Subgroups — C₃₁×#36738 #21493497

Order 7936.

2522 conjugacy classes of subgroups.

The subgroup lattice has 1002 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#538	C₂	1	2	yes	maximal, complemented
2	C₃₁×#2847	C₂	1	2	yes	maximal, complemented
3	C₃₁×#2722	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#2715	C₂	1	2	yes	maximal, complemented
5	C₃₁×#2712	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#2695	C₂	1	2	yes	maximal, complemented
7	C₃₁×#2693	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#2691	C₂	1	2	yes	maximal, complemented
9	C₃₁×#2676	C₂	1	2	yes	maximal, complemented
10	C₃₁×#2675	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#2672	C₂	1	2	yes	maximal, complemented
12	C₃₁×#2671	C₂	1	2	yes	maximal, complemented
13	C₃₁×#2617	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#2617	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#2564	C₂	1	2	yes	maximal, complemented
16	C₃₁×#2543	C₂	1	2	yes	maximal, complemented
17	C₃₁×#2417	C₂	1	2	yes	maximal, complemented
18	C₃₁×#2416	C₂	1	2	yes	maximal, complemented
19	C₂×C₃₁×#385	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂⁴×C₄×C₃₁	C₂²	1	1	yes	characteristic
21	C₃₁×#538	—	2	16	no	—
22	C₂×C₃₁×#126	C₂²	1	2	yes	—
23	C₂×C₃₁×#126	C₂²	1	2	yes	—
24	C₂×C₃₁×#124	C₂²	1	2	yes	—
25	C₂×C₃₁×#124	C₂²	1	2	yes	—
26	C₂×C₃₁×#123	C₂²	1	2	yes	—
27	C₂×C₃₁×#123	C₂²	1	2	yes	—
28	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	—
29	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	complemented
30	C₂×C₃₁×#121	C₂²	1	2	yes	—
31	C₂×C₃₁×#121	C₂²	1	2	yes	—
32	C₂×C₃₁×#121	C₂²	1	2	yes	—
33	C₂×C₃₁×#121	C₂²	1	2	yes	—
34	C₂×C₃₁×#121	C₂²	1	2	yes	—
35	C₂×C₃₁×#121	C₂²	1	2	yes	—
36	C₂×C₃₁×#121	C₂²	1	1	yes	characteristic
37	C₂×C₃₁×#121	C₂²	1	1	yes	characteristic
38	C₂×C₃₁×#121	C₂²	1	2	yes	complemented
39	C₂×C₃₁×#120	C₂²	1	2	yes	—
40	C₂×C₃₁×#120	C₂²	1	2	yes	—
41	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
42	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
43	C₂²×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
44	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
45	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
46	C₃₁×#400	C₂²	1	2	yes	complemented
47	C₃₁×#399	C₂²	1	2	yes	complemented
48	C₃₁×#398	C₂²	1	2	yes	complemented
49	C₃₁×#398	C₂²	1	2	yes	complemented
50	C₃₁×#398	C₂²	1	2	yes	complemented
51	C₃₁×#397	C₂²	1	1	yes	characteristic
52	C₃₁×#397	C₂²	1	1	yes	characteristic
53	C₃₁×#397	C₂²	1	1	yes	characteristic
54	C₃₁×#397	C₂²	1	1	yes	characteristic
55	C₃₁×#397	C₂²	1	2	yes	complemented
56	C₃₁×#396	C₂²	1	2	yes	complemented
57	C₃₁×#396	C₂²	1	2	yes	complemented
58	C₃₁×#396	C₂²	1	2	yes	complemented
59	C₃₁×#396	C₂²	1	2	yes	complemented
60	C₃₁×#395	C₂²	1	2	yes	complemented
61	C₃₁×#394	C₂²	1	2	yes	—
62	C₃₁×#394	C₂²	1	2	yes	—
63	C₃₁×#394	C₂²	1	2	yes	—
64	C₃₁×#394	C₂²	1	2	yes	—
65	C₃₁×#394	C₂²	1	2	yes	complemented
66	C₃₁×#394	C₂²	1	2	yes	complemented
67	C₃₁×#394	C₂²	1	2	yes	complemented
68	C₃₁×#393	C₂²	1	2	yes	complemented
69	C₃₁×#392	C₂²	1	1	yes	characteristic
70	C₃₁×#392	C₂²	1	1	yes	characteristic
71	C₃₁×#392	C₂²	1	1	yes	characteristic
72	C₃₁×#392	C₂²	1	1	yes	characteristic
73	C₃₁×#392	C₂²	1	2	yes	complemented
74	C₃₁×#391	C₂²	1	2	yes	complemented
75	C₃₁×#390	C₂²	1	2	yes	complemented
76	C₃₁×#389	C₂²	1	2	yes	complemented
77	C₃₁×#389	C₂²	1	2	yes	complemented
78	C₃₁×#388	C₂²	1	2	yes	complemented
79	C₃₁×#388	C₂²	1	2	yes	complemented
80	C₃₁×#387	C₂²	1	2	yes	complemented
81	C₃₁×#387	C₂²	1	2	yes	complemented
82	C₃₁×#386	C₂²	1	2	yes	—
83	C₃₁×#386	C₂²	1	2	yes	—
84	C₃₁×#386	C₂²	1	2	yes	—
85	C₃₁×#386	C₂²	1	2	yes	—
86	C₃₁×#386	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	complemented
91	C₃₁×#386	C₂²	1	2	yes	complemented
92	C₃₁×#385	C₂²	1	2	yes	—
93	C₃₁×#385	C₂²	1	1	yes	characteristic
94	C₃₁×#385	C₂²	1	1	yes	characteristic
95	C₃₁×#385	C₂²	1	2	yes	—
96	C₃₁×#385	C₂²	1	1	yes	characteristic
97	C₃₁×#385	C₂²	1	1	yes	characteristic
98	C₃₁×#385	C₂²	1	2	yes	complemented
99	C₃₁×#385	C₂²	1	2	yes	complemented
100	C₃₁×#380	C₂²	1	1	yes	characteristic
101	C₃₁×#380	C₂²	1	2	yes	—
102	C₃₁×#380	C₂²	1	2	yes	—
103	C₃₁×#380	C₂²	1	2	yes	—
104	C₃₁×#380	C₂²	1	1	yes	characteristic
105	C₃₁×#380	C₂²	1	2	yes	complemented
106	C₃₁×#380	C₂²	1	2	yes	complemented
107	C₂×C₃₁×#95	C₂²	1	2	yes	—
108	C₂⁵×C₃₁	C₂³	1	1	yes	characteristic
109	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
110	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
111	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
112	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
113	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
114	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
115	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
116	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
117	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
118	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
119	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
120	C₂³×C₄×C₃₁	—	4	4	no	—
121	C₂³×C₄×C₃₁	—	4	2	no	—
122	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
123	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
124	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
125	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
126	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
127	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
128	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
129	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
130	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
131	C₃₁×#126	—	2	8	no	—
132	C₃₁×#126	—	2	8	no	—
133	C₃₁×#124	—	2	8	no	—
134	C₃₁×#124	—	2	8	no	—
135	C₃₁×#123	—	2	8	no	—
136	C₃₁×#123	—	2	8	no	—
137	C₃₁×C₂²⋊Q₈	—	2	8	no	—
138	C₃₁×C₂²⋊Q₈	—	4	4	no	—
139	C₃₁×#121	—	2	8	no	—
140	C₃₁×#121	—	2	8	no	—
141	C₃₁×#121	—	2	8	no	—
142	C₃₁×#121	—	4	4	no	—
143	C₃₁×#121	—	4	4	no	—
144	C₃₁×#121	—	4	4	no	—
145	C₃₁×#121	—	4	4	no	—
146	C₃₁×#121	—	4	2	no	—
147	C₃₁×#121	—	4	2	no	—
148	C₃₁×#120	—	2	8	no	—
149	C₃₁×#120	—	2	8	no	—
150	C₄×D₄×C₃₁	—	2	8	no	—
151	C₄×D₄×C₃₁	—	2	8	no	—
152	C₂×C₄⋊C₄×C₃₁	—	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	2	yes	—
156	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
157	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
158	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
159	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
160	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
161	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
162	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
163	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
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	1	yes	characteristic
170	C₂×C₂²⋊C₄×C₃₁	—	4	2	no	—
171	C₂×C₂²⋊C₄×C₃₁	D₄	1	8	yes	complemented
172	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
173	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
174	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
175	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
176	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
177	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
178	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
179	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
180	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
181	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
182	C₂×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	1	yes	characteristic
190	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
191	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
195	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
196	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
197	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
198	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
199	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
200	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
201	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
202	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
203	C₃₁×#95	C₂³	1	2	yes	—
204	C₃₁×#95	C₂³	1	2	yes	—
205	C₃₁×#95	C₂³	1	2	yes	—
206	C₃₁×#95	C₂³	1	1	yes	characteristic
207	C₃₁×#95	C₂³	1	2	yes	—
208	C₃₁×#95	C₂³	1	2	yes	—
209	C₃₁×#95	C₂³	1	2	yes	—
210	C₃₁×#95	C₂³	1	1	yes	characteristic
211	C₃₁×#95	C₂³	1	2	yes	—
212	C₃₁×#95	C₂³	1	2	yes	—
213	C₃₁×#95	C₂³	1	1	yes	characteristic
214	C₃₁×#95	C₂³	1	1	yes	characteristic
215	C₃₁×#95	C₂³	1	2	yes	—
216	C₃₁×#95	C₂³	1	2	yes	—
217	C₃₁×#95	C₂³	1	2	yes	—
218	C₃₁×#95	C₂³	1	2	yes	—
219	C₃₁×#95	C₂³	1	2	yes	—
220	C₃₁×#95	C₂³	1	2	yes	—
221	C₂⁴×C₃₁	—	2	2	no	—
222	C₂⁴×C₃₁	—	2	2	no	—
223	C₂⁴×C₃₁	—	4	2	no	—
224	C₂⁴×C₃₁	—	4	2	no	—
225	C₂⁴×C₃₁	C₂×D₄	1	4	yes	—
226	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
227	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
228	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
229	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
230	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
231	C₂×Q₈×C₃₁	—	2	4	no	—
232	C₂×Q₈×C₃₁	—	4	2	no	—
233	C₂×Q₈×C₃₁	—	4	2	no	—
234	C₂×D₄×C₃₁	—	2	4	no	—
235	C₂×D₄×C₃₁	—	2	4	no	—
236	C₂×D₄×C₃₁	—	2	4	no	—
237	C₂×D₄×C₃₁	—	2	4	no	—
238	C₂×D₄×C₃₁	—	2	4	no	—
239	C₂×D₄×C₃₁	—	2	4	no	—
240	C₂×D₄×C₃₁	—	2	4	no	—
241	C₂×D₄×C₃₁	—	2	4	no	—
242	C₂×D₄×C₃₁	—	2	4	no	—
243	C₂×D₄×C₃₁	—	2	4	no	—
244	C₂×D₄×C₃₁	—	2	4	no	—
245	C₂×D₄×C₃₁	—	2	4	no	—
246	C₂×D₄×C₃₁	—	4	2	no	—
247	C₂×D₄×C₃₁	—	4	2	no	—
248	C₂×D₄×C₃₁	—	4	2	no	—
249	C₂×D₄×C₃₁	—	4	2	no	—
250	C₂×D₄×C₃₁	—	4	2	no	—
251	C₂×D₄×C₃₁	—	4	2	no	—
252	C₂×D₄×C₃₁	—	4	1	no	—
253	C₂×D₄×C₃₁	—	4	1	no	—
254	C₂×D₄×C₃₁	—	4	2	no	—
255	C₂×D₄×C₃₁	—	4	2	no	—
256	C₂×D₄×C₃₁	—	4	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	—	4	2	no	—
262	C₂²×C₄×C₃₁	—	2	4	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	4	no	—
267	C₂²×C₄×C₃₁	—	2	4	no	—
268	C₂²×C₄×C₃₁	—	2	4	no	—
269	C₂²×C₄×C₃₁	—	2	4	no	—
270	C₂²×C₄×C₃₁	—	4	2	no	—
271	C₂²×C₄×C₃₁	—	4	1	no	—
272	C₂²×C₄×C₃₁	—	4	2	no	—
273	C₂²×C₄×C₃₁	—	4	2	no	—
274	C₂²×C₄×C₃₁	—	4	2	no	—
275	C₂²×C₄×C₃₁	—	4	1	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	16	no	—
285	C₂²×C₄×C₃₁	C₂×D₄	1	8	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	2	yes	—
289	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
290	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
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	2	yes	—
295	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
296	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
297	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
298	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
299	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
300	C₄⋊C₄×C₃₁	—	2	4	no	—
301	C₄⋊C₄×C₃₁	—	2	4	no	—
302	C₄⋊C₄×C₃₁	—	2	4	no	—
303	C₄⋊C₄×C₃₁	—	2	4	no	—
304	C₄⋊C₄×C₃₁	—	2	4	no	—
305	C₄⋊C₄×C₃₁	—	2	4	no	—
306	C₄⋊C₄×C₃₁	—	2	4	no	—
307	C₄⋊C₄×C₃₁	—	2	4	no	—
308	C₄⋊C₄×C₃₁	—	2	4	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	1	no	—
315	C₄⋊C₄×C₃₁	—	4	1	no	—
316	C₄⋊C₄×C₃₁	—	4	2	no	—
317	C₂²⋊C₄×C₃₁	—	2	4	no	—
318	C₂²⋊C₄×C₃₁	—	2	4	no	—
319	C₂²⋊C₄×C₃₁	—	2	4	no	—
320	C₂²⋊C₄×C₃₁	—	2	4	no	—
321	C₂²⋊C₄×C₃₁	—	2	4	no	—
322	C₂²⋊C₄×C₃₁	—	2	4	no	—
323	C₂²⋊C₄×C₃₁	—	2	4	no	—
324	C₂²⋊C₄×C₃₁	—	2	4	no	—
325	C₂²⋊C₄×C₃₁	—	2	4	no	—
326	C₂²⋊C₄×C₃₁	—	2	4	no	—
327	C₂²⋊C₄×C₃₁	—	2	4	no	—
328	C₂²⋊C₄×C₃₁	—	2	4	no	—
329	C₂²⋊C₄×C₃₁	—	4	1	no	—
330	C₂²⋊C₄×C₃₁	—	4	1	no	—
331	C₂²⋊C₄×C₃₁	—	4	1	no	—
332	C₂²⋊C₄×C₃₁	—	4	1	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	—	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	C₂×D₄	1	4	yes	—
344	C₂²⋊C₄×C₃₁	C₂×D₄	1	8	yes	—
345	C₂²⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
346	C₄²×C₃₁	—	2	4	no	—
347	C₄²×C₃₁	—	2	4	no	—
348	#36738	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
349	C₂³×C₃₁	—	2	2	no	—
350	C₂³×C₃₁	—	2	2	no	—
351	C₂³×C₃₁	—	2	8	no	—
352	C₂³×C₃₁	—	2	1	no	—
353	C₂³×C₃₁	—	2	1	no	—
354	C₂³×C₃₁	—	2	2	no	—
355	C₂³×C₃₁	—	2	2	no	—
356	C₂³×C₃₁	—	2	1	no	—
357	C₂³×C₃₁	—	2	1	no	—
358	C₂³×C₃₁	—	2	2	no	—
359	C₂³×C₃₁	—	2	2	no	—
360	C₂³×C₃₁	—	2	2	no	—
361	C₂³×C₃₁	—	2	2	no	—
362	C₂³×C₃₁	—	2	2	no	—
363	C₂³×C₃₁	—	2	2	no	—
364	C₂³×C₃₁	—	2	2	no	—
365	C₂³×C₃₁	—	2	2	no	—
366	C₂³×C₃₁	—	2	2	no	—
367	C₂³×C₃₁	—	2	2	no	—
368	C₂³×C₃₁	—	2	2	no	—
369	C₂³×C₃₁	—	2	2	no	—
370	C₂³×C₃₁	—	2	2	no	—
371	C₂³×C₃₁	—	2	2	no	—
372	C₂³×C₃₁	—	2	2	no	—
373	C₂³×C₃₁	—	2	2	no	—
374	C₂³×C₃₁	—	4	8	no	—
375	C₂³×C₃₁	—	4	4	no	—
376	C₂³×C₃₁	—	4	4	no	—
377	C₂³×C₃₁	—	4	8	no	—
378	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
379	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
380	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
381	C₂³×C₃₁	H(5,𝔽₂)	1	2	yes	—
382	C₂³×C₃₁	2₋¹⁺⁴	1	2	yes	—
383	C₂³×C₃₁	C₂⁵	1	1	yes	characteristic
384	Q₈×C₃₁	—	8	4	no	—
385	D₄×C₃₁	—	4	8	no	—
386	D₄×C₃₁	—	4	8	no	—
387	D₄×C₃₁	—	8	4	no	—
388	D₄×C₃₁	—	8	4	no	—
389	D₄×C₃₁	—	8	4	no	—
390	D₄×C₃₁	—	8	4	no	—
391	D₄×C₃₁	—	8	4	no	—
392	D₄×C₃₁	—	8	4	no	—
393	D₄×C₃₁	—	8	2	no	—
394	D₄×C₃₁	—	8	2	no	—
395	C₂×C₄×C₃₁	—	2	2	no	—
396	C₂×C₄×C₃₁	—	2	2	no	—
397	C₂×C₄×C₃₁	—	2	2	no	—
398	C₂×C₄×C₃₁	—	2	2	no	—
399	C₂×C₄×C₃₁	—	2	2	no	—
400	C₂×C₄×C₃₁	—	2	2	no	—
401	C₂×C₄×C₃₁	—	2	2	no	—
402	C₂×C₄×C₃₁	—	2	2	no	—
403	C₂×C₄×C₃₁	—	2	2	no	—
404	C₂×C₄×C₃₁	—	2	2	no	—
405	C₂×C₄×C₃₁	—	2	2	no	—
406	C₂×C₄×C₃₁	—	2	2	no	—
407	C₂×C₄×C₃₁	—	2	2	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	2	no	—
412	C₂×C₄×C₃₁	—	2	2	no	—
413	C₂×C₄×C₃₁	—	2	2	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	2	no	—
418	C₂×C₄×C₃₁	—	2	2	no	—
419	C₂×C₄×C₃₁	—	2	2	no	—
420	C₂×C₄×C₃₁	—	2	2	no	—
421	C₂×C₄×C₃₁	—	2	2	no	—
422	C₂×C₄×C₃₁	—	2	2	no	—
423	C₂×C₄×C₃₁	—	2	2	no	—
424	C₂×C₄×C₃₁	—	2	2	no	—
425	C₂×C₄×C₃₁	—	2	2	no	—
426	C₂×C₄×C₃₁	—	2	2	no	—
427	C₂×C₄×C₃₁	—	2	2	no	—
428	C₂×C₄×C₃₁	—	2	2	no	—
429	C₂×C₄×C₃₁	—	2	2	no	—
430	C₂×C₄×C₃₁	—	4	8	no	—
431	C₂×C₄×C₃₁	—	4	4	no	—
432	C₂×C₄×C₃₁	—	4	8	no	—
433	C₂×C₄×C₃₁	—	4	8	no	—
434	C₂×C₄×C₃₁	—	4	4	no	—
435	C₂×C₄×C₃₁	—	8	4	no	—
436	C₂×C₄×C₃₁	—	8	4	no	—
437	C₂×C₄×C₃₁	—	8	2	no	—
438	C₂×C₄×C₃₁	—	8	2	no	—
439	C₂×C₄×C₃₁	C₂²×D₄	1	4	yes	—
440	C₂×C₄×C₃₁	C₂²×D₄	1	4	yes	—
441	C₂×C₄×C₃₁	H(5,𝔽₂)	1	4	yes	—
442	C₂×#538	C₂×C₃₁	1	2	yes	complemented
443	#2847	C₂×C₃₁	1	2	yes	complemented
444	#2722	C₂×C₃₁	1	1	yes	characteristic, complemented
445	#2715	C₂×C₃₁	1	2	yes	complemented
446	#2712	C₂×C₃₁	1	1	yes	characteristic, complemented
447	#2695	C₂×C₃₁	1	2	yes	complemented
448	#2693	C₂×C₃₁	1	1	yes	characteristic, complemented
449	#2691	C₂×C₃₁	1	2	yes	complemented
450	#2676	C₂×C₃₁	1	2	yes	complemented
451	#2675	C₂×C₃₁	1	1	yes	characteristic, complemented
452	#2672	C₂×C₃₁	1	2	yes	complemented
453	#2671	C₂×C₃₁	1	2	yes	complemented
454	#2617	C₂×C₃₁	1	1	yes	characteristic, complemented
455	#2617	C₂×C₃₁	1	1	yes	characteristic, complemented
456	#2564	C₂×C₃₁	1	2	yes	complemented
457	#2543	C₂×C₃₁	1	2	yes	complemented
458	#2417	C₂×C₃₁	1	2	yes	complemented
459	#2416	C₂×C₃₁	1	2	yes	complemented
460	C₂×#385	C₂×C₃₁	1	1	yes	characteristic, complemented
461	C₂²×C₃₁	—	2	4	no	—
462	C₂²×C₃₁	—	2	2	no	—
463	C₂²×C₃₁	—	2	2	no	—
464	C₂²×C₃₁	—	2	4	no	—
465	C₂²×C₃₁	—	2	2	no	—
466	C₂²×C₃₁	—	2	2	no	—
467	C₂²×C₃₁	—	2	4	no	—
468	C₂²×C₃₁	—	2	4	no	—
469	C₂²×C₃₁	—	4	16	no	—
470	C₂²×C₃₁	—	4	1	no	—
471	C₂²×C₃₁	—	4	1	no	—
472	C₂²×C₃₁	—	4	1	no	—
473	C₂²×C₃₁	—	4	1	no	—
474	C₂²×C₃₁	—	4	2	no	—
475	C₂²×C₃₁	—	4	2	no	—
476	C₂²×C₃₁	—	4	2	no	—
477	C₂²×C₃₁	—	4	2	no	—
478	C₂²×C₃₁	—	4	2	no	—
479	C₂²×C₃₁	—	4	2	no	—
480	C₂²×C₃₁	—	4	2	no	—
481	C₂²×C₃₁	—	4	2	no	—
482	C₂²×C₃₁	—	4	2	no	—
483	C₂²×C₃₁	—	4	2	no	—
484	C₂²×C₃₁	—	4	2	no	—
485	C₂²×C₃₁	—	4	2	no	—
486	C₂²×C₃₁	—	4	2	no	—
487	C₂²×C₃₁	—	4	2	no	—
488	C₂²×C₃₁	—	4	2	no	—
489	C₂²×C₃₁	—	4	2	no	—
490	C₂²×C₃₁	#537	1	4	yes	—
491	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
492	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
493	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	2	yes	—
494	C₂²×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
495	C₂²×C₃₁	#585	1	2	yes	—
496	C₄×C₃₁	—	2	4	no	—
497	C₄×C₃₁	—	2	4	no	—
498	C₄×C₃₁	—	2	4	no	—
499	C₄×C₃₁	—	4	2	no	—
500	C₄×C₃₁	—	4	2	no	—
501	C₄×C₃₁	—	4	2	no	—
502	C₄×C₃₁	—	4	2	no	—
503	C₄×C₃₁	—	4	2	no	—
504	C₄×C₃₁	—	4	2	no	—
505	C₄×C₃₁	—	4	2	no	—
506	C₄×C₃₁	—	4	1	no	—
507	C₄×C₃₁	—	4	1	no	—
508	C₄×C₃₁	—	4	1	no	—
509	C₄×C₃₁	—	4	1	no	—
510	C₂⁴×C₄	C₂²×C₃₁	1	1	yes	characteristic
511	#538	—	2	16	no	—
512	C₂×#126	C₂²×C₃₁	1	2	yes	—
513	C₂×#126	C₂²×C₃₁	1	2	yes	—
514	C₂×#124	C₂²×C₃₁	1	2	yes	—
515	C₂×#124	C₂²×C₃₁	1	2	yes	—
516	C₂×#123	C₂²×C₃₁	1	2	yes	—
517	C₂×#123	C₂²×C₃₁	1	2	yes	—
518	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	—
519	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	complemented
520	C₂×#121	C₂²×C₃₁	1	2	yes	—
521	C₂×#121	C₂²×C₃₁	1	2	yes	—
522	C₂×#121	C₂²×C₃₁	1	2	yes	—
523	C₂×#121	C₂²×C₃₁	1	2	yes	—
524	C₂×#121	C₂²×C₃₁	1	2	yes	—
525	C₂×#121	C₂²×C₃₁	1	2	yes	—
526	C₂×#121	C₂²×C₃₁	1	1	yes	characteristic
527	C₂×#121	C₂²×C₃₁	1	1	yes	characteristic
528	C₂×#121	C₂²×C₃₁	1	2	yes	complemented
529	C₂×#120	C₂²×C₃₁	1	2	yes	—
530	C₂×#120	C₂²×C₃₁	1	2	yes	—
531	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
532	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
533	C₂²×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
534	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
535	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
536	#400	C₂²×C₃₁	1	2	yes	complemented
537	#399	C₂²×C₃₁	1	2	yes	complemented
538	#398	C₂²×C₃₁	1	2	yes	complemented
539	#398	C₂²×C₃₁	1	2	yes	complemented
540	#398	C₂²×C₃₁	1	2	yes	complemented
541	#397	C₂²×C₃₁	1	1	yes	characteristic
542	#397	C₂²×C₃₁	1	1	yes	characteristic
543	#397	C₂²×C₃₁	1	1	yes	characteristic
544	#397	C₂²×C₃₁	1	1	yes	characteristic
545	#397	C₂²×C₃₁	1	2	yes	complemented
546	#396	C₂²×C₃₁	1	2	yes	complemented
547	#396	C₂²×C₃₁	1	2	yes	complemented
548	#396	C₂²×C₃₁	1	2	yes	complemented
549	#396	C₂²×C₃₁	1	2	yes	complemented
550	#395	C₂²×C₃₁	1	2	yes	complemented
551	#394	C₂²×C₃₁	1	2	yes	—
552	#394	C₂²×C₃₁	1	2	yes	—
553	#394	C₂²×C₃₁	1	2	yes	—
554	#394	C₂²×C₃₁	1	2	yes	—
555	#394	C₂²×C₃₁	1	2	yes	complemented
556	#394	C₂²×C₃₁	1	2	yes	complemented
557	#394	C₂²×C₃₁	1	2	yes	complemented
558	#393	C₂²×C₃₁	1	2	yes	complemented
559	#392	C₂²×C₃₁	1	1	yes	characteristic
560	#392	C₂²×C₃₁	1	1	yes	characteristic
561	#392	C₂²×C₃₁	1	1	yes	characteristic
562	#392	C₂²×C₃₁	1	1	yes	characteristic
563	#392	C₂²×C₃₁	1	2	yes	complemented
564	#391	C₂²×C₃₁	1	2	yes	complemented
565	#390	C₂²×C₃₁	1	2	yes	complemented
566	#389	C₂²×C₃₁	1	2	yes	complemented
567	#389	C₂²×C₃₁	1	2	yes	complemented
568	#388	C₂²×C₃₁	1	2	yes	complemented
569	#388	C₂²×C₃₁	1	2	yes	complemented
570	#387	C₂²×C₃₁	1	2	yes	complemented
571	#387	C₂²×C₃₁	1	2	yes	complemented
572	#386	C₂²×C₃₁	1	2	yes	—
573	#386	C₂²×C₃₁	1	2	yes	—
574	#386	C₂²×C₃₁	1	2	yes	—
575	#386	C₂²×C₃₁	1	2	yes	—
576	#386	C₂²×C₃₁	1	2	yes	—
577	#386	C₂²×C₃₁	1	2	yes	—
578	#386	C₂²×C₃₁	1	2	yes	—
579	#386	C₂²×C₃₁	1	2	yes	—
580	#386	C₂²×C₃₁	1	2	yes	complemented
581	#386	C₂²×C₃₁	1	2	yes	complemented
582	#385	C₂²×C₃₁	1	2	yes	—
583	#385	C₂²×C₃₁	1	1	yes	characteristic
584	#385	C₂²×C₃₁	1	1	yes	characteristic
585	#385	C₂²×C₃₁	1	2	yes	—
586	#385	C₂²×C₃₁	1	1	yes	characteristic
587	#385	C₂²×C₃₁	1	1	yes	characteristic
588	#385	C₂²×C₃₁	1	2	yes	complemented
589	#385	C₂²×C₃₁	1	2	yes	complemented
590	#380	C₂²×C₃₁	1	1	yes	characteristic
591	#380	C₂²×C₃₁	1	2	yes	—
592	#380	C₂²×C₃₁	1	2	yes	—
593	#380	C₂²×C₃₁	1	2	yes	—
594	#380	C₂²×C₃₁	1	1	yes	characteristic
595	#380	C₂²×C₃₁	1	2	yes	complemented
596	#380	C₂²×C₃₁	1	2	yes	complemented
597	C₂×#95	C₂²×C₃₁	1	2	yes	—
598	C₂×C₃₁	—	2	4	no	—
599	C₂×C₃₁	—	4	2	no	—
600	C₂×C₃₁	—	4	2	no	—
601	C₂×C₃₁	—	8	2	no	—
602	C₂×C₃₁	—	8	2	no	—
603	C₂×C₃₁	C₂×#537	1	1	yes	characteristic
604	C₂×C₃₁	#3496	1	2	yes	—
605	C₂×C₃₁	#3532	1	1	yes	characteristic
606	C₂×C₃₁	#3533	1	1	yes	characteristic
607	C₂×C₃₁	#3541	1	2	yes	—
608	C₂⁵	C₂³×C₃₁	1	1	yes	characteristic
609	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
610	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
611	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
612	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
613	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
614	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
615	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
616	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
617	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
618	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
619	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
620	C₂³×C₄	—	4	4	no	—
621	C₂³×C₄	—	4	2	no	—
622	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
623	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
624	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
625	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
626	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
627	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
628	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
629	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
630	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
631	#126	—	2	8	no	—
632	#126	—	2	8	no	—
633	#124	—	2	8	no	—
634	#124	—	2	8	no	—
635	#123	—	2	8	no	—
636	#123	—	2	8	no	—
637	C₂²⋊Q₈	—	2	8	no	—
638	C₂²⋊Q₈	—	4	4	no	—
639	#121	—	2	8	no	—
640	#121	—	2	8	no	—
641	#121	—	2	8	no	—
642	#121	—	4	4	no	—
643	#121	—	4	4	no	—
644	#121	—	4	4	no	—
645	#121	—	4	4	no	—
646	#121	—	4	2	no	—
647	#121	—	4	2	no	—
648	#120	—	2	8	no	—
649	#120	—	2	8	no	—
650	C₄×D₄	—	2	8	no	—
651	C₄×D₄	—	2	8	no	—
652	C₂×C₄⋊C₄	—	4	4	no	—
653	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
654	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
655	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
656	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
657	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
658	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
659	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
660	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
661	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
662	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
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	2	yes	—
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	2	yes	—
669	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
670	C₂×C₂²⋊C₄	—	4	2	no	—
671	C₂×C₂²⋊C₄	D₄×C₃₁	1	8	yes	complemented
672	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
673	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
674	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
675	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
676	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
677	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
678	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
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	2	yes	—
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	1	yes	characteristic
699	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
700	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
701	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
702	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
703	#95	C₂³×C₃₁	1	2	yes	—
704	#95	C₂³×C₃₁	1	2	yes	—
705	#95	C₂³×C₃₁	1	2	yes	—
706	#95	C₂³×C₃₁	1	2	yes	—
707	#95	C₂³×C₃₁	1	1	yes	characteristic
708	#95	C₂³×C₃₁	1	2	yes	—
709	#95	C₂³×C₃₁	1	2	yes	—
710	#95	C₂³×C₃₁	1	1	yes	characteristic
711	#95	C₂³×C₃₁	1	2	yes	—
712	#95	C₂³×C₃₁	1	2	yes	—
713	#95	C₂³×C₃₁	1	2	yes	—
714	#95	C₂³×C₃₁	1	2	yes	—
715	#95	C₂³×C₃₁	1	1	yes	characteristic
716	#95	C₂³×C₃₁	1	1	yes	characteristic
717	#95	C₂³×C₃₁	1	2	yes	—
718	#95	C₂³×C₃₁	1	2	yes	—
719	#95	C₂³×C₃₁	1	2	yes	—
720	#95	C₂³×C₃₁	1	2	yes	—
721	C₃₁	#36738	1	1	yes	characteristic, direct product factor, Sylow
722	C₂⁴	—	2	2	no	—
723	C₂⁴	—	2	2	no	—
724	C₂⁴	—	4	2	no	—
725	C₂⁴	—	4	2	no	—
726	C₂⁴	C₂×D₄×C₃₁	1	4	yes	—
727	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
728	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
729	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
730	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
731	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
732	C₂×Q₈	—	2	4	no	—
733	C₂×Q₈	—	4	2	no	—
734	C₂×Q₈	—	4	2	no	—
735	C₂×D₄	—	2	4	no	—
736	C₂×D₄	—	2	4	no	—
737	C₂×D₄	—	2	4	no	—
738	C₂×D₄	—	2	4	no	—
739	C₂×D₄	—	2	4	no	—
740	C₂×D₄	—	2	4	no	—
741	C₂×D₄	—	2	4	no	—
742	C₂×D₄	—	2	4	no	—
743	C₂×D₄	—	2	4	no	—
744	C₂×D₄	—	2	4	no	—
745	C₂×D₄	—	2	4	no	—
746	C₂×D₄	—	2	4	no	—
747	C₂×D₄	—	4	2	no	—
748	C₂×D₄	—	4	2	no	—
749	C₂×D₄	—	4	2	no	—
750	C₂×D₄	—	4	2	no	—
751	C₂×D₄	—	4	2	no	—
752	C₂×D₄	—	4	2	no	—
753	C₂×D₄	—	4	1	no	—
754	C₂×D₄	—	4	1	no	—
755	C₂×D₄	—	4	2	no	—
756	C₂×D₄	—	4	2	no	—
757	C₂×D₄	—	4	2	no	—
758	C₂×D₄	—	4	2	no	—
759	C₂×D₄	—	4	2	no	—
760	C₂×D₄	—	4	2	no	—
761	C₂×D₄	—	4	2	no	—
762	C₂×D₄	—	4	2	no	—
763	C₂²×C₄	—	2	4	no	—
764	C₂²×C₄	—	2	2	no	—
765	C₂²×C₄	—	2	2	no	—
766	C₂²×C₄	—	2	4	no	—
767	C₂²×C₄	—	2	4	no	—
768	C₂²×C₄	—	2	4	no	—
769	C₂²×C₄	—	2	4	no	—
770	C₂²×C₄	—	2	4	no	—
771	C₂²×C₄	—	4	2	no	—
772	C₂²×C₄	—	4	1	no	—
773	C₂²×C₄	—	4	2	no	—
774	C₂²×C₄	—	4	2	no	—
775	C₂²×C₄	—	4	2	no	—
776	C₂²×C₄	—	4	1	no	—
777	C₂²×C₄	—	4	2	no	—
778	C₂²×C₄	—	4	2	no	—
779	C₂²×C₄	—	4	2	no	—
780	C₂²×C₄	—	4	2	no	—
781	C₂²×C₄	—	4	2	no	—
782	C₂²×C₄	—	4	2	no	—
783	C₂²×C₄	—	4	2	no	—
784	C₂²×C₄	—	4	2	no	—
785	C₂²×C₄	—	4	16	no	—
786	C₂²×C₄	C₂×D₄×C₃₁	1	8	yes	—
787	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
788	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
789	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
790	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
791	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
792	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
793	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
794	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
795	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
796	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
797	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
798	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
799	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
800	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
801	C₄⋊C₄	—	2	4	no	—
802	C₄⋊C₄	—	2	4	no	—
803	C₄⋊C₄	—	2	4	no	—
804	C₄⋊C₄	—	2	4	no	—
805	C₄⋊C₄	—	2	4	no	—
806	C₄⋊C₄	—	2	4	no	—
807	C₄⋊C₄	—	2	4	no	—
808	C₄⋊C₄	—	2	4	no	—
809	C₄⋊C₄	—	2	4	no	—
810	C₄⋊C₄	—	4	2	no	—
811	C₄⋊C₄	—	4	2	no	—
812	C₄⋊C₄	—	4	2	no	—
813	C₄⋊C₄	—	4	2	no	—
814	C₄⋊C₄	—	4	2	no	—
815	C₄⋊C₄	—	4	1	no	—
816	C₄⋊C₄	—	4	1	no	—
817	C₄⋊C₄	—	4	2	no	—
818	C₂²⋊C₄	—	2	4	no	—
819	C₂²⋊C₄	—	2	4	no	—
820	C₂²⋊C₄	—	2	4	no	—
821	C₂²⋊C₄	—	2	4	no	—
822	C₂²⋊C₄	—	2	4	no	—
823	C₂²⋊C₄	—	2	4	no	—
824	C₂²⋊C₄	—	2	4	no	—
825	C₂²⋊C₄	—	2	4	no	—
826	C₂²⋊C₄	—	2	4	no	—
827	C₂²⋊C₄	—	2	4	no	—
828	C₂²⋊C₄	—	2	4	no	—
829	C₂²⋊C₄	—	2	4	no	—
830	C₂²⋊C₄	—	4	1	no	—
831	C₂²⋊C₄	—	4	1	no	—
832	C₂²⋊C₄	—	4	1	no	—
833	C₂²⋊C₄	—	4	1	no	—
834	C₂²⋊C₄	—	4	2	no	—
835	C₂²⋊C₄	—	4	2	no	—
836	C₂²⋊C₄	—	4	2	no	—
837	C₂²⋊C₄	—	4	2	no	—
838	C₂²⋊C₄	—	4	2	no	—
839	C₂²⋊C₄	—	4	2	no	—
840	C₂²⋊C₄	—	4	2	no	—
841	C₂²⋊C₄	—	4	2	no	—
842	C₂²⋊C₄	—	4	2	no	—
843	C₂²⋊C₄	—	4	2	no	—
844	C₂²⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
845	C₂²⋊C₄	C₂×D₄×C₃₁	1	8	yes	—
846	C₂²⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
847	C₄²	—	2	4	no	—
848	C₄²	—	2	4	no	—
849	C₂³	—	2	2	no	—
850	C₂³	—	2	2	no	—
851	C₂³	—	2	8	no	—
852	C₂³	—	2	1	no	—
853	C₂³	—	2	1	no	—
854	C₂³	—	2	2	no	—
855	C₂³	—	2	2	no	—
856	C₂³	—	2	1	no	—
857	C₂³	—	2	1	no	—
858	C₂³	—	2	2	no	—
859	C₂³	—	2	2	no	—
860	C₂³	—	2	2	no	—
861	C₂³	—	2	2	no	—
862	C₂³	—	2	2	no	—
863	C₂³	—	2	2	no	—
864	C₂³	—	2	2	no	—
865	C₂³	—	2	2	no	—
866	C₂³	—	2	2	no	—
867	C₂³	—	2	2	no	—
868	C₂³	—	2	2	no	—
869	C₂³	—	2	2	no	—
870	C₂³	—	2	2	no	—
871	C₂³	—	2	2	no	—
872	C₂³	—	2	2	no	—
873	C₂³	—	2	2	no	—
874	C₂³	—	4	8	no	—
875	C₂³	—	4	4	no	—
876	C₂³	—	4	4	no	—
877	C₂³	—	4	8	no	—
878	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
879	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
880	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
881	C₂³	C₃₁×H(5,𝔽₂)	1	2	yes	—
882	C₂³	C₃₁×2₋¹⁺⁴	1	2	yes	—
883	C₂³	C₂⁵×C₃₁	1	1	yes	characteristic
884	Q₈	—	8	4	no	—
885	D₄	—	4	8	no	—
886	D₄	—	4	8	no	—
887	D₄	—	8	4	no	—
888	D₄	—	8	4	no	—
889	D₄	—	8	4	no	—
890	D₄	—	8	4	no	—
891	D₄	—	8	4	no	—
892	D₄	—	8	4	no	—
893	D₄	—	8	2	no	—
894	D₄	—	8	2	no	—
895	C₂×C₄	—	2	2	no	—
896	C₂×C₄	—	2	2	no	—
897	C₂×C₄	—	2	2	no	—
898	C₂×C₄	—	2	2	no	—
899	C₂×C₄	—	2	2	no	—
900	C₂×C₄	—	2	2	no	—
901	C₂×C₄	—	2	2	no	—
902	C₂×C₄	—	2	2	no	—
903	C₂×C₄	—	2	2	no	—
904	C₂×C₄	—	2	2	no	—
905	C₂×C₄	—	2	2	no	—
906	C₂×C₄	—	2	2	no	—
907	C₂×C₄	—	2	2	no	—
908	C₂×C₄	—	2	2	no	—
909	C₂×C₄	—	2	1	no	—
910	C₂×C₄	—	2	1	no	—
911	C₂×C₄	—	2	2	no	—
912	C₂×C₄	—	2	2	no	—
913	C₂×C₄	—	2	2	no	—
914	C₂×C₄	—	2	1	no	—
915	C₂×C₄	—	2	1	no	—
916	C₂×C₄	—	2	2	no	—
917	C₂×C₄	—	2	2	no	—
918	C₂×C₄	—	2	2	no	—
919	C₂×C₄	—	2	2	no	—
920	C₂×C₄	—	2	2	no	—
921	C₂×C₄	—	2	2	no	—
922	C₂×C₄	—	2	2	no	—
923	C₂×C₄	—	2	2	no	—
924	C₂×C₄	—	2	2	no	—
925	C₂×C₄	—	2	2	no	—
926	C₂×C₄	—	2	2	no	—
927	C₂×C₄	—	2	2	no	—
928	C₂×C₄	—	2	2	no	—
929	C₂×C₄	—	2	2	no	—
930	C₂×C₄	—	4	8	no	—
931	C₂×C₄	—	4	4	no	—
932	C₂×C₄	—	4	8	no	—
933	C₂×C₄	—	4	8	no	—
934	C₂×C₄	—	4	4	no	—
935	C₂×C₄	—	8	4	no	—
936	C₂×C₄	—	8	4	no	—
937	C₂×C₄	—	8	2	no	—
938	C₂×C₄	—	8	2	no	—
939	C₂×C₄	C₂²×D₄×C₃₁	1	4	yes	—
940	C₂×C₄	C₂²×D₄×C₃₁	1	4	yes	—
941	C₂×C₄	C₃₁×H(5,𝔽₂)	1	4	yes	—
942	C₂²	—	2	4	no	—
943	C₂²	—	2	2	no	—
944	C₂²	—	2	2	no	—
945	C₂²	—	2	4	no	—
946	C₂²	—	2	2	no	—
947	C₂²	—	2	2	no	—
948	C₂²	—	2	4	no	—
949	C₂²	—	2	4	no	—
950	C₂²	—	4	16	no	—
951	C₂²	—	4	1	no	—
952	C₂²	—	4	1	no	—
953	C₂²	—	4	1	no	—
954	C₂²	—	4	1	no	—
955	C₂²	—	4	2	no	—
956	C₂²	—	4	2	no	—
957	C₂²	—	4	2	no	—
958	C₂²	—	4	2	no	—
959	C₂²	—	4	2	no	—
960	C₂²	—	4	2	no	—
961	C₂²	—	4	2	no	—
962	C₂²	—	4	2	no	—
963	C₂²	—	4	2	no	—
964	C₂²	—	4	2	no	—
965	C₂²	—	4	2	no	—
966	C₂²	—	4	2	no	—
967	C₂²	—	4	2	no	—
968	C₂²	—	4	2	no	—
969	C₂²	—	4	2	no	—
970	C₂²	—	4	2	no	—
971	C₂²	C₃₁×#537	1	4	yes	—
972	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
973	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
974	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	2	yes	—
975	C₂²	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
976	C₂²	C₃₁×#585	1	2	yes	—
977	C₄	—	2	4	no	—
978	C₄	—	2	4	no	—
979	C₄	—	2	4	no	—
980	C₄	—	4	2	no	—
981	C₄	—	4	2	no	—
982	C₄	—	4	2	no	—
983	C₄	—	4	2	no	—
984	C₄	—	4	2	no	—
985	C₄	—	4	2	no	—
986	C₄	—	4	2	no	—
987	C₄	—	4	1	no	—
988	C₄	—	4	1	no	—
989	C₄	—	4	1	no	—
990	C₄	—	4	1	no	—
991	C₂	—	2	4	no	—
992	C₂	—	4	2	no	—
993	C₂	—	4	2	no	—
994	C₂	—	8	2	no	—
995	C₂	—	8	2	no	—
996	C₂	C₂×C₃₁×#537	1	1	yes	characteristic
997	C₂	C₃₁×#3496	1	2	yes	—
998	C₂	C₃₁×#3532	1	1	yes	characteristic
999	C₂	C₃₁×#3533	1	1	yes	characteristic
1000	C₂	C₃₁×#3541	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃₁	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₃₁
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃₁×#538	C₂	semidirect
2. C₃₁×#2847	C₂	semidirect
3. C₃₁×#2722	C₂	semidirect
4. C₃₁×#2715	C₂	semidirect
5. C₃₁×#2712	C₂	semidirect
6. C₃₁×#2695	C₂	semidirect
7. C₃₁×#2693	C₂	semidirect
8. C₃₁×#2691	C₂	semidirect
9. C₃₁×#2676	C₂	semidirect
10. C₃₁×#2675	C₂	semidirect
11. C₃₁×#2672	C₂	semidirect
12. C₃₁×#2671	C₂	semidirect
13. C₃₁×#2617	C₂	semidirect
14. C₃₁×#2617	C₂	semidirect
15. C₃₁×#2564	C₂	semidirect
16. C₃₁×#2543	C₂	semidirect
17. C₃₁×#2417	C₂	semidirect
18. C₃₁×#2416	C₂	semidirect
19. C₂×C₃₁×#385	C₂	semidirect
29. C₂×C₃₁×C₂²⋊Q₈	C₂²	semidirect
38. C₂×C₃₁×#121	C₂²	semidirect
46. C₃₁×#400	C₂²	semidirect
47. C₃₁×#399	C₂²	semidirect
48. C₃₁×#398	C₂²	semidirect
49. C₃₁×#398	C₂²	semidirect
50. C₃₁×#398	C₂²	semidirect
55. C₃₁×#397	C₂²	semidirect
56. C₃₁×#396	C₂²	semidirect
57. C₃₁×#396	C₂²	semidirect
58. C₃₁×#396	C₂²	semidirect
59. C₃₁×#396	C₂²	semidirect
60. C₃₁×#395	C₂²	semidirect
65. C₃₁×#394	C₂²	semidirect
66. C₃₁×#394	C₂²	semidirect
67. C₃₁×#394	C₂²	semidirect
68. C₃₁×#393	C₂²	semidirect
73. C₃₁×#392	C₂²	semidirect
74. C₃₁×#391	C₂²	semidirect
75. C₃₁×#390	C₂²	semidirect
76. C₃₁×#389	C₂²	semidirect
77. C₃₁×#389	C₂²	semidirect
78. C₃₁×#388	C₂²	semidirect
79. C₃₁×#388	C₂²	semidirect
80. C₃₁×#387	C₂²	semidirect
81. C₃₁×#387	C₂²	semidirect
90. C₃₁×#386	C₂²	semidirect
91. C₃₁×#386	C₂²	semidirect
98. C₃₁×#385	C₂²	semidirect
99. C₃₁×#385	C₂²	semidirect
105. C₃₁×#380	C₂²	semidirect
106. C₃₁×#380	C₂²	semidirect
171. C₂×C₂²⋊C₄×C₃₁	D₄	semidirect
348. #36738	C₃₁	direct (N × H)
442. C₂×#538	C₂×C₃₁	semidirect
443. #2847	C₂×C₃₁	semidirect
444. #2722	C₂×C₃₁	semidirect
445. #2715	C₂×C₃₁	semidirect
446. #2712	C₂×C₃₁	semidirect
447. #2695	C₂×C₃₁	semidirect
448. #2693	C₂×C₃₁	semidirect
449. #2691	C₂×C₃₁	semidirect
450. #2676	C₂×C₃₁	semidirect
451. #2675	C₂×C₃₁	semidirect
452. #2672	C₂×C₃₁	semidirect
453. #2671	C₂×C₃₁	semidirect
454. #2617	C₂×C₃₁	semidirect
455. #2617	C₂×C₃₁	semidirect
456. #2564	C₂×C₃₁	semidirect
457. #2543	C₂×C₃₁	semidirect
458. #2417	C₂×C₃₁	semidirect
459. #2416	C₂×C₃₁	semidirect
460. C₂×#385	C₂×C₃₁	semidirect
519. C₂×C₂²⋊Q₈	C₂²×C₃₁	semidirect
528. C₂×#121	C₂²×C₃₁	semidirect
536. #400	C₂²×C₃₁	semidirect
537. #399	C₂²×C₃₁	semidirect
538. #398	C₂²×C₃₁	semidirect
539. #398	C₂²×C₃₁	semidirect
540. #398	C₂²×C₃₁	semidirect
545. #397	C₂²×C₃₁	semidirect
546. #396	C₂²×C₃₁	semidirect
547. #396	C₂²×C₃₁	semidirect
548. #396	C₂²×C₃₁	semidirect
549. #396	C₂²×C₃₁	semidirect
550. #395	C₂²×C₃₁	semidirect
555. #394	C₂²×C₃₁	semidirect
556. #394	C₂²×C₃₁	semidirect
557. #394	C₂²×C₃₁	semidirect
558. #393	C₂²×C₃₁	semidirect
563. #392	C₂²×C₃₁	semidirect
564. #391	C₂²×C₃₁	semidirect
565. #390	C₂²×C₃₁	semidirect
566. #389	C₂²×C₃₁	semidirect
567. #389	C₂²×C₃₁	semidirect
568. #388	C₂²×C₃₁	semidirect
569. #388	C₂²×C₃₁	semidirect
570. #387	C₂²×C₃₁	semidirect
571. #387	C₂²×C₃₁	semidirect
580. #386	C₂²×C₃₁	semidirect
581. #386	C₂²×C₃₁	semidirect
588. #385	C₂²×C₃₁	semidirect
589. #385	C₂²×C₃₁	semidirect
595. #380	C₂²×C₃₁	semidirect
596. #380	C₂²×C₃₁	semidirect
671. C₂×C₂²⋊C₄	D₄×C₃₁	semidirect
721. C₃₁	#36738	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃₁×#538	2
C₃₁×#2847	2
C₃₁×#2722	2
C₃₁×#2715	2
C₃₁×#2712	2
C₃₁×#2695	2
C₃₁×#2693	2
C₃₁×#2691	2
C₃₁×#2676	2
C₃₁×#2675	2
C₃₁×#2672	2
C₃₁×#2671	2
C₃₁×#2617	2
C₃₁×#2564	2
C₃₁×#2543	2
C₃₁×#2417	2
C₃₁×#2416	2
C₂×C₃₁×#385	2
#36738	31

Subgroups — C31×#36738 #21493497

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#36738 #21493497