4	2	no	—
1050	C₄	—	4	1	no	—
1051	C₄	—	4	2	no	—
1052	C₄	—	4	1	no	—
1053	C₄	—	4	2	no	—
1054	C₄	—	4	1	no	—
1055	C₄	—	4	1	no	—
1056	C₄	C₂×C₃₁×#117	1	4	yes	—
1057	C₂	—	2	8	no	—
1058	C₂	—	4	2	no	—
1059	C₂	—	4	4	no	—
1060	C₂	C₂²×C₃₁×#117	1	1	yes	characteristic
1061	C₂	C₄×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
1062	C₂	C₄×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
1063	C₂	C₃₁×#3513	1	1	yes	characteristic
1064	C₂	C₃₁×#3514	1	1	yes	characteristic
1065	C₂	C₃₁×#3519	1	1	yes	characteristic
1066	C₂	C₃₁×#3521	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃₁	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₃₁
Frattini, cosocle	C₂³	C₂⁵×C₃₁
prime radical	C₂³×D₄×C₃₁	C₂²
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×#2357	C₂	semidirect
3. C₃₁×#2354	C₂	semidirect
4. C₃₁×#2353	C₂	semidirect
5. C₃₁×#2352	C₂	semidirect
6. C₃₁×#2349	C₂	semidirect
7. D₄×C₄⋊C₄×C₃₁	C₂	semidirect
8. C₃₁×#2347	C₂	semidirect
9. C₃₁×#2346	C₂	semidirect
10. C₃₁×#2342	C₂	semidirect
11. C₃₁×#2342	C₂	semidirect
14. C₃₁×#2319	C₂	semidirect
15. C₃₁×#2318	C₂	semidirect
16. C₃₁×#2314	C₂	semidirect
17. C₃₁×#2312	C₂	semidirect
18. C₃₁×#2298	C₂	semidirect
19. C₃₁×#2293	C₂	semidirect
20. C₃₁×#2290	C₂	semidirect
21. C₂×C₃₁×#388	C₂	semidirect
22. C₃₁×#2275	C₂	semidirect
23. C₄²×D₄×C₃₁	C₂	semidirect
25. C₃₁×#518	C₄	semidirect
38. C₂×C₃₁×#117	C₂²	semidirect
39. C₂×C₃₁×#117	C₂²	semidirect
40. C₂²×C₄⋊C₄×C₃₁	C₂²	semidirect
45. C₂²×C₄²×C₃₁	C₂²	semidirect
50. C₃₁×#389	C₂²	semidirect
51. C₃₁×#389	C₂²	semidirect
52. C₃₁×#389	C₂²	semidirect
53. C₃₁×#389	C₂²	semidirect
64. C₃₁×#388	C₂²	semidirect
65. C₃₁×#388	C₂²	semidirect
66. C₃₁×#388	C₂²	semidirect
67. C₃₁×#388	C₂²	semidirect
68. C₃₁×#388	C₂²	semidirect
69. C₃₁×#388	C₂²	semidirect
70. C₃₁×#388	C₂²	semidirect
71. C₃₁×#388	C₂²	semidirect
72. C₃₁×#387	C₂²	semidirect
73. C₃₁×#387	C₂²	semidirect
74. C₃₁×#387	C₂²	semidirect
75. C₃₁×#387	C₂²	semidirect
76. C₃₁×#387	C₂²	semidirect
77. C₃₁×#387	C₂²	semidirect
82. C₃₁×#385	C₂²	semidirect
83. C₃₁×#385	C₂²	semidirect
84. C₃₁×#385	C₂²	semidirect
85. C₃₁×#385	C₂²	semidirect
86. C₃₁×#384	C₂²	semidirect
87. C₃₁×#383	C₂²	semidirect
88. C₃₁×#382	C₂²	semidirect
89. C₃₁×#382	C₂²	semidirect
90. C₃₁×#381	C₂²	semidirect
91. C₃₁×#381	C₂²	semidirect
94. C₃₁×#380	C₂²	semidirect
95. C₃₁×#380	C₂²	semidirect
96. C₃₁×#380	C₂²	semidirect
97. C₃₁×#380	C₂²	semidirect
100. C₄×C₄⋊C₄×C₃₁	C₂²	semidirect
101. C₄×C₄⋊C₄×C₃₁	C₂²	semidirect
102. C₄×C₄⋊C₄×C₃₁	C₂²	semidirect
103. C₄×C₄⋊C₄×C₃₁	C₂²	semidirect
104. C₄×C₄⋊C₄×C₃₁	C₂²	semidirect
105. C₄×C₄⋊C₄×C₃₁	C₂²	semidirect
106. C₄×C₄⋊C₄×C₃₁	C₂²	semidirect
107. C₄×C₄⋊C₄×C₃₁	C₂²	semidirect
108. C₄×C₄⋊C₄×C₃₁	C₂²	semidirect
111. C₄×C₂²⋊C₄×C₃₁	C₂²	semidirect
112. C₄×C₂²⋊C₄×C₃₁	C₂²	semidirect
113. C₄×C₂²⋊C₄×C₃₁	C₂²	semidirect
114. C₄×C₂²⋊C₄×C₃₁	C₂²	semidirect
115. C₄×C₂²⋊C₄×C₃₁	C₂²	semidirect
116. C₄×C₂²⋊C₄×C₃₁	C₂²	semidirect
117. C₄×C₂²⋊C₄×C₃₁	C₂²	semidirect
118. C₄×C₂²⋊C₄×C₃₁	C₂²	semidirect
119. C₃₁×#376	C₂²	semidirect
120. C₃₁×#376	C₂²	semidirect
121. C₂×C₃₁×#95	C₂²	semidirect
122. C₂×C₃₁×#95	C₂²	semidirect
123. C₄³×C₃₁	C₂²	semidirect
146. C₄×D₄×C₃₁	C₂×C₄	semidirect
147. C₄×D₄×C₃₁	C₂×C₄	semidirect
148. C₄×D₄×C₃₁	C₂×C₄	semidirect
149. C₄×D₄×C₃₁	C₂×C₄	semidirect
152. C₃₁×#117	C₂×C₄	semidirect
153. C₃₁×#117	C₂×C₄	semidirect
175. C₂×C₂²⋊C₄×C₃₁	C₂×C₄	semidirect
176. C₂×C₂²⋊C₄×C₃₁	C₂×C₄	semidirect
373. #34261	C₃₁	direct (N × H)
405. D₄×C₃₁	#117	semidirect
476. #2357	C₂×C₃₁	semidirect
477. #2354	C₂×C₃₁	semidirect
478. #2353	C₂×C₃₁	semidirect
479. #2352	C₂×C₃₁	semidirect
480. #2349	C₂×C₃₁	semidirect
481. D₄×C₄⋊C₄	C₂×C₃₁	semidirect
482. #2347	C₂×C₃₁	semidirect
483. #2346	C₂×C₃₁	semidirect
484. #2342	C₂×C₃₁	semidirect
485. #2342	C₂×C₃₁	semidirect
488. #2319	C₂×C₃₁	semidirect
489. #2318	C₂×C₃₁	semidirect
490. #2314	C₂×C₃₁	semidirect
491. #2312	C₂×C₃₁	semidirect
492. #2298	C₂×C₃₁	semidirect
493. #2293	C₂×C₃₁	semidirect
494. #2290	C₂×C₃₁	semidirect
495. C₂×#388	C₂×C₃₁	semidirect
496. #2275	C₂×C₃₁	semidirect
497. C₄²×D₄	C₂×C₃₁	semidirect
548. #518	C₄×C₃₁	semidirect
561. C₂×#117	C₂²×C₃₁	semidirect
562. C₂×#117	C₂²×C₃₁	semidirect
563. C₂²×C₄⋊C₄	C₂²×C₃₁	semidirect
568. C₂²×C₄²	C₂²×C₃₁	semidirect
573. #389	C₂²×C₃₁	semidirect
574. #389	C₂²×C₃₁	semidirect
575. #389	C₂²×C₃₁	semidirect
576. #389	C₂²×C₃₁	semidirect
587. #388	C₂²×C₃₁	semidirect
588. #388	C₂²×C₃₁	semidirect
589. #388	C₂²×C₃₁	semidirect
590. #388	C₂²×C₃₁	semidirect
591. #388	C₂²×C₃₁	semidirect
592. #388	C₂²×C₃₁	semidirect
593. #388	C₂²×C₃₁	semidirect
594. #388	C₂²×C₃₁	semidirect
595. #387	C₂²×C₃₁	semidirect
596. #387	C₂²×C₃₁	semidirect
597. #387	C₂²×C₃₁	semidirect
598. #387	C₂²×C₃₁	semidirect
599. #387	C₂²×C₃₁	semidirect
600. #387	C₂²×C₃₁	semidirect
605. #385	C₂²×C₃₁	semidirect
606. #385	C₂²×C₃₁	semidirect
607. #385	C₂²×C₃₁	semidirect
608. #385	C₂²×C₃₁	semidirect
609. #384	C₂²×C₃₁	semidirect
610. #383	C₂²×C₃₁	semidirect
611. #382	C₂²×C₃₁	semidirect
612. #382	C₂²×C₃₁	semidirect
613. #381	C₂²×C₃₁	semidirect
614. #381	C₂²×C₃₁	semidirect
617. #380	C₂²×C₃₁	semidirect
618. #380	C₂²×C₃₁	semidirect
619. #380	C₂²×C₃₁	semidirect
620. #380	C₂²×C₃₁	semidirect
623. C₄×C₄⋊C₄	C₂²×C₃₁	semidirect
624. C₄×C₄⋊C₄	C₂²×C₃₁	semidirect
625. C₄×C₄⋊C₄	C₂²×C₃₁	semidirect
626. C₄×C₄⋊C₄	C₂²×C₃₁	semidirect
627. C₄×C₄⋊C₄	C₂²×C₃₁	semidirect
628. C₄×C₄⋊C₄	C₂²×C₃₁	semidirect
629. C₄×C₄⋊C₄	C₂²×C₃₁	semidirect
630. C₄×C₄⋊C₄	C₂²×C₃₁	semidirect
631. C₄×C₄⋊C₄	C₂²×C₃₁	semidirect
634. C₄×C₂²⋊C₄	C₂²×C₃₁	semidirect
635. C₄×C₂²⋊C₄	C₂²×C₃₁	semidirect
636. C₄×C₂²⋊C₄	C₂²×C₃₁	semidirect
637. C₄×C₂²⋊C₄	C₂²×C₃₁	semidirect
638. C₄×C₂²⋊C₄	C₂²×C₃₁	semidirect
639. C₄×C₂²⋊C₄	C₂²×C₃₁	semidirect
640. C₄×C₂²⋊C₄	C₂²×C₃₁	semidirect
641. C₄×C₂²⋊C₄	C₂²×C₃₁	semidirect
642. #376	C₂²×C₃₁	semidirect
643. #376	C₂²×C₃₁	semidirect
644. C₂×#95	C₂²×C₃₁	semidirect
645. C₂×#95	C₂²×C₃₁	semidirect
646. C₄³	C₂²×C₃₁	semidirect
679. C₄×D₄	C₂×C₄×C₃₁	semidirect
680. C₄×D₄	C₂×C₄×C₃₁	semidirect
681. C₄×D₄	C₂×C₄×C₃₁	semidirect
682. C₄×D₄	C₂×C₄×C₃₁	semidirect
685. #117	C₂×C₄×C₃₁	semidirect
686. #117	C₂×C₄×C₃₁	semidirect
708. C₂×C₂²⋊C₄	C₂×C₄×C₃₁	semidirect
709. C₂×C₂²⋊C₄	C₂×C₄×C₃₁	semidirect
779. C₃₁	#34261	direct (N × H)
938. D₄	C₃₁×#117	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃₁×#518	2
C₃₁×#2357	2
C₃₁×#2354	2
C₃₁×#2353	2
C₃₁×#2352	2
C₃₁×#2349	2
D₄×C₄⋊C₄×C₃₁	2
C₃₁×#2347	2
C₃₁×#2346	2
C₃₁×#2342	2
D₄×C₂²⋊C₄×C₃₁	2
C₃₁×#2319	2
C₃₁×#2318	2
C₃₁×#2314	2
C₃₁×#2312	2
C₃₁×#2298	2
C₃₁×#2293	2
C₃₁×#2290	2
C₂×C₃₁×#388	2
C₃₁×#2275	2
C₄²×D₄×C₃₁	2
#34261	31

Subgroups — C31×#34261 #21491020

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#34261 #21491020