Subgroups — C₃₁×#34800 #21491559

Order 7936.

1992 conjugacy classes of subgroups.

The subgroup lattice has 1024 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#2532	C₂	1	2	yes	maximal, complemented
2	C₃₁×#2526	C₂	1	2	yes	maximal, complemented
3	C₃₁×#2518	C₂	1	2	yes	maximal, complemented
4	C₃₁×#2513	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#2508	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#2500	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#2497	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#2491	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#2485	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#2459	C₂	1	2	yes	maximal, complemented
11	C₃₁×#2439	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#2414	C₂	1	1	yes	maximal, characteristic
13	C₃₁×#2398	C₂	1	2	yes	maximal, complemented
14	C₃₁×#2392	C₂	1	2	yes	maximal, complemented
15	C₄×C₃₁×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×C₃₁×#124	C₂	1	2	yes	maximal, complemented
17	C₄×C₃₁×#121	C₂	1	1	yes	maximal, characteristic, complemented
18	C₄×C₃₁×#121	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#2298	C₂	1	2	yes	maximal, complemented
20	C₃₁×#2293	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃₁×#2283	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×C₄⋊Q₈	C₂²	1	1	yes	characteristic
25	C₂×C₃₁×#124	C₂²	1	2	yes	—
26	C₂×C₃₁×#121	C₂²	1	1	yes	characteristic
27	C₂×C₃₁×#121	C₂²	1	1	yes	characteristic
28	C₂×C₄×Q₈×C₃₁	C₂²	1	2	yes	—
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	1	yes	characteristic
33	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
34	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
35	C₂×C₃₁×#117	C₂²	1	2	yes	—
36	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
37	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
38	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
39	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
40	C₃₁×#400	C₂²	1	2	yes	—
41	C₃₁×#400	C₂²	1	2	yes	—
42	C₃₁×#398	C₂²	1	2	yes	—
43	C₃₁×#397	C₂²	1	2	yes	—
44	C₃₁×#397	C₂²	1	2	yes	—
45	C₃₁×#397	C₂²	1	2	yes	—
46	C₃₁×#396	C₂²	1	2	yes	—
47	C₃₁×#396	C₂²	1	2	yes	—
48	C₃₁×#394	C₂²	1	2	yes	—
49	C₃₁×#394	C₂²	1	2	yes	—
50	C₃₁×#394	C₂²	1	2	yes	—
51	C₃₁×#394	C₂²	1	2	yes	—
52	C₃₁×#394	C₂²	1	2	yes	—
53	C₃₁×#393	C₂²	1	2	yes	—
54	C₃₁×#393	C₂²	1	2	yes	—
55	C₃₁×#392	C₂²	1	2	yes	—
56	C₃₁×#391	C₂²	1	2	yes	—
57	C₃₁×#391	C₂²	1	2	yes	—
58	C₃₁×#390	C₂²	1	1	yes	characteristic
59	C₃₁×#390	C₂²	1	2	yes	—
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×#389	C₂²	1	1	yes	characteristic
64	C₃₁×#389	C₂²	1	1	yes	characteristic
65	C₃₁×#389	C₂²	1	2	yes	—
66	C₃₁×#389	C₂²	1	1	yes	characteristic
67	C₃₁×#389	C₂²	1	1	yes	characteristic
68	C₃₁×#389	C₂²	1	1	yes	characteristic
69	C₃₁×#389	C₂²	1	1	yes	characteristic
70	C₃₁×#388	C₂²	1	2	yes	—
71	C₃₁×#388	C₂²	1	2	yes	—
72	C₃₁×#388	C₂²	1	2	yes	—
73	C₃₁×#388	C₂²	1	2	yes	—
74	C₃₁×#388	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×#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×#386	C₂²	1	2	yes	—
87	C₃₁×#386	C₂²	1	2	yes	—
88	C₃₁×#384	C₂²	1	1	yes	characteristic
89	C₃₁×#383	C₂²	1	2	yes	—
90	C₃₁×#382	C₂²	1	1	yes	characteristic
91	C₃₁×#382	C₂²	1	1	yes	characteristic
92	C₃₁×#382	C₂²	1	2	yes	—
93	C₃₁×#381	C₂²	1	2	yes	—
94	C₃₁×#380	C₂²	1	1	yes	characteristic
95	C₃₁×#380	C₂²	1	1	yes	characteristic
96	C₃₁×#380	C₂²	1	1	yes	characteristic
97	C₃₁×#380	C₂²	1	1	yes	characteristic
98	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
99	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
100	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
101	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
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×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
108	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
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	1	yes	characteristic
113	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
114	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
115	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
116	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
117	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
118	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
119	C₃₁×#376	C₂²	1	2	yes	—
120	C₃₁×#376	C₂²	1	2	yes	—
121	C₄³×C₃₁	C₂²	1	1	yes	characteristic
122	C₄³×C₃₁	C₂²	1	2	yes	—
123	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
124	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
125	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
126	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
127	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
128	C₂³×C₄×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	2	yes	—
132	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
133	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
134	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
135	C₃₁×C₄⋊Q₈	—	2	4	no	—
136	C₃₁×#124	—	2	8	no	—
137	C₃₁×#121	—	2	4	no	—
138	C₃₁×#121	—	2	4	no	—
139	C₄×Q₈×C₃₁	—	4	4	no	—
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	—	4	4	no	—
145	C₄×D₄×C₃₁	—	4	4	no	—
146	C₃₁×#117	—	2	4	no	—
147	C₃₁×#117	—	2	4	no	—
148	C₃₁×#117	—	2	8	no	—
149	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
150	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
151	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
152	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
153	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
154	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
155	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
156	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
157	C₂×C₄⋊C₄×C₃₁	C₂³	1	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	2	yes	—
162	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
163	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
164	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
165	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
166	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
167	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
168	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
169	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
170	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
171	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
176	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
177	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
178	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
179	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
180	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
181	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
182	C₂×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	1	yes	characteristic
191	C₂×C₄²×C₃₁	—	2	4	no	—
192	C₂×C₄²×C₃₁	—	2	4	no	—
193	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
194	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
195	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
196	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
197	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
198	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
199	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
200	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
201	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
202	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
203	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
204	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
205	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
206	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
207	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
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	C₃₁×#95	C₂³	1	2	yes	—
214	C₃₁×#95	C₂³	1	2	yes	—
215	C₃₁×#95	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
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	1	yes	characteristic
232	C₃₁×#95	C₂³	1	1	yes	characteristic
233	C₃₁×#95	C₂³	1	1	yes	characteristic
234	C₃₁×#95	C₂³	1	1	yes	characteristic
235	C₃₁×#95	C₂³	1	2	yes	—
236	C₃₁×#95	C₂³	1	2	yes	—
237	C₃₁×#95	C₂³	1	2	yes	—
238	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
239	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
240	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
241	C₂×Q₈×C₃₁	—	2	4	no	—
242	C₂×Q₈×C₃₁	—	2	4	no	—
243	C₂×Q₈×C₃₁	—	4	2	no	—
244	C₂×D₄×C₃₁	—	2	2	no	—
245	C₂×D₄×C₃₁	—	2	2	no	—
246	C₂×D₄×C₃₁	—	2	4	no	—
247	C₂×D₄×C₃₁	—	2	4	no	—
248	C₂×D₄×C₃₁	—	2	2	no	—
249	C₂×D₄×C₃₁	—	2	2	no	—
250	C₂×D₄×C₃₁	—	2	4	no	—
251	C₂×D₄×C₃₁	—	2	2	no	—
252	C₂×D₄×C₃₁	—	2	2	no	—
253	C₂×D₄×C₃₁	—	4	2	no	—
254	C₂×D₄×C₃₁	—	4	2	no	—
255	C₂×D₄×C₃₁	—	4	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	4	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	2	no	—
269	C₂²×C₄×C₃₁	—	2	4	no	—
270	C₂²×C₄×C₃₁	—	2	2	no	—
271	C₂²×C₄×C₃₁	—	2	2	no	—
272	C₂²×C₄×C₃₁	—	2	2	no	—
273	C₂²×C₄×C₃₁	—	2	4	no	—
274	C₂²×C₄×C₃₁	—	4	1	no	—
275	C₂²×C₄×C₃₁	—	4	1	no	—
276	C₂²×C₄×C₃₁	#41	1	4	yes	—
277	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
278	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
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	2	yes	—
284	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
285	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
286	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
287	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
288	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
289	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
290	C₂²×C₄×C₃₁	C₂⁴	1	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	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	C₄⋊C₄×C₃₁	—	2	2	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	4	no	—
302	C₄⋊C₄×C₃₁	—	2	2	no	—
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	4	no	—
308	C₄⋊C₄×C₃₁	—	2	2	no	—
309	C₄⋊C₄×C₃₁	—	4	2	no	—
310	C₄⋊C₄×C₃₁	—	4	2	no	—
311	C₄⋊C₄×C₃₁	—	4	2	no	—
312	C₄⋊C₄×C₃₁	—	4	2	no	—
313	C₄⋊C₄×C₃₁	—	4	2	no	—
314	C₄⋊C₄×C₃₁	—	4	2	no	—
315	C₄⋊C₄×C₃₁	#41	1	4	yes	—
316	C₂²⋊C₄×C₃₁	—	2	4	no	—
317	C₂²⋊C₄×C₃₁	—	2	2	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	2	no	—
323	C₂²⋊C₄×C₃₁	—	2	4	no	—
324	C₂²⋊C₄×C₃₁	—	2	2	no	—
325	C₂²⋊C₄×C₃₁	—	2	2	no	—
326	C₂²⋊C₄×C₃₁	—	2	2	no	—
327	C₂²⋊C₄×C₃₁	—	2	4	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	—	4	2	no	—
332	C₂²⋊C₄×C₃₁	—	4	2	no	—
333	C₂²⋊C₄×C₃₁	—	4	2	no	—
334	C₂²⋊C₄×C₃₁	—	4	2	no	—
335	C₂²⋊C₄×C₃₁	—	4	2	no	—
336	C₂²⋊C₄×C₃₁	—	4	2	no	—
337	C₂²⋊C₄×C₃₁	—	4	2	no	—
338	C₂²⋊C₄×C₃₁	#41	1	4	yes	—
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	4	no	—
346	C₄²×C₃₁	—	2	4	no	—
347	C₄²×C₃₁	—	2	4	no	—
348	C₄²×C₃₁	—	2	2	no	—
349	C₄²×C₃₁	—	2	2	no	—
350	C₄²×C₃₁	—	2	4	no	—
351	C₄²×C₃₁	—	2	2	no	—
352	C₄²×C₃₁	—	2	4	no	—
353	C₄²×C₃₁	—	2	4	no	—
354	C₄²×C₃₁	—	2	2	no	—
355	C₄²×C₃₁	—	4	2	no	—
356	C₄²×C₃₁	—	4	1	no	—
357	C₄²×C₃₁	#41	1	4	yes	—
358	C₄²×C₃₁	#41	1	4	yes	—
359	#34800	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	1	no	—
365	C₂³×C₃₁	—	2	1	no	—
366	C₂³×C₃₁	—	2	1	no	—
367	C₂³×C₃₁	—	2	1	no	—
368	C₂³×C₃₁	—	2	1	no	—
369	C₂³×C₃₁	—	2	1	no	—
370	C₂³×C₃₁	—	2	1	no	—
371	C₂³×C₃₁	—	2	1	no	—
372	C₂³×C₃₁	—	2	2	no	—
373	C₂³×C₃₁	—	2	2	no	—
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	2	no	—
379	C₂³×C₃₁	C₂×#41	1	2	yes	—
380	C₂³×C₃₁	C₂×#41	1	2	yes	—
381	C₂³×C₃₁	C₂⁵	1	1	yes	characteristic
382	Q₈×C₃₁	—	4	8	no	—
383	D₄×C₃₁	—	2	8	no	—
384	D₄×C₃₁	—	4	8	no	—
385	D₄×C₃₁	—	4	8	no	—
386	D₄×C₃₁	—	4	4	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	2	no	—
395	C₂×C₄×C₃₁	—	2	1	no	—
396	C₂×C₄×C₃₁	—	2	2	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	8	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	2	no	—
407	C₂×C₄×C₃₁	—	2	1	no	—
408	C₂×C₄×C₃₁	—	2	2	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	1	no	—
414	C₂×C₄×C₃₁	—	2	2	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	1	no	—
419	C₂×C₄×C₃₁	—	2	1	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	1	no	—
426	C₂×C₄×C₃₁	—	2	2	no	—
427	C₂×C₄×C₃₁	—	2	1	no	—
428	C₂×C₄×C₃₁	—	2	1	no	—
429	C₂×C₄×C₃₁	—	2	2	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	1	no	—
434	C₂×C₄×C₃₁	—	2	2	no	—
435	C₂×C₄×C₃₁	—	4	4	no	—
436	C₂×C₄×C₃₁	—	4	4	no	—
437	C₂×C₄×C₃₁	—	4	4	no	—
438	C₂×C₄×C₃₁	—	4	4	no	—
439	C₂×C₄×C₃₁	—	4	4	no	—
440	C₂×C₄×C₃₁	—	4	8	no	—
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	4	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	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
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	H(5,𝔽₂)	1	2	yes	—
454	#2532	C₂×C₃₁	1	2	yes	complemented
455	#2526	C₂×C₃₁	1	2	yes	complemented
456	#2518	C₂×C₃₁	1	2	yes	complemented
457	#2513	C₂×C₃₁	1	1	yes	characteristic, complemented
458	#2508	C₂×C₃₁	1	1	yes	characteristic, complemented
459	#2500	C₂×C₃₁	1	1	yes	characteristic, complemented
460	#2497	C₂×C₃₁	1	1	yes	characteristic, complemented
461	#2491	C₂×C₃₁	1	1	yes	characteristic, complemented
462	#2485	C₂×C₃₁	1	1	yes	characteristic, complemented
463	#2459	C₂×C₃₁	1	2	yes	complemented
464	#2439	C₂×C₃₁	1	1	yes	characteristic, complemented
465	#2414	C₂×C₃₁	1	1	yes	characteristic
466	#2398	C₂×C₃₁	1	2	yes	complemented
467	#2392	C₂×C₃₁	1	2	yes	complemented
468	C₄×C₄⋊Q₈	C₂×C₃₁	1	1	yes	characteristic, complemented
469	C₄×#124	C₂×C₃₁	1	2	yes	complemented
470	C₄×#121	C₂×C₃₁	1	1	yes	characteristic, complemented
471	C₄×#121	C₂×C₃₁	1	1	yes	characteristic, complemented
472	#2298	C₂×C₃₁	1	2	yes	complemented
473	#2293	C₂×C₃₁	1	1	yes	characteristic, complemented
474	#2283	C₂×C₃₁	1	1	yes	characteristic, complemented
475	C₄²×D₄	C₂×C₃₁	1	1	yes	characteristic, complemented
476	C₄×#117	C₂×C₃₁	1	1	yes	characteristic, complemented
477	C₂²×C₃₁	—	2	2	no	—
478	C₂²×C₃₁	—	2	2	no	—
479	C₂²×C₃₁	—	2	2	no	—
480	C₂²×C₃₁	—	2	2	no	—
481	C₂²×C₃₁	—	2	2	no	—
482	C₂²×C₃₁	—	2	2	no	—
483	C₂²×C₃₁	—	4	1	no	—
484	C₂²×C₃₁	—	4	1	no	—
485	C₂²×C₃₁	—	4	1	no	—
486	C₂²×C₃₁	—	4	1	no	—
487	C₂²×C₃₁	—	4	1	no	—
488	C₂²×C₃₁	—	4	1	no	—
489	C₂²×C₃₁	—	4	1	no	—
490	C₂²×C₃₁	—	4	1	no	—
491	C₂²×C₃₁	—	4	2	no	—
492	C₂²×C₃₁	—	4	2	no	—
493	C₂²×C₃₁	—	4	2	no	—
494	C₂²×C₃₁	—	4	2	no	—
495	C₂²×C₃₁	—	4	2	no	—
496	C₂²×C₃₁	—	4	2	no	—
497	C₂²×C₃₁	—	4	2	no	—
498	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
499	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
500	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
501	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
502	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
503	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
504	C₂²×C₃₁	#585	1	1	yes	characteristic
505	C₄×C₃₁	—	2	2	no	—
506	C₄×C₃₁	—	2	2	no	—
507	C₄×C₃₁	—	2	2	no	—
508	C₄×C₃₁	—	2	2	no	—
509	C₄×C₃₁	—	2	2	no	—
510	C₄×C₃₁	—	2	4	no	—
511	C₄×C₃₁	—	2	2	no	—
512	C₄×C₃₁	—	4	1	no	—
513	C₄×C₃₁	—	4	2	no	—
514	C₄×C₃₁	—	4	1	no	—
515	C₄×C₃₁	—	4	2	no	—
516	C₄×C₃₁	—	4	2	no	—
517	C₄×C₃₁	—	4	1	no	—
518	C₄×C₃₁	—	4	1	no	—
519	C₄×C₃₁	—	4	2	no	—
520	C₄×C₃₁	—	4	1	no	—
521	C₄×C₃₁	—	4	2	no	—
522	C₄×C₃₁	—	4	2	no	—
523	C₄×C₃₁	#529	1	4	yes	—
524	C₄×C₃₁	#555	1	4	yes	—
525	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
526	C₂×#124	C₂²×C₃₁	1	2	yes	—
527	C₂×#121	C₂²×C₃₁	1	1	yes	characteristic
528	C₂×#121	C₂²×C₃₁	1	1	yes	characteristic
529	C₂×C₄×Q₈	C₂²×C₃₁	1	2	yes	—
530	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
531	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
532	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
533	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
534	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
535	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
536	C₂×#117	C₂²×C₃₁	1	2	yes	—
537	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
538	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
539	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
540	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
541	#400	C₂²×C₃₁	1	2	yes	—
542	#400	C₂²×C₃₁	1	2	yes	—
543	#398	C₂²×C₃₁	1	2	yes	—
544	#397	C₂²×C₃₁	1	2	yes	—
545	#397	C₂²×C₃₁	1	2	yes	—
546	#397	C₂²×C₃₁	1	2	yes	—
547	#396	C₂²×C₃₁	1	2	yes	—
548	#396	C₂²×C₃₁	1	2	yes	—
549	#394	C₂²×C₃₁	1	2	yes	—
550	#394	C₂²×C₃₁	1	2	yes	—
551	#394	C₂²×C₃₁	1	2	yes	—
552	#394	C₂²×C₃₁	1	2	yes	—
553	#394	C₂²×C₃₁	1	2	yes	—
554	#393	C₂²×C₃₁	1	2	yes	—
555	#393	C₂²×C₃₁	1	2	yes	—
556	#392	C₂²×C₃₁	1	2	yes	—
557	#391	C₂²×C₃₁	1	2	yes	—
558	#391	C₂²×C₃₁	1	2	yes	—
559	#390	C₂²×C₃₁	1	1	yes	characteristic
560	#390	C₂²×C₃₁	1	2	yes	—
561	#390	C₂²×C₃₁	1	1	yes	characteristic
562	#390	C₂²×C₃₁	1	1	yes	characteristic
563	#390	C₂²×C₃₁	1	1	yes	characteristic
564	#389	C₂²×C₃₁	1	1	yes	characteristic
565	#389	C₂²×C₃₁	1	1	yes	characteristic
566	#389	C₂²×C₃₁	1	2	yes	—
567	#389	C₂²×C₃₁	1	1	yes	characteristic
568	#389	C₂²×C₃₁	1	1	yes	characteristic
569	#389	C₂²×C₃₁	1	1	yes	characteristic
570	#389	C₂²×C₃₁	1	1	yes	characteristic
571	#388	C₂²×C₃₁	1	2	yes	—
572	#388	C₂²×C₃₁	1	2	yes	—
573	#388	C₂²×C₃₁	1	2	yes	—
574	#388	C₂²×C₃₁	1	2	yes	—
575	#388	C₂²×C₃₁	1	2	yes	—
576	#388	C₂²×C₃₁	1	2	yes	—
577	#388	C₂²×C₃₁	1	2	yes	—
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	2	yes	—
583	#387	C₂²×C₃₁	1	2	yes	—
584	#387	C₂²×C₃₁	1	2	yes	—
585	#387	C₂²×C₃₁	1	2	yes	—
586	#387	C₂²×C₃₁	1	2	yes	—
587	#386	C₂²×C₃₁	1	2	yes	—
588	#386	C₂²×C₃₁	1	2	yes	—
589	#384	C₂²×C₃₁	1	1	yes	characteristic
590	#383	C₂²×C₃₁	1	2	yes	—
591	#382	C₂²×C₃₁	1	1	yes	characteristic
592	#382	C₂²×C₃₁	1	1	yes	characteristic
593	#382	C₂²×C₃₁	1	2	yes	—
594	#381	C₂²×C₃₁	1	2	yes	—
595	#380	C₂²×C₃₁	1	1	yes	characteristic
596	#380	C₂²×C₃₁	1	1	yes	characteristic
597	#380	C₂²×C₃₁	1	1	yes	characteristic
598	#380	C₂²×C₃₁	1	1	yes	characteristic
599	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
600	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
601	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
602	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
603	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
604	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
605	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
606	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
607	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
608	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
609	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
610	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
611	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
612	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
613	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
614	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
615	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
616	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
617	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
618	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
619	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
620	#376	C₂²×C₃₁	1	2	yes	—
621	#376	C₂²×C₃₁	1	2	yes	—
622	C₄³	C₂²×C₃₁	1	1	yes	characteristic
623	C₄³	C₂²×C₃₁	1	2	yes	—
624	C₂×C₃₁	—	4	2	no	—
625	C₂×C₃₁	—	4	2	no	—
626	C₂×C₃₁	—	8	2	no	—
627	C₂×C₃₁	C₂×#529	1	1	yes	characteristic
628	C₂×C₃₁	#3444	1	1	yes	characteristic
629	C₂×C₃₁	#3460	1	1	yes	characteristic
630	C₂×C₃₁	C₂×#555	1	1	yes	characteristic
631	C₂×C₃₁	#3475	1	1	yes	characteristic
632	C₂×C₃₁	#3480	1	1	yes	characteristic
633	C₂×C₃₁	#3481	1	1	yes	characteristic
634	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
635	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
636	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
637	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
638	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
639	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
640	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
641	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
642	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
643	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
644	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
645	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
646	C₄⋊Q₈	—	2	4	no	—
647	#124	—	2	8	no	—
648	#121	—	2	4	no	—
649	#121	—	2	4	no	—
650	C₄×Q₈	—	4	4	no	—
651	C₄×D₄	—	2	4	no	—
652	C₄×D₄	—	2	4	no	—
653	C₄×D₄	—	2	4	no	—
654	C₄×D₄	—	2	4	no	—
655	C₄×D₄	—	4	4	no	—
656	C₄×D₄	—	4	4	no	—
657	#117	—	2	4	no	—
658	#117	—	2	4	no	—
659	#117	—	2	8	no	—
660	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
661	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
662	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
663	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
664	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
665	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
666	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
667	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
668	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
669	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
670	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
671	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
672	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
673	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
674	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
675	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
676	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
677	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
678	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
679	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
680	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
681	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
682	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
683	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
684	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
685	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
686	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
687	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
688	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
689	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
690	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
691	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
692	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
693	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
694	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
695	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
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	1	yes	characteristic
702	C₂×C₄²	—	2	4	no	—
703	C₂×C₄²	—	2	4	no	—
704	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
705	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
706	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
707	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
708	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
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	2	yes	—
713	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
714	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
715	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
716	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
717	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
718	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
719	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
720	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
721	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
722	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
723	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
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	1	yes	characteristic
733	#95	C₂³×C₃₁	1	1	yes	characteristic
734	#95	C₂³×C₃₁	1	1	yes	characteristic
735	#95	C₂³×C₃₁	1	1	yes	characteristic
736	#95	C₂³×C₃₁	1	1	yes	characteristic
737	#95	C₂³×C₃₁	1	1	yes	characteristic
738	#95	C₂³×C₃₁	1	2	yes	—
739	#95	C₂³×C₃₁	1	2	yes	—
740	#95	C₂³×C₃₁	1	2	yes	—
741	#95	C₂³×C₃₁	1	2	yes	—
742	#95	C₂³×C₃₁	1	2	yes	—
743	#95	C₂³×C₃₁	1	2	yes	—
744	#95	C₂³×C₃₁	1	2	yes	—
745	#95	C₂³×C₃₁	1	2	yes	—
746	#95	C₂³×C₃₁	1	2	yes	—
747	#95	C₂³×C₃₁	1	2	yes	—
748	#95	C₂³×C₃₁	1	2	yes	—
749	C₃₁	#34800	1	1	yes	characteristic, direct product factor, Sylow
750	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
751	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
752	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
753	C₂×Q₈	—	2	4	no	—
754	C₂×Q₈	—	2	4	no	—
755	C₂×Q₈	—	4	2	no	—
756	C₂×D₄	—	2	2	no	—
757	C₂×D₄	—	2	2	no	—
758	C₂×D₄	—	2	4	no	—
759	C₂×D₄	—	2	4	no	—
760	C₂×D₄	—	2	2	no	—
761	C₂×D₄	—	2	2	no	—
762	C₂×D₄	—	2	4	no	—
763	C₂×D₄	—	2	2	no	—
764	C₂×D₄	—	2	2	no	—
765	C₂×D₄	—	4	2	no	—
766	C₂×D₄	—	4	2	no	—
767	C₂×D₄	—	4	2	no	—
768	C₂²×C₄	—	2	2	no	—
769	C₂²×C₄	—	2	2	no	—
770	C₂²×C₄	—	2	2	no	—
771	C₂²×C₄	—	2	2	no	—
772	C₂²×C₄	—	2	2	no	—
773	C₂²×C₄	—	2	2	no	—
774	C₂²×C₄	—	2	2	no	—
775	C₂²×C₄	—	2	2	no	—
776	C₂²×C₄	—	2	4	no	—
777	C₂²×C₄	—	2	2	no	—
778	C₂²×C₄	—	2	2	no	—
779	C₂²×C₄	—	2	2	no	—
780	C₂²×C₄	—	2	2	no	—
781	C₂²×C₄	—	2	4	no	—
782	C₂²×C₄	—	2	2	no	—
783	C₂²×C₄	—	2	2	no	—
784	C₂²×C₄	—	2	2	no	—
785	C₂²×C₄	—	2	4	no	—
786	C₂²×C₄	—	4	1	no	—
787	C₂²×C₄	—	4	1	no	—
788	C₂²×C₄	#41×C₃₁	1	4	yes	—
789	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
790	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
791	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
792	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
793	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
794	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
795	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
796	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
797	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
798	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
799	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
800	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
801	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
802	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
803	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
804	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
805	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
806	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
807	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
808	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
809	C₄⋊C₄	—	2	2	no	—
810	C₄⋊C₄	—	2	2	no	—
811	C₄⋊C₄	—	2	2	no	—
812	C₄⋊C₄	—	2	4	no	—
813	C₄⋊C₄	—	2	4	no	—
814	C₄⋊C₄	—	2	2	no	—
815	C₄⋊C₄	—	2	2	no	—
816	C₄⋊C₄	—	2	2	no	—
817	C₄⋊C₄	—	2	2	no	—
818	C₄⋊C₄	—	2	2	no	—
819	C₄⋊C₄	—	2	4	no	—
820	C₄⋊C₄	—	2	2	no	—
821	C₄⋊C₄	—	4	2	no	—
822	C₄⋊C₄	—	4	2	no	—
823	C₄⋊C₄	—	4	2	no	—
824	C₄⋊C₄	—	4	2	no	—
825	C₄⋊C₄	—	4	2	no	—
826	C₄⋊C₄	—	4	2	no	—
827	C₄⋊C₄	#41×C₃₁	1	4	yes	—
828	C₂²⋊C₄	—	2	4	no	—
829	C₂²⋊C₄	—	2	2	no	—
830	C₂²⋊C₄	—	2	4	no	—
831	C₂²⋊C₄	—	2	4	no	—
832	C₂²⋊C₄	—	2	4	no	—
833	C₂²⋊C₄	—	2	4	no	—
834	C₂²⋊C₄	—	2	2	no	—
835	C₂²⋊C₄	—	2	4	no	—
836	C₂²⋊C₄	—	2	2	no	—
837	C₂²⋊C₄	—	2	2	no	—
838	C₂²⋊C₄	—	2	2	no	—
839	C₂²⋊C₄	—	2	4	no	—
840	C₂²⋊C₄	—	2	4	no	—
841	C₂²⋊C₄	—	2	4	no	—
842	C₂²⋊C₄	—	2	4	no	—
843	C₂²⋊C₄	—	4	2	no	—
844	C₂²⋊C₄	—	4	2	no	—
845	C₂²⋊C₄	—	4	2	no	—
846	C₂²⋊C₄	—	4	2	no	—
847	C₂²⋊C₄	—	4	2	no	—
848	C₂²⋊C₄	—	4	2	no	—
849	C₂²⋊C₄	—	4	2	no	—
850	C₂²⋊C₄	#41×C₃₁	1	4	yes	—
851	C₄²	—	2	2	no	—
852	C₄²	—	2	2	no	—
853	C₄²	—	2	2	no	—
854	C₄²	—	2	2	no	—
855	C₄²	—	2	2	no	—
856	C₄²	—	2	2	no	—
857	C₄²	—	2	4	no	—
858	C₄²	—	2	4	no	—
859	C₄²	—	2	4	no	—
860	C₄²	—	2	2	no	—
861	C₄²	—	2	2	no	—
862	C₄²	—	2	4	no	—
863	C₄²	—	2	2	no	—
864	C₄²	—	2	4	no	—
865	C₄²	—	2	4	no	—
866	C₄²	—	2	2	no	—
867	C₄²	—	4	2	no	—
868	C₄²	—	4	1	no	—
869	C₄²	#41×C₃₁	1	4	yes	—
870	C₄²	#41×C₃₁	1	4	yes	—
871	C₂³	—	2	1	no	—
872	C₂³	—	2	1	no	—
873	C₂³	—	2	1	no	—
874	C₂³	—	2	1	no	—
875	C₂³	—	2	1	no	—
876	C₂³	—	2	1	no	—
877	C₂³	—	2	1	no	—
878	C₂³	—	2	1	no	—
879	C₂³	—	2	1	no	—
880	C₂³	—	2	1	no	—
881	C₂³	—	2	1	no	—
882	C₂³	—	2	1	no	—
883	C₂³	—	2	2	no	—
884	C₂³	—	2	2	no	—
885	C₂³	—	2	2	no	—
886	C₂³	—	2	2	no	—
887	C₂³	—	2	2	no	—
888	C₂³	—	2	2	no	—
889	C₂³	—	2	2	no	—
890	C₂³	C₂×#41×C₃₁	1	2	yes	—
891	C₂³	C₂×#41×C₃₁	1	2	yes	—
892	C₂³	C₂⁵×C₃₁	1	1	yes	characteristic
893	Q₈	—	4	8	no	—
894	D₄	—	2	8	no	—
895	D₄	—	4	8	no	—
896	D₄	—	4	8	no	—
897	D₄	—	4	4	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	2	no	—
906	C₂×C₄	—	2	1	no	—
907	C₂×C₄	—	2	2	no	—
908	C₂×C₄	—	2	1	no	—
909	C₂×C₄	—	2	1	no	—
910	C₂×C₄	—	2	1	no	—
911	C₂×C₄	—	2	1	no	—
912	C₂×C₄	—	2	8	no	—
913	C₂×C₄	—	2	1	no	—
914	C₂×C₄	—	2	1	no	—
915	C₂×C₄	—	2	1	no	—
916	C₂×C₄	—	2	1	no	—
917	C₂×C₄	—	2	2	no	—
918	C₂×C₄	—	2	1	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	1	no	—
925	C₂×C₄	—	2	2	no	—
926	C₂×C₄	—	2	1	no	—
927	C₂×C₄	—	2	2	no	—
928	C₂×C₄	—	2	1	no	—
929	C₂×C₄	—	2	1	no	—
930	C₂×C₄	—	2	1	no	—
931	C₂×C₄	—	2	2	no	—
932	C₂×C₄	—	2	2	no	—
933	C₂×C₄	—	2	2	no	—
934	C₂×C₄	—	2	2	no	—
935	C₂×C₄	—	2	2	no	—
936	C₂×C₄	—	2	1	no	—
937	C₂×C₄	—	2	2	no	—
938	C₂×C₄	—	2	1	no	—
939	C₂×C₄	—	2	1	no	—
940	C₂×C₄	—	2	2	no	—
941	C₂×C₄	—	2	1	no	—
942	C₂×C₄	—	2	2	no	—
943	C₂×C₄	—	2	2	no	—
944	C₂×C₄	—	2	1	no	—
945	C₂×C₄	—	2	2	no	—
946	C₂×C₄	—	4	4	no	—
947	C₂×C₄	—	4	4	no	—
948	C₂×C₄	—	4	4	no	—
949	C₂×C₄	—	4	4	no	—
950	C₂×C₄	—	4	4	no	—
951	C₂×C₄	—	4	8	no	—
952	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
953	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
954	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
955	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
956	C₂×C₄	C₂×#41×C₃₁	1	4	yes	—
957	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
958	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
959	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
960	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
961	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
962	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
963	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
964	C₂×C₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
965	C₂²	—	2	2	no	—
966	C₂²	—	2	2	no	—
967	C₂²	—	2	2	no	—
968	C₂²	—	2	2	no	—
969	C₂²	—	2	2	no	—
970	C₂²	—	2	2	no	—
971	C₂²	—	4	1	no	—
972	C₂²	—	4	1	no	—
973	C₂²	—	4	1	no	—
974	C₂²	—	4	1	no	—
975	C₂²	—	4	1	no	—
976	C₂²	—	4	1	no	—
977	C₂²	—	4	1	no	—
978	C₂²	—	4	1	no	—
979	C₂²	—	4	2	no	—
980	C₂²	—	4	2	no	—
981	C₂²	—	4	2	no	—
982	C₂²	—	4	2	no	—
983	C₂²	—	4	2	no	—
984	C₂²	—	4	2	no	—
985	C₂²	—	4	2	no	—
986	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
987	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
988	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
989	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
990	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
991	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
992	C₂²	C₃₁×#585	1	1	yes	characteristic
993	C₄	—	2	2	no	—
994	C₄	—	2	2	no	—
995	C₄	—	2	2	no	—
996	C₄	—	2	2	no	—
997	C₄	—	2	2	no	—
998	C₄	—	2	4	no	—
999	C₄	—	2	2	no	—
1000	C₄	—	4	1	no	—
1001	C₄	—	4	2	no	—
1002	C₄	—	4	2	no	—
1003	C₄	—	4	1	no	—
1004	C₄	—	4	2	no	—
1005	C₄	—	4	1	no	—
1006	C₄	—	4	1	no	—
1007	C₄	—	4	2	no	—
1008	C₄	—	4	1	no	—
1009	C₄	—	4	2	no	—
1010	C₄	—	4	2	no	—
1011	C₄	C₃₁×#529	1	4	yes	—
1012	C₄	C₃₁×#555	1	4	yes	—
1013	C₂	—	4	2	no	—
1014	C₂	—	4	2	no	—
1015	C₂	—	8	2	no	—
1016	C₂	C₂×C₃₁×#529	1	1	yes	characteristic
1017	C₂	C₃₁×#3444	1	1	yes	characteristic
1018	C₂	C₃₁×#3460	1	1	yes	characteristic
1019	C₂	C₂×C₃₁×#555	1	1	yes	characteristic
1020	C₂	C₃₁×#3475	1	1	yes	characteristic
1021	C₂	C₃₁×#3480	1	1	yes	characteristic
1022	C₂	C₃₁×#3481	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×#2414	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×#2532	C₂	semidirect
2. C₃₁×#2526	C₂	semidirect
3. C₃₁×#2518	C₂	semidirect
4. C₃₁×#2513	C₂	semidirect
5. C₃₁×#2508	C₂	semidirect
6. C₃₁×#2500	C₂	semidirect
7. C₃₁×#2497	C₂	semidirect
8. C₃₁×#2491	C₂	semidirect
9. C₃₁×#2485	C₂	semidirect
10. C₃₁×#2459	C₂	semidirect
11. C₃₁×#2439	C₂	semidirect
13. C₃₁×#2398	C₂	semidirect
14. C₃₁×#2392	C₂	semidirect
15. C₄×C₃₁×C₄⋊Q₈	C₂	semidirect
16. C₄×C₃₁×#124	C₂	semidirect
17. C₄×C₃₁×#121	C₂	semidirect
18. C₄×C₃₁×#121	C₂	semidirect
19. C₃₁×#2298	C₂	semidirect
20. C₃₁×#2293	C₂	semidirect
21. C₃₁×#2283	C₂	semidirect
22. C₄²×D₄×C₃₁	C₂	semidirect
23. C₄×C₃₁×#117	C₂	semidirect
359. #34800	C₃₁	direct (N × H)
454. #2532	C₂×C₃₁	semidirect
455. #2526	C₂×C₃₁	semidirect
456. #2518	C₂×C₃₁	semidirect
457. #2513	C₂×C₃₁	semidirect
458. #2508	C₂×C₃₁	semidirect
459. #2500	C₂×C₃₁	semidirect
460. #2497	C₂×C₃₁	semidirect
461. #2491	C₂×C₃₁	semidirect
462. #2485	C₂×C₃₁	semidirect
463. #2459	C₂×C₃₁	semidirect
464. #2439	C₂×C₃₁	semidirect
466. #2398	C₂×C₃₁	semidirect
467. #2392	C₂×C₃₁	semidirect
468. C₄×C₄⋊Q₈	C₂×C₃₁	semidirect
469. C₄×#124	C₂×C₃₁	semidirect
470. C₄×#121	C₂×C₃₁	semidirect
471. C₄×#121	C₂×C₃₁	semidirect
472. #2298	C₂×C₃₁	semidirect
473. #2293	C₂×C₃₁	semidirect
474. #2283	C₂×C₃₁	semidirect
475. C₄²×D₄	C₂×C₃₁	semidirect
476. C₄×#117	C₂×C₃₁	semidirect
749. C₃₁	#34800	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×#2532	2
C₃₁×#2526	2
C₃₁×#2518	2
C₃₁×#2513	2
C₃₁×#2508	2
C₃₁×#2500	2
C₃₁×#2497	2
C₃₁×#2491	2
C₃₁×#2485	2
C₃₁×#2459	2
C₃₁×#2439	2
C₃₁×#2414	2
C₃₁×#2398	2
C₃₁×#2392	2
C₄×C₃₁×C₄⋊Q₈	2
C₄×C₃₁×#124	2
C₄×C₃₁×#121	2
C₃₁×#2298	2
C₃₁×#2293	2
C₃₁×#2283	2
C₄²×D₄×C₃₁	2
C₄×C₃₁×#117	2
#34800	31

Subgroups — C31×#34800 #21491559

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#34800 #21491559