Subgroups — C₃₁×#34970 #21491729

Order 7936.

2142 conjugacy classes of subgroups.

The subgroup lattice has 1042 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#2531	C₂	1	2	yes	maximal, complemented
2	C₃₁×#2526	C₂	1	2	yes	maximal, complemented
3	C₃₁×#2513	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#2507	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#2497	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#2490	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#2476	C₂	1	2	yes	maximal, complemented
8	C₃₁×#2471	C₂	1	2	yes	maximal, complemented
9	C₃₁×#2454	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#2445	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#2428	C₂	1	1	yes	maximal, characteristic
12	C₃₁×#2420	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#2395	C₂	1	2	yes	maximal, complemented
14	C₃₁×#2392	C₂	1	2	yes	maximal, complemented
15	C₄×C₃₁×#127	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×C₃₁×#125	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, complemented
19	C₄×C₃₁×#121	C₂	1	1	yes	maximal, characteristic, complemented
20	C₄×C₃₁×#121	C₂	1	2	yes	maximal, complemented
21	C₃₁×#2293	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄²×D₄×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄×C₃₁×#117	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₃₁×#127	C₂²	1	1	yes	characteristic
25	C₂×C₃₁×#125	C₂²	1	1	yes	characteristic
26	C₂×C₃₁×#123	C₂²	1	2	yes	—
27	C₂×C₃₁×#121	C₂²	1	1	yes	characteristic
28	C₂×C₃₁×#121	C₂²	1	2	yes	—
29	C₂×C₃₁×#121	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	1	yes	characteristic
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	2	yes	—
36	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
37	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
38	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
39	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
40	C₂×C₃₁×#117	C₂²	1	2	yes	—
41	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
42	C₂²×C₄²×C₃₁	C₂²	1	2	yes	—
43	C₃₁×#400	C₂²	1	2	yes	—
44	C₃₁×#399	C₂²	1	2	yes	—
45	C₃₁×#398	C₂²	1	2	yes	—
46	C₃₁×#398	C₂²	1	2	yes	—
47	C₃₁×#397	C₂²	1	2	yes	—
48	C₃₁×#397	C₂²	1	2	yes	—
49	C₃₁×#397	C₂²	1	2	yes	—
50	C₃₁×#397	C₂²	1	2	yes	—
51	C₃₁×#396	C₂²	1	2	yes	—
52	C₃₁×#396	C₂²	1	2	yes	—
53	C₃₁×#394	C₂²	1	2	yes	—
54	C₃₁×#394	C₂²	1	2	yes	—
55	C₃₁×#394	C₂²	1	2	yes	—
56	C₃₁×#394	C₂²	1	2	yes	—
57	C₃₁×#394	C₂²	1	2	yes	—
58	C₃₁×#392	C₂²	1	2	yes	—
59	C₃₁×#390	C₂²	1	1	yes	characteristic
60	C₃₁×#390	C₂²	1	1	yes	characteristic
61	C₃₁×#390	C₂²	1	1	yes	characteristic
62	C₃₁×#390	C₂²	1	1	yes	characteristic
63	C₃₁×#390	C₂²	1	1	yes	characteristic
64	C₃₁×#390	C₂²	1	2	yes	—
65	C₃₁×#390	C₂²	1	2	yes	—
66	C₃₁×#390	C₂²	1	2	yes	—
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	1	yes	characteristic
71	C₃₁×#389	C₂²	1	1	yes	characteristic
72	C₃₁×#389	C₂²	1	1	yes	characteristic
73	C₃₁×#389	C₂²	1	1	yes	characteristic
74	C₃₁×#389	C₂²	1	2	yes	—
75	C₃₁×#388	C₂²	1	2	yes	—
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×#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×#386	C₂²	1	2	yes	—
88	C₃₁×#386	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×#385	C₂²	1	2	yes	—
93	C₃₁×#384	C₂²	1	1	yes	characteristic
94	C₃₁×#382	C₂²	1	1	yes	characteristic
95	C₃₁×#381	C₂²	1	2	yes	—
96	C₃₁×#380	C₂²	1	1	yes	characteristic
97	C₃₁×#380	C₂²	1	2	yes	—
98	C₃₁×#380	C₂²	1	1	yes	characteristic
99	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
100	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
101	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
102	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
103	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
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	1	yes	characteristic
107	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
108	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
109	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
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	1	yes	characteristic
114	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
115	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
116	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
117	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
118	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
119	C₃₁×#376	C₂²	1	1	yes	characteristic
120	C₃₁×#376	C₂²	1	1	yes	characteristic
121	C₄³×C₃₁	C₂²	1	1	yes	characteristic
122	C₄³×C₃₁	C₂²	1	1	yes	characteristic
123	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
124	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
125	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
126	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
127	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
128	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
129	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
130	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
131	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
132	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
133	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
134	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
135	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
136	C₃₁×#127	—	2	4	no	—
137	C₃₁×#125	—	2	4	no	—
138	C₃₁×#123	—	2	8	no	—
139	C₃₁×#121	—	2	4	no	—
140	C₃₁×#121	—	2	4	no	—
141	C₃₁×#121	—	2	8	no	—
142	C₄×D₄×C₃₁	—	2	4	no	—
143	C₄×D₄×C₃₁	—	2	4	no	—
144	C₄×D₄×C₃₁	—	2	4	no	—
145	C₄×D₄×C₃₁	—	2	4	no	—
146	C₄×D₄×C₃₁	—	4	4	no	—
147	C₄×D₄×C₃₁	—	4	4	no	—
148	C₄×D₄×C₃₁	—	4	4	no	—
149	C₄×D₄×C₃₁	—	4	4	no	—
150	C₃₁×#117	—	2	4	no	—
151	C₃₁×#117	—	2	4	no	—
152	C₃₁×#117	—	4	4	no	—
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	2	yes	—
157	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
158	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
159	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
160	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
161	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
162	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
163	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
164	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
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	2	yes	—
169	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
170	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
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	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
181	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
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	2	yes	—
192	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
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	2	yes	—
196	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
197	C₂×C₄²×C₃₁	—	2	4	no	—
198	C₂×C₄²×C₃₁	—	4	4	no	—
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	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	1	yes	characteristic
212	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
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	2	yes	—
218	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
219	C₃₁×#95	C₂³	1	1	yes	characteristic
220	C₃₁×#95	C₂³	1	2	yes	—
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	2	yes	—
230	C₃₁×#95	C₂³	1	2	yes	—
231	C₃₁×#95	C₂³	1	1	yes	characteristic
232	C₃₁×#95	C₂³	1	2	yes	—
233	C₃₁×#95	C₂³	1	1	yes	characteristic
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	2	yes	—
241	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
242	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
243	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
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	4	no	—
248	C₂×D₄×C₃₁	—	2	4	no	—
249	C₂×D₄×C₃₁	—	2	2	no	—
250	C₂×D₄×C₃₁	—	2	2	no	—
251	C₂×D₄×C₃₁	—	2	2	no	—
252	C₂×D₄×C₃₁	—	2	4	no	—
253	C₂×D₄×C₃₁	—	2	4	no	—
254	C₂×D₄×C₃₁	—	2	2	no	—
255	C₂×D₄×C₃₁	—	2	4	no	—
256	C₂×D₄×C₃₁	—	2	2	no	—
257	C₂×D₄×C₃₁	—	4	2	no	—
258	C₂×D₄×C₃₁	—	4	2	no	—
259	C₂×D₄×C₃₁	—	4	2	no	—
260	C₂×D₄×C₃₁	—	4	2	no	—
261	C₂×D₄×C₃₁	#41	1	4	yes	—
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	4	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	—	2	4	no	—
272	C₂²×C₄×C₃₁	—	2	2	no	—
273	C₂²×C₄×C₃₁	—	2	2	no	—
274	C₂²×C₄×C₃₁	—	2	4	no	—
275	C₂²×C₄×C₃₁	—	2	4	no	—
276	C₂²×C₄×C₃₁	—	2	4	no	—
277	C₂²×C₄×C₃₁	—	2	2	no	—
278	C₂²×C₄×C₃₁	—	2	2	no	—
279	C₂²×C₄×C₃₁	—	2	4	no	—
280	C₂²×C₄×C₃₁	—	2	4	no	—
281	C₂²×C₄×C₃₁	—	4	2	no	—
282	C₂²×C₄×C₃₁	—	4	2	no	—
283	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
284	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
285	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
286	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
287	C₂²×C₄×C₃₁	C₂⁴	1	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	2	yes	—
292	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
293	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
294	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
295	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
296	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
297	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
298	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
299	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
300	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
301	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
302	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
303	C₄⋊C₄×C₃₁	—	2	2	no	—
304	C₄⋊C₄×C₃₁	—	2	2	no	—
305	C₄⋊C₄×C₃₁	—	2	2	no	—
306	C₄⋊C₄×C₃₁	—	2	2	no	—
307	C₄⋊C₄×C₃₁	—	2	2	no	—
308	C₄⋊C₄×C₃₁	—	2	2	no	—
309	C₄⋊C₄×C₃₁	—	2	4	no	—
310	C₄⋊C₄×C₃₁	—	2	2	no	—
311	C₄⋊C₄×C₃₁	—	2	4	no	—
312	C₄⋊C₄×C₃₁	—	2	4	no	—
313	C₄⋊C₄×C₃₁	—	2	4	no	—
314	C₄⋊C₄×C₃₁	—	2	2	no	—
315	C₄⋊C₄×C₃₁	—	4	2	no	—
316	C₄⋊C₄×C₃₁	—	4	2	no	—
317	C₄⋊C₄×C₃₁	—	4	2	no	—
318	C₄⋊C₄×C₃₁	—	4	2	no	—
319	C₄⋊C₄×C₃₁	—	4	2	no	—
320	C₄⋊C₄×C₃₁	—	4	2	no	—
321	C₄⋊C₄×C₃₁	#41	1	4	yes	—
322	C₄⋊C₄×C₃₁	#41	1	4	yes	—
323	C₂²⋊C₄×C₃₁	—	2	2	no	—
324	C₂²⋊C₄×C₃₁	—	2	4	no	—
325	C₂²⋊C₄×C₃₁	—	2	4	no	—
326	C₂²⋊C₄×C₃₁	—	2	2	no	—
327	C₂²⋊C₄×C₃₁	—	2	2	no	—
328	C₂²⋊C₄×C₃₁	—	2	4	no	—
329	C₂²⋊C₄×C₃₁	—	2	4	no	—
330	C₂²⋊C₄×C₃₁	—	2	4	no	—
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	4	no	—
336	C₂²⋊C₄×C₃₁	—	4	2	no	—
337	C₂²⋊C₄×C₃₁	—	4	2	no	—
338	C₂²⋊C₄×C₃₁	—	4	2	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	2	no	—
344	C₂²⋊C₄×C₃₁	—	4	2	no	—
345	C₂²⋊C₄×C₃₁	—	4	2	no	—
346	C₂²⋊C₄×C₃₁	#41	1	4	yes	—
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	2	no	—
353	C₄²×C₃₁	—	2	2	no	—
354	C₄²×C₃₁	—	2	2	no	—
355	C₄²×C₃₁	—	2	2	no	—
356	C₄²×C₃₁	—	2	2	no	—
357	C₄²×C₃₁	—	2	2	no	—
358	C₄²×C₃₁	—	2	2	no	—
359	C₄²×C₃₁	—	2	4	no	—
360	C₄²×C₃₁	—	2	2	no	—
361	C₄²×C₃₁	—	2	4	no	—
362	C₄²×C₃₁	—	2	2	no	—
363	C₄²×C₃₁	—	2	2	no	—
364	C₄²×C₃₁	—	4	2	no	—
365	C₄²×C₃₁	—	4	2	no	—
366	C₄²×C₃₁	#41	1	4	yes	—
367	#34970	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
368	C₂³×C₃₁	—	2	1	no	—
369	C₂³×C₃₁	—	2	2	no	—
370	C₂³×C₃₁	—	2	2	no	—
371	C₂³×C₃₁	—	2	2	no	—
372	C₂³×C₃₁	—	2	1	no	—
373	C₂³×C₃₁	—	2	1	no	—
374	C₂³×C₃₁	—	2	1	no	—
375	C₂³×C₃₁	—	2	2	no	—
376	C₂³×C₃₁	—	2	1	no	—
377	C₂³×C₃₁	—	2	2	no	—
378	C₂³×C₃₁	—	2	1	no	—
379	C₂³×C₃₁	—	2	2	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	2	no	—
385	C₂³×C₃₁	—	2	2	no	—
386	C₂³×C₃₁	—	2	2	no	—
387	C₂³×C₃₁	C₂×#41	1	4	yes	—
388	C₂³×C₃₁	C₂×#41	1	2	yes	—
389	C₂³×C₃₁	C₂⁵	1	1	yes	characteristic
390	D₄×C₃₁	—	2	8	no	—
391	D₄×C₃₁	—	4	8	no	—
392	D₄×C₃₁	—	4	8	no	—
393	D₄×C₃₁	—	4	8	no	—
394	D₄×C₃₁	—	4	8	no	—
395	D₄×C₃₁	—	4	4	no	—
396	C₂×C₄×C₃₁	—	2	8	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	2	no	—
406	C₂×C₄×C₃₁	—	2	1	no	—
407	C₂×C₄×C₃₁	—	2	1	no	—
408	C₂×C₄×C₃₁	—	2	2	no	—
409	C₂×C₄×C₃₁	—	2	1	no	—
410	C₂×C₄×C₃₁	—	2	1	no	—
411	C₂×C₄×C₃₁	—	2	1	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	1	no	—
417	C₂×C₄×C₃₁	—	2	1	no	—
418	C₂×C₄×C₃₁	—	2	1	no	—
419	C₂×C₄×C₃₁	—	2	1	no	—
420	C₂×C₄×C₃₁	—	2	1	no	—
421	C₂×C₄×C₃₁	—	2	2	no	—
422	C₂×C₄×C₃₁	—	2	1	no	—
423	C₂×C₄×C₃₁	—	2	1	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	—	2	2	no	—
431	C₂×C₄×C₃₁	—	2	2	no	—
432	C₂×C₄×C₃₁	—	2	1	no	—
433	C₂×C₄×C₃₁	—	2	1	no	—
434	C₂×C₄×C₃₁	—	2	2	no	—
435	C₂×C₄×C₃₁	—	2	1	no	—
436	C₂×C₄×C₃₁	—	2	1	no	—
437	C₂×C₄×C₃₁	—	2	2	no	—
438	C₂×C₄×C₃₁	—	2	2	no	—
439	C₂×C₄×C₃₁	—	2	1	no	—
440	C₂×C₄×C₃₁	—	2	2	no	—
441	C₂×C₄×C₃₁	—	2	1	no	—
442	C₂×C₄×C₃₁	—	2	2	no	—
443	C₂×C₄×C₃₁	—	2	2	no	—
444	C₂×C₄×C₃₁	—	4	8	no	—
445	C₂×C₄×C₃₁	—	4	8	no	—
446	C₂×C₄×C₃₁	—	4	4	no	—
447	C₂×C₄×C₃₁	—	4	4	no	—
448	C₂×C₄×C₃₁	—	4	8	no	—
449	C₂×C₄×C₃₁	—	4	8	no	—
450	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
451	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
452	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
453	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
454	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
455	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
456	C₂×C₄×C₃₁	C₂×#41	1	4	yes	—
457	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
458	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
459	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
460	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
461	C₂×C₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
462	C₂×C₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
463	#2531	C₂×C₃₁	1	2	yes	complemented
464	#2526	C₂×C₃₁	1	2	yes	complemented
465	#2513	C₂×C₃₁	1	1	yes	characteristic, complemented
466	#2507	C₂×C₃₁	1	1	yes	characteristic, complemented
467	#2497	C₂×C₃₁	1	1	yes	characteristic, complemented
468	#2490	C₂×C₃₁	1	1	yes	characteristic, complemented
469	#2476	C₂×C₃₁	1	2	yes	complemented
470	#2471	C₂×C₃₁	1	2	yes	complemented
471	#2454	C₂×C₃₁	1	1	yes	characteristic, complemented
472	#2445	C₂×C₃₁	1	1	yes	characteristic, complemented
473	#2428	C₂×C₃₁	1	1	yes	characteristic
474	#2420	C₂×C₃₁	1	1	yes	characteristic, complemented
475	#2395	C₂×C₃₁	1	2	yes	complemented
476	#2392	C₂×C₃₁	1	2	yes	complemented
477	C₄×#127	C₂×C₃₁	1	1	yes	characteristic, complemented
478	C₄×#125	C₂×C₃₁	1	1	yes	characteristic, complemented
479	C₄×#123	C₂×C₃₁	1	2	yes	complemented
480	C₄×#121	C₂×C₃₁	1	1	yes	characteristic, complemented
481	C₄×#121	C₂×C₃₁	1	1	yes	characteristic, complemented
482	C₄×#121	C₂×C₃₁	1	2	yes	complemented
483	#2293	C₂×C₃₁	1	1	yes	characteristic, complemented
484	C₄²×D₄	C₂×C₃₁	1	1	yes	characteristic, complemented
485	C₄×#117	C₂×C₃₁	1	1	yes	characteristic, complemented
486	C₂²×C₃₁	—	2	4	no	—
487	C₂²×C₃₁	—	2	2	no	—
488	C₂²×C₃₁	—	2	4	no	—
489	C₂²×C₃₁	—	2	2	no	—
490	C₂²×C₃₁	—	2	4	no	—
491	C₂²×C₃₁	—	2	2	no	—
492	C₂²×C₃₁	—	4	1	no	—
493	C₂²×C₃₁	—	4	2	no	—
494	C₂²×C₃₁	—	4	2	no	—
495	C₂²×C₃₁	—	4	1	no	—
496	C₂²×C₃₁	—	4	2	no	—
497	C₂²×C₃₁	—	4	1	no	—
498	C₂²×C₃₁	—	4	1	no	—
499	C₂²×C₃₁	—	4	2	no	—
500	C₂²×C₃₁	—	4	2	no	—
501	C₂²×C₃₁	—	4	2	no	—
502	C₂²×C₃₁	—	4	2	no	—
503	C₂²×C₃₁	—	4	2	no	—
504	C₂²×C₃₁	—	4	2	no	—
505	C₂²×C₃₁	—	4	2	no	—
506	C₂²×C₃₁	—	4	2	no	—
507	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
508	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
509	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
510	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
511	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
512	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
513	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
514	C₄×C₃₁	—	2	2	no	—
515	C₄×C₃₁	—	2	2	no	—
516	C₄×C₃₁	—	2	2	no	—
517	C₄×C₃₁	—	2	2	no	—
518	C₄×C₃₁	—	2	4	no	—
519	C₄×C₃₁	—	2	2	no	—
520	C₄×C₃₁	—	2	2	no	—
521	C₄×C₃₁	—	4	1	no	—
522	C₄×C₃₁	—	4	1	no	—
523	C₄×C₃₁	—	4	2	no	—
524	C₄×C₃₁	—	4	2	no	—
525	C₄×C₃₁	—	4	1	no	—
526	C₄×C₃₁	—	4	1	no	—
527	C₄×C₃₁	—	4	2	no	—
528	C₄×C₃₁	—	4	2	no	—
529	C₄×C₃₁	—	4	1	no	—
530	C₄×C₃₁	—	4	1	no	—
531	C₄×C₃₁	—	4	2	no	—
532	C₄×C₃₁	#529	1	4	yes	—
533	C₄×C₃₁	#540	1	4	yes	—
534	C₂×#127	C₂²×C₃₁	1	1	yes	characteristic
535	C₂×#125	C₂²×C₃₁	1	1	yes	characteristic
536	C₂×#123	C₂²×C₃₁	1	2	yes	—
537	C₂×#121	C₂²×C₃₁	1	1	yes	characteristic
538	C₂×#121	C₂²×C₃₁	1	2	yes	—
539	C₂×#121	C₂²×C₃₁	1	1	yes	characteristic
540	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
541	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
542	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
543	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
544	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
545	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
546	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
547	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
548	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
549	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
550	C₂×#117	C₂²×C₃₁	1	2	yes	—
551	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
552	C₂²×C₄²	C₂²×C₃₁	1	2	yes	—
553	#400	C₂²×C₃₁	1	2	yes	—
554	#399	C₂²×C₃₁	1	2	yes	—
555	#398	C₂²×C₃₁	1	2	yes	—
556	#398	C₂²×C₃₁	1	2	yes	—
557	#397	C₂²×C₃₁	1	2	yes	—
558	#397	C₂²×C₃₁	1	2	yes	—
559	#397	C₂²×C₃₁	1	2	yes	—
560	#397	C₂²×C₃₁	1	2	yes	—
561	#396	C₂²×C₃₁	1	2	yes	—
562	#396	C₂²×C₃₁	1	2	yes	—
563	#394	C₂²×C₃₁	1	2	yes	—
564	#394	C₂²×C₃₁	1	2	yes	—
565	#394	C₂²×C₃₁	1	2	yes	—
566	#394	C₂²×C₃₁	1	2	yes	—
567	#394	C₂²×C₃₁	1	2	yes	—
568	#392	C₂²×C₃₁	1	2	yes	—
569	#390	C₂²×C₃₁	1	1	yes	characteristic
570	#390	C₂²×C₃₁	1	2	yes	—
571	#390	C₂²×C₃₁	1	2	yes	—
572	#390	C₂²×C₃₁	1	1	yes	characteristic
573	#390	C₂²×C₃₁	1	1	yes	characteristic
574	#390	C₂²×C₃₁	1	1	yes	characteristic
575	#390	C₂²×C₃₁	1	1	yes	characteristic
576	#390	C₂²×C₃₁	1	1	yes	characteristic
577	#390	C₂²×C₃₁	1	2	yes	—
578	#389	C₂²×C₃₁	1	1	yes	characteristic
579	#389	C₂²×C₃₁	1	1	yes	characteristic
580	#389	C₂²×C₃₁	1	1	yes	characteristic
581	#389	C₂²×C₃₁	1	1	yes	characteristic
582	#389	C₂²×C₃₁	1	1	yes	characteristic
583	#389	C₂²×C₃₁	1	1	yes	characteristic
584	#389	C₂²×C₃₁	1	2	yes	—
585	#388	C₂²×C₃₁	1	2	yes	—
586	#388	C₂²×C₃₁	1	2	yes	—
587	#388	C₂²×C₃₁	1	2	yes	—
588	#388	C₂²×C₃₁	1	2	yes	—
589	#388	C₂²×C₃₁	1	2	yes	—
590	#388	C₂²×C₃₁	1	2	yes	—
591	#388	C₂²×C₃₁	1	2	yes	—
592	#388	C₂²×C₃₁	1	2	yes	—
593	#387	C₂²×C₃₁	1	2	yes	—
594	#387	C₂²×C₃₁	1	2	yes	—
595	#387	C₂²×C₃₁	1	2	yes	—
596	#387	C₂²×C₃₁	1	2	yes	—
597	#386	C₂²×C₃₁	1	2	yes	—
598	#386	C₂²×C₃₁	1	2	yes	—
599	#386	C₂²×C₃₁	1	2	yes	—
600	#386	C₂²×C₃₁	1	2	yes	—
601	#386	C₂²×C₃₁	1	2	yes	—
602	#385	C₂²×C₃₁	1	2	yes	—
603	#384	C₂²×C₃₁	1	1	yes	characteristic
604	#382	C₂²×C₃₁	1	1	yes	characteristic
605	#381	C₂²×C₃₁	1	2	yes	—
606	#380	C₂²×C₃₁	1	1	yes	characteristic
607	#380	C₂²×C₃₁	1	2	yes	—
608	#380	C₂²×C₃₁	1	1	yes	characteristic
609	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
610	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
611	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
612	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
613	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
614	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
615	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
616	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
617	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
618	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
619	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
620	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
621	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
622	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
623	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
624	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
625	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
626	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
627	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
628	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
629	#376	C₂²×C₃₁	1	1	yes	characteristic
630	#376	C₂²×C₃₁	1	1	yes	characteristic
631	C₄³	C₂²×C₃₁	1	1	yes	characteristic
632	C₄³	C₂²×C₃₁	1	1	yes	characteristic
633	C₂×C₃₁	—	4	4	no	—
634	C₂×C₃₁	—	4	2	no	—
635	C₂×C₃₁	—	8	2	no	—
636	C₂×C₃₁	C₂×#529	1	1	yes	characteristic
637	C₂×C₃₁	#3444	1	1	yes	characteristic
638	C₂×C₃₁	C₂×#540	1	1	yes	characteristic
639	C₂×C₃₁	#3481	1	1	yes	characteristic
640	C₂×C₃₁	#3481	1	1	yes	characteristic
641	C₂×C₃₁	#3481	1	1	yes	characteristic
642	C₂×C₃₁	#3483	1	1	yes	characteristic
643	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
644	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
645	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
646	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
647	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
648	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
649	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
650	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
651	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
652	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
653	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
654	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
655	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
656	#127	—	2	4	no	—
657	#125	—	2	4	no	—
658	#123	—	2	8	no	—
659	#121	—	2	4	no	—
660	#121	—	2	4	no	—
661	#121	—	2	8	no	—
662	C₄×D₄	—	2	4	no	—
663	C₄×D₄	—	2	4	no	—
664	C₄×D₄	—	2	4	no	—
665	C₄×D₄	—	2	4	no	—
666	C₄×D₄	—	4	4	no	—
667	C₄×D₄	—	4	4	no	—
668	C₄×D₄	—	4	4	no	—
669	C₄×D₄	—	4	4	no	—
670	#117	—	2	4	no	—
671	#117	—	2	4	no	—
672	#117	—	4	4	no	—
673	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
674	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
675	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
676	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
677	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
678	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
679	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
680	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
681	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
682	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
683	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
684	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
685	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
686	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
687	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
688	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
689	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
690	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
691	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
692	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
693	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
694	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
695	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
696	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
697	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
698	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
699	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
700	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
701	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
702	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
703	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
704	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
705	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
706	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
707	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
708	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
709	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
710	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
711	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
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	1	yes	characteristic
717	C₂×C₄²	—	2	4	no	—
718	C₂×C₄²	—	4	4	no	—
719	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
720	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
721	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
722	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
723	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
724	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
725	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
726	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
727	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
728	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
729	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
730	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
731	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
732	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
733	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
734	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
735	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
736	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
737	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
738	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
739	#95	C₂³×C₃₁	1	1	yes	characteristic
740	#95	C₂³×C₃₁	1	1	yes	characteristic
741	#95	C₂³×C₃₁	1	1	yes	characteristic
742	#95	C₂³×C₃₁	1	1	yes	characteristic
743	#95	C₂³×C₃₁	1	1	yes	characteristic
744	#95	C₂³×C₃₁	1	1	yes	characteristic
745	#95	C₂³×C₃₁	1	1	yes	characteristic
746	#95	C₂³×C₃₁	1	1	yes	characteristic
747	#95	C₂³×C₃₁	1	2	yes	—
748	#95	C₂³×C₃₁	1	2	yes	—
749	#95	C₂³×C₃₁	1	2	yes	—
750	#95	C₂³×C₃₁	1	2	yes	—
751	#95	C₂³×C₃₁	1	2	yes	—
752	#95	C₂³×C₃₁	1	2	yes	—
753	#95	C₂³×C₃₁	1	2	yes	—
754	#95	C₂³×C₃₁	1	2	yes	—
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	C₃₁	#34970	1	1	yes	characteristic, direct product factor, Sylow
762	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
763	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
764	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
765	C₂×D₄	—	2	4	no	—
766	C₂×D₄	—	2	4	no	—
767	C₂×D₄	—	2	4	no	—
768	C₂×D₄	—	2	4	no	—
769	C₂×D₄	—	2	4	no	—
770	C₂×D₄	—	2	2	no	—
771	C₂×D₄	—	2	2	no	—
772	C₂×D₄	—	2	2	no	—
773	C₂×D₄	—	2	4	no	—
774	C₂×D₄	—	2	4	no	—
775	C₂×D₄	—	2	2	no	—
776	C₂×D₄	—	2	4	no	—
777	C₂×D₄	—	2	2	no	—
778	C₂×D₄	—	4	2	no	—
779	C₂×D₄	—	4	2	no	—
780	C₂×D₄	—	4	2	no	—
781	C₂×D₄	—	4	2	no	—
782	C₂×D₄	#41×C₃₁	1	4	yes	—
783	C₂²×C₄	—	2	2	no	—
784	C₂²×C₄	—	2	2	no	—
785	C₂²×C₄	—	2	2	no	—
786	C₂²×C₄	—	2	4	no	—
787	C₂²×C₄	—	2	2	no	—
788	C₂²×C₄	—	2	2	no	—
789	C₂²×C₄	—	2	4	no	—
790	C₂²×C₄	—	2	4	no	—
791	C₂²×C₄	—	2	4	no	—
792	C₂²×C₄	—	2	4	no	—
793	C₂²×C₄	—	2	2	no	—
794	C₂²×C₄	—	2	2	no	—
795	C₂²×C₄	—	2	4	no	—
796	C₂²×C₄	—	2	4	no	—
797	C₂²×C₄	—	2	4	no	—
798	C₂²×C₄	—	2	2	no	—
799	C₂²×C₄	—	2	2	no	—
800	C₂²×C₄	—	2	4	no	—
801	C₂²×C₄	—	2	4	no	—
802	C₂²×C₄	—	4	2	no	—
803	C₂²×C₄	—	4	2	no	—
804	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
805	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
806	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
807	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
808	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
809	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
810	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
811	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
812	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
813	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
814	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
815	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
816	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
817	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
818	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
819	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
820	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
821	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
822	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
823	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
824	C₄⋊C₄	—	2	2	no	—
825	C₄⋊C₄	—	2	2	no	—
826	C₄⋊C₄	—	2	2	no	—
827	C₄⋊C₄	—	2	2	no	—
828	C₄⋊C₄	—	2	2	no	—
829	C₄⋊C₄	—	2	2	no	—
830	C₄⋊C₄	—	2	4	no	—
831	C₄⋊C₄	—	2	2	no	—
832	C₄⋊C₄	—	2	4	no	—
833	C₄⋊C₄	—	2	4	no	—
834	C₄⋊C₄	—	2	4	no	—
835	C₄⋊C₄	—	2	2	no	—
836	C₄⋊C₄	—	4	2	no	—
837	C₄⋊C₄	—	4	2	no	—
838	C₄⋊C₄	—	4	2	no	—
839	C₄⋊C₄	—	4	2	no	—
840	C₄⋊C₄	—	4	2	no	—
841	C₄⋊C₄	—	4	2	no	—
842	C₄⋊C₄	#41×C₃₁	1	4	yes	—
843	C₄⋊C₄	#41×C₃₁	1	4	yes	—
844	C₂²⋊C₄	—	2	2	no	—
845	C₂²⋊C₄	—	2	4	no	—
846	C₂²⋊C₄	—	2	4	no	—
847	C₂²⋊C₄	—	2	2	no	—
848	C₂²⋊C₄	—	2	2	no	—
849	C₂²⋊C₄	—	2	4	no	—
850	C₂²⋊C₄	—	2	4	no	—
851	C₂²⋊C₄	—	2	4	no	—
852	C₂²⋊C₄	—	2	4	no	—
853	C₂²⋊C₄	—	2	4	no	—
854	C₂²⋊C₄	—	2	4	no	—
855	C₂²⋊C₄	—	2	4	no	—
856	C₂²⋊C₄	—	2	4	no	—
857	C₂²⋊C₄	—	4	2	no	—
858	C₂²⋊C₄	—	4	2	no	—
859	C₂²⋊C₄	—	4	2	no	—
860	C₂²⋊C₄	—	4	2	no	—
861	C₂²⋊C₄	—	4	2	no	—
862	C₂²⋊C₄	—	4	2	no	—
863	C₂²⋊C₄	—	4	2	no	—
864	C₂²⋊C₄	—	4	2	no	—
865	C₂²⋊C₄	—	4	2	no	—
866	C₂²⋊C₄	—	4	2	no	—
867	C₂²⋊C₄	#41×C₃₁	1	4	yes	—
868	C₄²	—	2	2	no	—
869	C₄²	—	2	2	no	—
870	C₄²	—	2	2	no	—
871	C₄²	—	2	2	no	—
872	C₄²	—	2	2	no	—
873	C₄²	—	2	2	no	—
874	C₄²	—	2	2	no	—
875	C₄²	—	2	2	no	—
876	C₄²	—	2	2	no	—
877	C₄²	—	2	2	no	—
878	C₄²	—	2	2	no	—
879	C₄²	—	2	2	no	—
880	C₄²	—	2	4	no	—
881	C₄²	—	2	2	no	—
882	C₄²	—	2	4	no	—
883	C₄²	—	2	2	no	—
884	C₄²	—	2	2	no	—
885	C₄²	—	4	2	no	—
886	C₄²	—	4	2	no	—
887	C₄²	#41×C₃₁	1	4	yes	—
888	C₂³	—	2	1	no	—
889	C₂³	—	2	2	no	—
890	C₂³	—	2	2	no	—
891	C₂³	—	2	2	no	—
892	C₂³	—	2	1	no	—
893	C₂³	—	2	1	no	—
894	C₂³	—	2	1	no	—
895	C₂³	—	2	2	no	—
896	C₂³	—	2	1	no	—
897	C₂³	—	2	2	no	—
898	C₂³	—	2	1	no	—
899	C₂³	—	2	2	no	—
900	C₂³	—	2	2	no	—
901	C₂³	—	2	2	no	—
902	C₂³	—	2	2	no	—
903	C₂³	—	2	2	no	—
904	C₂³	—	2	2	no	—
905	C₂³	—	2	2	no	—
906	C₂³	—	2	2	no	—
907	C₂³	C₂×#41×C₃₁	1	4	yes	—
908	C₂³	C₂×#41×C₃₁	1	2	yes	—
909	C₂³	C₂⁵×C₃₁	1	1	yes	characteristic
910	D₄	—	2	8	no	—
911	D₄	—	4	8	no	—
912	D₄	—	4	8	no	—
913	D₄	—	4	8	no	—
914	D₄	—	4	8	no	—
915	D₄	—	4	4	no	—
916	C₂×C₄	—	2	8	no	—
917	C₂×C₄	—	2	1	no	—
918	C₂×C₄	—	2	1	no	—
919	C₂×C₄	—	2	1	no	—
920	C₂×C₄	—	2	1	no	—
921	C₂×C₄	—	2	1	no	—
922	C₂×C₄	—	2	1	no	—
923	C₂×C₄	—	2	1	no	—
924	C₂×C₄	—	2	1	no	—
925	C₂×C₄	—	2	2	no	—
926	C₂×C₄	—	2	1	no	—
927	C₂×C₄	—	2	1	no	—
928	C₂×C₄	—	2	2	no	—
929	C₂×C₄	—	2	1	no	—
930	C₂×C₄	—	2	1	no	—
931	C₂×C₄	—	2	1	no	—
932	C₂×C₄	—	2	1	no	—
933	C₂×C₄	—	2	1	no	—
934	C₂×C₄	—	2	1	no	—
935	C₂×C₄	—	2	1	no	—
936	C₂×C₄	—	2	1	no	—
937	C₂×C₄	—	2	1	no	—
938	C₂×C₄	—	2	1	no	—
939	C₂×C₄	—	2	1	no	—
940	C₂×C₄	—	2	1	no	—
941	C₂×C₄	—	2	2	no	—
942	C₂×C₄	—	2	1	no	—
943	C₂×C₄	—	2	1	no	—
944	C₂×C₄	—	2	2	no	—
945	C₂×C₄	—	2	2	no	—
946	C₂×C₄	—	2	2	no	—
947	C₂×C₄	—	2	2	no	—
948	C₂×C₄	—	2	2	no	—
949	C₂×C₄	—	2	2	no	—
950	C₂×C₄	—	2	2	no	—
951	C₂×C₄	—	2	2	no	—
952	C₂×C₄	—	2	1	no	—
953	C₂×C₄	—	2	1	no	—
954	C₂×C₄	—	2	2	no	—
955	C₂×C₄	—	2	1	no	—
956	C₂×C₄	—	2	1	no	—
957	C₂×C₄	—	2	2	no	—
958	C₂×C₄	—	2	2	no	—
959	C₂×C₄	—	2	1	no	—
960	C₂×C₄	—	2	2	no	—
961	C₂×C₄	—	2	1	no	—
962	C₂×C₄	—	2	2	no	—
963	C₂×C₄	—	2	2	no	—
964	C₂×C₄	—	4	8	no	—
965	C₂×C₄	—	4	8	no	—
966	C₂×C₄	—	4	4	no	—
967	C₂×C₄	—	4	4	no	—
968	C₂×C₄	—	4	8	no	—
969	C₂×C₄	—	4	8	no	—
970	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
971	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
972	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
973	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
974	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
975	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
976	C₂×C₄	C₂×#41×C₃₁	1	4	yes	—
977	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
978	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
979	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
980	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
981	C₂×C₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
982	C₂×C₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
983	C₂²	—	2	4	no	—
984	C₂²	—	2	2	no	—
985	C₂²	—	2	4	no	—
986	C₂²	—	2	2	no	—
987	C₂²	—	2	4	no	—
988	C₂²	—	2	2	no	—
989	C₂²	—	4	1	no	—
990	C₂²	—	4	2	no	—
991	C₂²	—	4	2	no	—
992	C₂²	—	4	1	no	—
993	C₂²	—	4	2	no	—
994	C₂²	—	4	1	no	—
995	C₂²	—	4	1	no	—
996	C₂²	—	4	2	no	—
997	C₂²	—	4	2	no	—
998	C₂²	—	4	2	no	—
999	C₂²	—	4	2	no	—
1000	C₂²	—	4	2	no	—
1001	C₂²	—	4	2	no	—
1002	C₂²	—	4	2	no	—
1003	C₂²	—	4	2	no	—
1004	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
1005	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
1006	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
1007	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
1008	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
1009	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
1010	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
1011	C₄	—	2	2	no	—
1012	C₄	—	2	2	no	—
1013	C₄	—	2	2	no	—
1014	C₄	—	2	2	no	—
1015	C₄	—	2	4	no	—
1016	C₄	—	2	2	no	—
1017	C₄	—	2	2	no	—
1018	C₄	—	4	1	no	—
1019	C₄	—	4	1	no	—
1020	C₄	—	4	2	no	—
1021	C₄	—	4	2	no	—
1022	C₄	—	4	2	no	—
1023	C₄	—	4	2	no	—
1024	C₄	—	4	1	no	—
1025	C₄	—	4	1	no	—
1026	C₄	—	4	1	no	—
1027	C₄	—	4	1	no	—
1028	C₄	—	4	2	no	—
1029	C₄	C₃₁×#529	1	4	yes	—
1030	C₄	C₃₁×#540	1	4	yes	—
1031	C₂	—	4	4	no	—
1032	C₂	—	4	2	no	—
1033	C₂	—	8	2	no	—
1034	C₂	C₂×C₃₁×#529	1	1	yes	characteristic
1035	C₂	C₃₁×#3444	1	1	yes	characteristic
1036	C₂	C₂×C₃₁×#540	1	1	yes	characteristic
1037	C₂	C₃₁×#3481	1	1	yes	characteristic
1038	C₂	C₃₁×#3481	1	1	yes	characteristic
1039	C₂	C₃₁×#3481	1	1	yes	characteristic
1040	C₂	C₃₁×#3483	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₃₁	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₃₁
socle	C₂³×C₃₁	C₂⁵
prime radical	C₃₁×#2428	C₂
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×#2531	C₂	semidirect
2. C₃₁×#2526	C₂	semidirect
3. C₃₁×#2513	C₂	semidirect
4. C₃₁×#2507	C₂	semidirect
5. C₃₁×#2497	C₂	semidirect
6. C₃₁×#2490	C₂	semidirect
7. C₃₁×#2476	C₂	semidirect
8. C₃₁×#2471	C₂	semidirect
9. C₃₁×#2454	C₂	semidirect
10. C₃₁×#2445	C₂	semidirect
12. C₃₁×#2420	C₂	semidirect
13. C₃₁×#2395	C₂	semidirect
14. C₃₁×#2392	C₂	semidirect
15. C₄×C₃₁×#127	C₂	semidirect
16. C₄×C₃₁×#125	C₂	semidirect
17. C₄×C₃₁×#123	C₂	semidirect
18. C₄×C₃₁×#121	C₂	semidirect
19. C₄×C₃₁×#121	C₂	semidirect
20. C₄×C₃₁×#121	C₂	semidirect
21. C₃₁×#2293	C₂	semidirect
22. C₄²×D₄×C₃₁	C₂	semidirect
23. C₄×C₃₁×#117	C₂	semidirect
367. #34970	C₃₁	direct (N × H)
463. #2531	C₂×C₃₁	semidirect
464. #2526	C₂×C₃₁	semidirect
465. #2513	C₂×C₃₁	semidirect
466. #2507	C₂×C₃₁	semidirect
467. #2497	C₂×C₃₁	semidirect
468. #2490	C₂×C₃₁	semidirect
469. #2476	C₂×C₃₁	semidirect
470. #2471	C₂×C₃₁	semidirect
471. #2454	C₂×C₃₁	semidirect
472. #2445	C₂×C₃₁	semidirect
474. #2420	C₂×C₃₁	semidirect
475. #2395	C₂×C₃₁	semidirect
476. #2392	C₂×C₃₁	semidirect
477. C₄×#127	C₂×C₃₁	semidirect
478. C₄×#125	C₂×C₃₁	semidirect
479. C₄×#123	C₂×C₃₁	semidirect
480. C₄×#121	C₂×C₃₁	semidirect
481. C₄×#121	C₂×C₃₁	semidirect
482. C₄×#121	C₂×C₃₁	semidirect
483. #2293	C₂×C₃₁	semidirect
484. C₄²×D₄	C₂×C₃₁	semidirect
485. C₄×#117	C₂×C₃₁	semidirect
761. C₃₁	#34970	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×#2531	2
C₃₁×#2526	2
C₃₁×#2513	2
C₃₁×#2507	2
C₃₁×#2497	2
C₃₁×#2490	2
C₃₁×#2476	2
C₃₁×#2471	2
C₃₁×#2454	2
C₃₁×#2445	2
C₃₁×#2428	2
C₃₁×#2420	2
C₃₁×#2395	2
C₃₁×#2392	2
C₄×C₃₁×#127	2
C₄×C₃₁×#125	2
C₄×C₃₁×#123	2
C₄×C₃₁×#121	2
C₃₁×#2293	2
C₄²×D₄×C₃₁	2
C₄×C₃₁×#117	2
#34970	31

Subgroups — C31×#34970 #21491729

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#34970 #21491729