Subgroups — C₃₁×#34136 #21490895

Order 7936.

3374 conjugacy classes of subgroups.

The subgroup lattice has 838 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#525	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×#41×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₃₁×#117	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#2363	C₂	1	2	yes	maximal, complemented
5	C₃₁×#2362	C₂	1	2	yes	maximal, complemented
6	C₃₁×#2361	C₂	1	2	yes	maximal, complemented
7	C₃₁×#2360	C₂	1	2	yes	maximal, complemented
8	C₃₁×#2359	C₂	1	4	yes	maximal, complemented
9	C₃₁×#2358	C₂	1	4	yes	maximal, complemented
10	C₃₁×#2297	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#2296	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#2293	C₂	1	2	yes	maximal, complemented
13	C₃₁×#2290	C₂	1	2	yes	maximal, complemented
14	C₃₁×#2290	C₂	1	2	yes	maximal, complemented
15	C₄²×D₄×C₃₁	C₂	1	2	yes	maximal, complemented
16	C₄×C₃₁×#117	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×C₄×C₂²⋊C₄×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×#41×C₃₁	C₂²	1	1	yes	characteristic
19	C₂⁴×C₄×C₃₁	C₂²	1	1	yes	characteristic
20	C₃₁×#525	C₄	1	16	yes	complemented
21	C₂×C₃₁×#123	C₂²	1	2	yes	—
22	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
23	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
24	C₂×C₃₁×#121	C₂²	1	1	yes	characteristic
25	C₂×C₃₁×#121	C₂²	1	1	yes	characteristic
26	C₂×C₃₁×#120	C₂²	1	2	yes	—
27	C₄×#41×C₃₁	—	2	8	no	—
28	C₂×C₄×Q₈×C₃₁	C₂²	1	2	yes	complemented
29	C₂×C₄×D₄×C₃₁	C₂²	1	4	yes	—
30	C₂×C₄×D₄×C₃₁	C₂²	1	4	yes	—
31	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
32	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
33	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	complemented
34	C₂×C₃₁×#117	—	2	8	no	—
35	C₂×C₃₁×#117	C₂²	1	2	yes	—
36	C₂×C₃₁×#117	C₂²	1	2	yes	—
37	C₂×C₃₁×#117	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	1	yes	characteristic
41	C₂×C₃₁×#117	C₂²	1	2	yes	complemented
42	C₂²×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
43	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
44	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
45	C₂²×C₄²×C₃₁	C₂²	1	2	yes	—
46	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
47	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
48	C₂²×C₄²×C₃₁	C₂²	1	2	yes	complemented
49	C₃₁×#391	C₂²	1	2	yes	complemented
50	C₃₁×#390	C₂²	1	4	yes	—
51	C₃₁×#390	C₂²	1	2	yes	complemented
52	C₃₁×#389	C₂²	1	4	yes	complemented
53	C₃₁×#389	C₂²	1	2	yes	complemented
54	C₃₁×#389	C₂²	1	2	yes	complemented
55	C₃₁×#388	C₂²	1	4	yes	—
56	C₃₁×#388	C₂²	1	4	yes	—
57	C₃₁×#388	C₂²	1	4	yes	complemented
58	C₃₁×#388	C₂²	1	4	yes	complemented
59	C₃₁×#387	C₂²	1	4	yes	complemented
60	C₃₁×#387	C₂²	1	4	yes	complemented
61	C₃₁×#386	C₂²	1	4	yes	—
62	C₃₁×#386	C₂²	1	4	yes	—
63	C₃₁×#386	C₂²	1	4	yes	—
64	C₃₁×#385	C₂²	1	4	yes	—
65	C₃₁×#385	C₂²	1	4	yes	—
66	C₃₁×#385	C₂²	1	4	yes	complemented
67	C₄×C₄⋊C₄×C₃₁	C₂²	1	4	yes	complemented
68	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	complemented
69	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	complemented
70	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	complemented
71	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	complemented
72	C₄×C₂²⋊C₄×C₃₁	C₂²	1	4	yes	—
73	C₄×C₂²⋊C₄×C₃₁	C₂²	1	4	yes	—
74	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
75	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
76	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
77	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
78	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
79	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
80	C₄×C₂²⋊C₄×C₃₁	C₂²	1	4	yes	complemented
81	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	complemented
82	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	complemented
83	C₃₁×#376	C₂²	1	2	yes	complemented
84	C₂×C₃₁×#95	C₂²	1	2	yes	—
85	C₄³×C₃₁	C₂²	1	2	yes	complemented
86	C₂⁵×C₃₁	C₂³	1	1	yes	characteristic
87	C₂×#41×C₃₁	—	2	4	no	—
88	C₂×#41×C₃₁	—	2	4	no	—
89	C₂×#41×C₃₁	C₂×C₄	1	8	yes	complemented
90	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
91	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
92	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
93	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
94	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
95	C₂³×C₄×C₃₁	—	2	4	no	—
96	C₂³×C₄×C₃₁	—	2	4	no	—
97	C₂³×C₄×C₃₁	C₂×C₄	1	8	yes	complemented
98	C₂³×C₄×C₃₁	C₂³	1	4	yes	—
99	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
100	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
101	C₂³×C₄×C₃₁	C₂³	1	4	yes	—
102	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
103	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
104	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
105	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
106	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
107	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
108	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
109	C₃₁×#123	C₂×C₄	1	16	yes	complemented
110	C₃₁×C₂²⋊Q₈	C₂×C₄	1	8	yes	complemented
111	C₃₁×C₂²⋊Q₈	C₂×C₄	1	8	yes	complemented
112	C₃₁×#121	C₂×C₄	1	8	yes	complemented
113	C₃₁×#121	C₂×C₄	1	8	yes	complemented
114	C₃₁×#120	C₂×C₄	1	16	yes	complemented
115	C₄×Q₈×C₃₁	—	2	8	no	—
116	C₄×D₄×C₃₁	—	2	8	no	—
117	C₄×D₄×C₃₁	—	2	16	no	—
118	C₄×D₄×C₃₁	—	2	16	no	—
119	C₄×D₄×C₃₁	C₂×C₄	1	16	yes	complemented
120	C₄×D₄×C₃₁	C₂×C₄	1	16	yes	complemented
121	C₃₁×#117	—	2	4	no	—
122	C₃₁×#117	—	2	8	no	—
123	C₃₁×#117	—	2	8	no	—
124	C₃₁×#117	—	2	8	no	—
125	C₃₁×#117	—	2	8	no	—
126	C₃₁×#117	C₂×C₄	1	8	yes	complemented
127	C₃₁×#117	D₄	1	8	yes	complemented
128	C₂×C₄⋊C₄×C₃₁	—	2	8	no	—
129	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
130	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
131	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
132	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
133	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
134	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
135	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
136	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
137	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
138	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
139	C₂×C₂²⋊C₄×C₃₁	—	2	8	no	—
140	C₂×C₂²⋊C₄×C₃₁	—	2	8	no	—
141	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
142	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
143	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
144	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
145	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
146	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
147	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
148	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
149	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
150	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
151	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
152	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
153	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
154	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
155	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
156	C₂×C₄²×C₃₁	—	2	4	no	—
157	C₂×C₄²×C₃₁	—	2	4	no	—
158	C₂×C₄²×C₃₁	—	2	8	no	—
159	C₂×C₄²×C₃₁	—	2	8	no	—
160	C₂×C₄²×C₃₁	C₂³	1	4	yes	—
161	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
162	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
163	C₂×C₄²×C₃₁	C₂³	1	4	yes	—
164	C₂×C₄²×C₃₁	C₂³	1	4	yes	—
165	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
166	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
167	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
168	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
169	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
170	C₂×C₄²×C₃₁	C₂³	1	4	yes	—
171	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
172	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
173	C₃₁×#95	C₂³	1	2	yes	—
174	C₃₁×#95	C₂³	1	2	yes	—
175	C₃₁×#95	C₂³	1	2	yes	—
176	C₃₁×#95	C₂³	1	2	yes	—
177	C₃₁×#95	C₂³	1	4	yes	—
178	C₃₁×#95	C₂³	1	4	yes	—
179	C₃₁×#95	C₂³	1	4	yes	—
180	C₃₁×#95	C₂³	1	4	yes	—
181	C₃₁×#95	C₂³	1	4	yes	—
182	C₃₁×#95	C₂³	1	4	yes	—
183	C₂⁴×C₃₁	—	2	2	no	—
184	C₂⁴×C₃₁	—	2	4	no	—
185	C₂⁴×C₃₁	—	2	2	no	—
186	C₂⁴×C₃₁	—	4	2	no	—
187	C₂⁴×C₃₁	C₂²×C₄	1	4	yes	—
188	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
189	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
190	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
191	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
192	#41×C₃₁	—	2	32	no	—
193	C₂×Q₈×C₃₁	—	2	2	no	—
194	C₂×Q₈×C₃₁	—	2	2	no	—
195	C₂×Q₈×C₃₁	C₂²×C₄	1	4	yes	—
196	C₂×D₄×C₃₁	—	2	4	no	—
197	C₂×D₄×C₃₁	—	2	8	no	—
198	C₂×D₄×C₃₁	—	2	4	no	—
199	C₂×D₄×C₃₁	—	2	2	no	—
200	C₂×D₄×C₃₁	—	2	2	no	—
201	C₂×D₄×C₃₁	—	4	4	no	—
202	C₂×D₄×C₃₁	C₂²×C₄	1	8	yes	—
203	C₂×D₄×C₃₁	C₂²×C₄	1	8	yes	—
204	C₂×D₄×C₃₁	C₂²×C₄	1	4	yes	—
205	C₂×D₄×C₃₁	C₂²×C₄	1	8	yes	—
206	C₂²×C₄×C₃₁	—	2	2	no	—
207	C₂²×C₄×C₃₁	—	2	2	no	—
208	C₂²×C₄×C₃₁	—	2	32	no	—
209	C₂²×C₄×C₃₁	—	2	2	no	—
210	C₂²×C₄×C₃₁	—	2	4	no	—
211	C₂²×C₄×C₃₁	—	2	2	no	—
212	C₂²×C₄×C₃₁	—	2	2	no	—
213	C₂²×C₄×C₃₁	—	2	2	no	—
214	C₂²×C₄×C₃₁	—	2	2	no	—
215	C₂²×C₄×C₃₁	—	2	2	no	—
216	C₂²×C₄×C₃₁	—	2	2	no	—
217	C₂²×C₄×C₃₁	—	2	2	no	—
218	C₂²×C₄×C₃₁	—	2	4	no	—
219	C₂²×C₄×C₃₁	—	2	4	no	—
220	C₂²×C₄×C₃₁	—	2	4	no	—
221	C₂²×C₄×C₃₁	—	2	8	no	—
222	C₂²×C₄×C₃₁	—	2	8	no	—
223	C₂²×C₄×C₃₁	—	2	8	no	—
224	C₂²×C₄×C₃₁	—	2	4	no	—
225	C₂²×C₄×C₃₁	—	2	4	no	—
226	C₂²×C₄×C₃₁	—	2	8	no	—
227	C₂²×C₄×C₃₁	—	4	2	no	—
228	C₂²×C₄×C₃₁	—	4	4	no	—
229	C₂²×C₄×C₃₁	—	4	4	no	—
230	C₂²×C₄×C₃₁	—	4	2	no	—
231	C₂²×C₄×C₃₁	C₂²×C₄	1	4	yes	—
232	C₂²×C₄×C₃₁	C₂²×C₄	1	4	yes	—
233	C₂²×C₄×C₃₁	C₂²×C₄	1	8	yes	—
234	C₂²×C₄×C₃₁	C₂²×C₄	1	4	yes	—
235	C₂²×C₄×C₃₁	C₂²×C₄	1	4	yes	—
236	C₂²×C₄×C₃₁	C₂²×C₄	1	4	yes	—
237	C₂²×C₄×C₃₁	C₂²×C₄	1	4	yes	—
238	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
239	C₂²×C₄×C₃₁	#41	1	4	yes	—
240	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
241	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
242	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
243	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
244	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
245	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
246	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
247	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
248	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
249	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
250	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
251	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
252	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
253	C₄⋊C₄×C₃₁	—	2	8	no	—
254	C₄⋊C₄×C₃₁	—	2	4	no	—
255	C₄⋊C₄×C₃₁	—	2	8	no	—
256	C₄⋊C₄×C₃₁	—	2	8	no	—
257	C₄⋊C₄×C₃₁	—	4	4	no	—
258	C₄⋊C₄×C₃₁	C₂²×C₄	1	4	yes	—
259	C₄⋊C₄×C₃₁	C₂²×C₄	1	4	yes	—
260	C₄⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
261	C₄⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
262	C₄⋊C₄×C₃₁	C₂×D₄	1	8	yes	—
263	C₂²⋊C₄×C₃₁	—	2	4	no	—
264	C₂²⋊C₄×C₃₁	—	2	4	no	—
265	C₂²⋊C₄×C₃₁	—	2	8	no	—
266	C₂²⋊C₄×C₃₁	—	2	8	no	—
267	C₂²⋊C₄×C₃₁	—	2	4	no	—
268	C₂²⋊C₄×C₃₁	—	2	4	no	—
269	C₂²⋊C₄×C₃₁	—	2	8	no	—
270	C₂²⋊C₄×C₃₁	—	4	4	no	—
271	C₂²⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
272	C₂²⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
273	C₂²⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
274	C₂²⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
275	C₂²⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
276	C₂²⋊C₄×C₃₁	C₂×D₄	1	8	yes	—
277	C₂²⋊C₄×C₃₁	#41	1	8	yes	complemented
278	C₄²×C₃₁	—	2	2	no	—
279	C₄²×C₃₁	—	2	8	no	—
280	C₄²×C₃₁	—	2	2	no	—
281	C₄²×C₃₁	—	2	4	no	—
282	C₄²×C₃₁	—	2	8	no	—
283	C₄²×C₃₁	—	2	4	no	—
284	C₄²×C₃₁	—	2	2	no	—
285	C₄²×C₃₁	—	2	4	no	—
286	C₄²×C₃₁	—	2	2	no	—
287	C₄²×C₃₁	—	2	8	no	—
288	C₄²×C₃₁	—	4	4	no	—
289	C₄²×C₃₁	C₂²×C₄	1	8	yes	—
290	C₄²×C₃₁	C₂×D₄	1	8	yes	—
291	#34136	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
292	C₂³×C₃₁	—	2	1	no	—
293	C₂³×C₃₁	—	2	1	no	—
294	C₂³×C₃₁	—	2	2	no	—
295	C₂³×C₃₁	—	2	2	no	—
296	C₂³×C₃₁	—	2	2	no	—
297	C₂³×C₃₁	—	2	8	no	—
298	C₂³×C₃₁	—	2	8	no	—
299	C₂³×C₃₁	—	2	1	no	—
300	C₂³×C₃₁	—	2	2	no	—
301	C₂³×C₃₁	—	2	2	no	—
302	C₂³×C₃₁	—	2	4	no	—
303	C₂³×C₃₁	—	2	1	no	—
304	C₂³×C₃₁	—	2	2	no	—
305	C₂³×C₃₁	—	2	4	no	—
306	C₂³×C₃₁	—	2	2	no	—
307	C₂³×C₃₁	—	4	4	no	—
308	C₂³×C₃₁	—	4	8	no	—
309	C₂³×C₃₁	—	4	8	no	—
310	C₂³×C₃₁	C₂³×C₄	1	2	yes	—
311	C₂³×C₃₁	C₂³×C₄	1	4	yes	—
312	C₂³×C₃₁	C₂³×C₄	1	2	yes	—
313	C₂³×C₃₁	C₂³×C₄	1	2	yes	—
314	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
315	C₂³×C₃₁	C₂×#41	1	2	yes	—
316	C₂³×C₃₁	C₂×#41	1	4	yes	—
317	C₂³×C₃₁	C₂⁵	1	1	yes	characteristic
318	Q₈×C₃₁	—	2	8	no	—
319	D₄×C₃₁	—	2	16	no	—
320	D₄×C₃₁	—	2	16	no	—
321	D₄×C₃₁	—	2	8	no	—
322	D₄×C₃₁	—	4	8	no	—
323	C₂×C₄×C₃₁	—	2	8	no	—
324	C₂×C₄×C₃₁	—	2	1	no	—
325	C₂×C₄×C₃₁	—	2	2	no	—
326	C₂×C₄×C₃₁	—	2	2	no	—
327	C₂×C₄×C₃₁	—	2	1	no	—
328	C₂×C₄×C₃₁	—	2	2	no	—
329	C₂×C₄×C₃₁	—	2	4	no	—
330	C₂×C₄×C₃₁	—	2	4	no	—
331	C₂×C₄×C₃₁	—	2	1	no	—
332	C₂×C₄×C₃₁	—	2	1	no	—
333	C₂×C₄×C₃₁	—	2	2	no	—
334	C₂×C₄×C₃₁	—	2	2	no	—
335	C₂×C₄×C₃₁	—	2	4	no	—
336	C₂×C₄×C₃₁	—	2	4	no	—
337	C₂×C₄×C₃₁	—	2	2	no	—
338	C₂×C₄×C₃₁	—	2	8	no	—
339	C₂×C₄×C₃₁	—	2	8	no	—
340	C₂×C₄×C₃₁	—	2	8	no	—
341	C₂×C₄×C₃₁	—	2	8	no	—
342	C₂×C₄×C₃₁	—	2	16	no	—
343	C₂×C₄×C₃₁	—	2	4	no	—
344	C₂×C₄×C₃₁	—	2	2	no	—
345	C₂×C₄×C₃₁	—	2	2	no	—
346	C₂×C₄×C₃₁	—	2	2	no	—
347	C₂×C₄×C₃₁	—	2	2	no	—
348	C₂×C₄×C₃₁	—	2	4	no	—
349	C₂×C₄×C₃₁	—	2	2	no	—
350	C₂×C₄×C₃₁	—	2	4	no	—
351	C₂×C₄×C₃₁	—	2	2	no	—
352	C₂×C₄×C₃₁	—	4	16	no	—
353	C₂×C₄×C₃₁	—	4	8	no	—
354	C₂×C₄×C₃₁	—	4	16	no	—
355	C₂×C₄×C₃₁	—	4	8	no	—
356	C₂×C₄×C₃₁	C₄×D₄	1	16	yes	complemented
357	C₂×C₄×C₃₁	C₂³×C₄	1	4	yes	—
358	C₂×C₄×C₃₁	C₂³×C₄	1	4	yes	—
359	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
360	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
361	C₂×C₄×C₃₁	C₂³×C₄	1	4	yes	—
362	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
363	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
364	C₂×C₄×C₃₁	C₂²×D₄	1	8	yes	—
365	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
366	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
367	C₂×C₄×C₃₁	C₂×#41	1	4	yes	—
368	C₂×C₄×C₃₁	C₂×#41	1	4	yes	—
369	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
370	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
371	C₂×#525	C₂×C₃₁	1	1	yes	characteristic
372	C₂×C₄×#41	C₂×C₃₁	1	1	yes	characteristic, complemented
373	C₂²×#117	C₂×C₃₁	1	1	yes	characteristic, complemented
374	#2363	C₂×C₃₁	1	2	yes	complemented
375	#2362	C₂×C₃₁	1	2	yes	complemented
376	#2361	C₂×C₃₁	1	2	yes	complemented
377	#2360	C₂×C₃₁	1	2	yes	complemented
378	#2359	C₂×C₃₁	1	4	yes	complemented
379	#2358	C₂×C₃₁	1	4	yes	complemented
380	#2297	C₂×C₃₁	1	1	yes	characteristic, complemented
381	#2296	C₂×C₃₁	1	1	yes	characteristic, complemented
382	#2293	C₂×C₃₁	1	2	yes	complemented
383	#2290	C₂×C₃₁	1	2	yes	complemented
384	#2290	C₂×C₃₁	1	2	yes	complemented
385	C₄²×D₄	C₂×C₃₁	1	2	yes	complemented
386	C₄×#117	C₂×C₃₁	1	1	yes	characteristic, complemented
387	C₂×C₄×C₂²⋊C₄	C₂×C₃₁	1	1	yes	characteristic, complemented
388	C₂²×C₃₁	—	2	2	no	—
389	C₂²×C₃₁	—	2	2	no	—
390	C₂²×C₃₁	—	2	2	no	—
391	C₂²×C₃₁	—	2	2	no	—
392	C₂²×C₃₁	—	2	4	no	—
393	C₂²×C₃₁	—	2	4	no	—
394	C₂²×C₃₁	—	2	4	no	—
395	C₂²×C₃₁	—	2	4	no	—
396	C₂²×C₃₁	—	2	2	no	—
397	C₂²×C₃₁	—	2	4	no	—
398	C₂²×C₃₁	—	2	4	no	—
399	C₂²×C₃₁	—	2	2	no	—
400	C₂²×C₃₁	—	2	2	no	—
401	C₂²×C₃₁	—	2	4	no	—
402	C₂²×C₃₁	—	4	16	no	—
403	C₂²×C₃₁	—	4	4	no	—
404	C₂²×C₃₁	—	4	2	no	—
405	C₂²×C₃₁	—	4	4	no	—
406	C₂²×C₃₁	—	4	2	no	—
407	C₂²×C₃₁	C₂×C₄×D₄	1	4	yes	—
408	C₂²×C₃₁	C₄×#41	1	4	yes	complemented
409	C₂²×C₃₁	C₂⁴×C₄	1	1	yes	characteristic
410	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
411	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
412	C₂²×C₃₁	C₂²×#41	1	2	yes	—
413	C₂²×C₃₁	#585	1	2	yes	—
414	C₄×C₃₁	—	2	2	no	—
415	C₄×C₃₁	—	2	2	no	—
416	C₄×C₃₁	—	2	4	no	—
417	C₄×C₃₁	—	2	4	no	—
418	C₄×C₃₁	—	2	4	no	—
419	C₄×C₃₁	—	2	4	no	—
420	C₄×C₃₁	—	2	8	no	—
421	C₄×C₃₁	—	2	4	no	—
422	C₄×C₃₁	—	4	2	no	—
423	C₄×C₃₁	—	4	4	no	—
424	C₄×C₃₁	—	4	2	no	—
425	C₄×C₃₁	C₂×C₄×D₄	1	4	yes	—
426	C₄×C₃₁	C₂×C₄×D₄	1	4	yes	—
427	C₂²×#41	C₂²×C₃₁	1	1	yes	characteristic
428	C₂⁴×C₄	C₂²×C₃₁	1	1	yes	characteristic
429	#525	C₄×C₃₁	1	16	yes	complemented
430	C₂×#123	C₂²×C₃₁	1	2	yes	—
431	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
432	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
433	C₂×#121	C₂²×C₃₁	1	1	yes	characteristic
434	C₂×#121	C₂²×C₃₁	1	1	yes	characteristic
435	C₂×#120	C₂²×C₃₁	1	2	yes	—
436	C₄×#41	—	2	8	no	—
437	C₂×C₄×Q₈	C₂²×C₃₁	1	2	yes	complemented
438	C₂×C₄×D₄	C₂²×C₃₁	1	4	yes	—
439	C₂×C₄×D₄	C₂²×C₃₁	1	4	yes	—
440	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
441	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
442	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	complemented
443	C₂×#117	—	2	8	no	—
444	C₂×#117	C₂²×C₃₁	1	2	yes	—
445	C₂×#117	C₂²×C₃₁	1	2	yes	—
446	C₂×#117	C₂²×C₃₁	1	2	yes	—
447	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
448	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
449	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
450	C₂×#117	C₂²×C₃₁	1	2	yes	complemented
451	C₂²×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
452	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
453	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
454	C₂²×C₄²	C₂²×C₃₁	1	2	yes	—
455	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
456	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
457	C₂²×C₄²	C₂²×C₃₁	1	2	yes	complemented
458	#391	C₂²×C₃₁	1	2	yes	complemented
459	#390	C₂²×C₃₁	1	4	yes	—
460	#390	C₂²×C₃₁	1	2	yes	complemented
461	#389	C₂²×C₃₁	1	4	yes	complemented
462	#389	C₂²×C₃₁	1	2	yes	complemented
463	#389	C₂²×C₃₁	1	2	yes	complemented
464	#388	C₂²×C₃₁	1	4	yes	—
465	#388	C₂²×C₃₁	1	4	yes	—
466	#388	C₂²×C₃₁	1	4	yes	complemented
467	#388	C₂²×C₃₁	1	4	yes	complemented
468	#387	C₂²×C₃₁	1	4	yes	complemented
469	#387	C₂²×C₃₁	1	4	yes	complemented
470	#386	C₂²×C₃₁	1	4	yes	—
471	#386	C₂²×C₃₁	1	4	yes	—
472	#386	C₂²×C₃₁	1	4	yes	—
473	#385	C₂²×C₃₁	1	4	yes	—
474	#385	C₂²×C₃₁	1	4	yes	—
475	#385	C₂²×C₃₁	1	4	yes	complemented
476	C₄×C₄⋊C₄	C₂²×C₃₁	1	4	yes	complemented
477	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	complemented
478	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	complemented
479	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	complemented
480	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	complemented
481	C₄×C₂²⋊C₄	C₂²×C₃₁	1	4	yes	—
482	C₄×C₂²⋊C₄	C₂²×C₃₁	1	4	yes	—
483	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
484	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
485	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
486	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
487	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
488	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
489	C₄×C₂²⋊C₄	C₂²×C₃₁	1	4	yes	complemented
490	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	complemented
491	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	complemented
492	#376	C₂²×C₃₁	1	2	yes	complemented
493	C₂×#95	C₂²×C₃₁	1	2	yes	—
494	C₄³	C₂²×C₃₁	1	2	yes	complemented
495	C₂×C₃₁	—	2	4	no	—
496	C₂×C₃₁	—	2	4	no	—
497	C₂×C₃₁	—	4	4	no	—
498	C₂×C₃₁	—	4	2	no	—
499	C₂×C₃₁	C₂²×C₄×D₄	1	1	yes	characteristic
500	C₂×C₃₁	C₂×C₄×#41	1	1	yes	characteristic
501	C₂×C₃₁	#3428	1	1	yes	characteristic
502	C₂×C₃₁	D₄×#41	1	2	yes	—
503	C₂×C₃₁	#3475	1	2	yes	—
504	C₂⁵	C₂³×C₃₁	1	1	yes	characteristic
505	C₂×#41	—	2	4	no	—
506	C₂×#41	—	2	4	no	—
507	C₂×#41	C₂×C₄×C₃₁	1	8	yes	complemented
508	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
509	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
510	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
511	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
512	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
513	C₂³×C₄	—	2	4	no	—
514	C₂³×C₄	—	2	4	no	—
515	C₂³×C₄	C₂×C₄×C₃₁	1	8	yes	complemented
516	C₂³×C₄	C₂³×C₃₁	1	4	yes	—
517	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
518	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
519	C₂³×C₄	C₂³×C₃₁	1	4	yes	—
520	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
521	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
522	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
523	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
524	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
525	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
526	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
527	#123	C₂×C₄×C₃₁	1	16	yes	complemented
528	C₂²⋊Q₈	C₂×C₄×C₃₁	1	8	yes	complemented
529	C₂²⋊Q₈	C₂×C₄×C₃₁	1	8	yes	complemented
530	#121	C₂×C₄×C₃₁	1	8	yes	complemented
531	#121	C₂×C₄×C₃₁	1	8	yes	complemented
532	#120	C₂×C₄×C₃₁	1	16	yes	complemented
533	C₄×Q₈	—	2	8	no	—
534	C₄×D₄	—	2	8	no	—
535	C₄×D₄	—	2	16	no	—
536	C₄×D₄	—	2	16	no	—
537	C₄×D₄	C₂×C₄×C₃₁	1	16	yes	complemented
538	C₄×D₄	C₂×C₄×C₃₁	1	16	yes	complemented
539	#117	—	2	4	no	—
540	#117	—	2	8	no	—
541	#117	—	2	8	no	—
542	#117	—	2	8	no	—
543	#117	—	2	8	no	—
544	#117	C₂×C₄×C₃₁	1	8	yes	complemented
545	#117	D₄×C₃₁	1	8	yes	complemented
546	C₂×C₄⋊C₄	—	2	8	no	—
547	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
548	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
549	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
550	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
551	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
552	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
553	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
554	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
555	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
556	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
557	C₂×C₂²⋊C₄	—	2	8	no	—
558	C₂×C₂²⋊C₄	—	2	8	no	—
559	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
560	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
561	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
562	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
563	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
564	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
565	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
566	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
567	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
568	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
569	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
570	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
571	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
572	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
573	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
574	C₂×C₄²	—	2	4	no	—
575	C₂×C₄²	—	2	4	no	—
576	C₂×C₄²	—	2	8	no	—
577	C₂×C₄²	—	2	8	no	—
578	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
579	C₂×C₄²	C₂³×C₃₁	1	4	yes	—
580	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
581	C₂×C₄²	C₂³×C₃₁	1	4	yes	—
582	C₂×C₄²	C₂³×C₃₁	1	4	yes	—
583	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
584	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
585	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
586	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
587	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
588	C₂×C₄²	C₂³×C₃₁	1	4	yes	—
589	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
590	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
591	#95	C₂³×C₃₁	1	2	yes	—
592	#95	C₂³×C₃₁	1	2	yes	—
593	#95	C₂³×C₃₁	1	2	yes	—
594	#95	C₂³×C₃₁	1	2	yes	—
595	#95	C₂³×C₃₁	1	4	yes	—
596	#95	C₂³×C₃₁	1	4	yes	—
597	#95	C₂³×C₃₁	1	4	yes	—
598	#95	C₂³×C₃₁	1	4	yes	—
599	#95	C₂³×C₃₁	1	4	yes	—
600	#95	C₂³×C₃₁	1	4	yes	—
601	C₃₁	#34136	1	1	yes	characteristic, direct product factor, Sylow
602	C₂⁴	—	2	2	no	—
603	C₂⁴	—	2	4	no	—
604	C₂⁴	—	2	2	no	—
605	C₂⁴	—	4	2	no	—
606	C₂⁴	C₂²×C₄×C₃₁	1	4	yes	—
607	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
608	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
609	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
610	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
611	#41	—	2	32	no	—
612	C₂×Q₈	—	2	2	no	—
613	C₂×Q₈	—	2	2	no	—
614	C₂×Q₈	C₂²×C₄×C₃₁	1	4	yes	—
615	C₂×D₄	—	2	4	no	—
616	C₂×D₄	—	2	8	no	—
617	C₂×D₄	—	2	4	no	—
618	C₂×D₄	—	2	2	no	—
619	C₂×D₄	—	2	2	no	—
620	C₂×D₄	—	4	4	no	—
621	C₂×D₄	C₂²×C₄×C₃₁	1	8	yes	—
622	C₂×D₄	C₂²×C₄×C₃₁	1	8	yes	—
623	C₂×D₄	C₂²×C₄×C₃₁	1	4	yes	—
624	C₂×D₄	C₂²×C₄×C₃₁	1	8	yes	—
625	C₂²×C₄	—	2	2	no	—
626	C₂²×C₄	—	2	2	no	—
627	C₂²×C₄	—	2	32	no	—
628	C₂²×C₄	—	2	2	no	—
629	C₂²×C₄	—	2	4	no	—
630	C₂²×C₄	—	2	2	no	—
631	C₂²×C₄	—	2	2	no	—
632	C₂²×C₄	—	2	2	no	—
633	C₂²×C₄	—	2	2	no	—
634	C₂²×C₄	—	2	2	no	—
635	C₂²×C₄	—	2	2	no	—
636	C₂²×C₄	—	2	2	no	—
637	C₂²×C₄	—	2	4	no	—
638	C₂²×C₄	—	2	4	no	—
639	C₂²×C₄	—	2	4	no	—
640	C₂²×C₄	—	2	8	no	—
641	C₂²×C₄	—	2	8	no	—
642	C₂²×C₄	—	2	8	no	—
643	C₂²×C₄	—	2	4	no	—
644	C₂²×C₄	—	2	4	no	—
645	C₂²×C₄	—	2	8	no	—
646	C₂²×C₄	—	4	2	no	—
647	C₂²×C₄	—	4	4	no	—
648	C₂²×C₄	—	4	4	no	—
649	C₂²×C₄	—	4	2	no	—
650	C₂²×C₄	C₂²×C₄×C₃₁	1	4	yes	—
651	C₂²×C₄	C₂²×C₄×C₃₁	1	4	yes	—
652	C₂²×C₄	C₂²×C₄×C₃₁	1	8	yes	—
653	C₂²×C₄	C₂²×C₄×C₃₁	1	4	yes	—
654	C₂²×C₄	C₂²×C₄×C₃₁	1	4	yes	—
655	C₂²×C₄	C₂²×C₄×C₃₁	1	4	yes	—
656	C₂²×C₄	C₂²×C₄×C₃₁	1	4	yes	—
657	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
658	C₂²×C₄	#41×C₃₁	1	4	yes	—
659	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
660	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
661	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
662	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
663	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
664	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
665	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
666	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
667	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
668	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
669	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
670	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
671	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
672	C₄⋊C₄	—	2	8	no	—
673	C₄⋊C₄	—	2	4	no	—
674	C₄⋊C₄	—	2	8	no	—
675	C₄⋊C₄	—	2	8	no	—
676	C₄⋊C₄	—	4	4	no	—
677	C₄⋊C₄	C₂²×C₄×C₃₁	1	4	yes	—
678	C₄⋊C₄	C₂²×C₄×C₃₁	1	4	yes	—
679	C₄⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
680	C₄⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
681	C₄⋊C₄	C₂×D₄×C₃₁	1	8	yes	—
682	C₂²⋊C₄	—	2	4	no	—
683	C₂²⋊C₄	—	2	4	no	—
684	C₂²⋊C₄	—	2	8	no	—
685	C₂²⋊C₄	—	2	8	no	—
686	C₂²⋊C₄	—	2	4	no	—
687	C₂²⋊C₄	—	2	4	no	—
688	C₂²⋊C₄	—	2	8	no	—
689	C₂²⋊C₄	—	4	4	no	—
690	C₂²⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
691	C₂²⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
692	C₂²⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
693	C₂²⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
694	C₂²⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
695	C₂²⋊C₄	C₂×D₄×C₃₁	1	8	yes	—
696	C₂²⋊C₄	#41×C₃₁	1	8	yes	complemented
697	C₄²	—	2	2	no	—
698	C₄²	—	2	8	no	—
699	C₄²	—	2	2	no	—
700	C₄²	—	2	4	no	—
701	C₄²	—	2	8	no	—
702	C₄²	—	2	4	no	—
703	C₄²	—	2	2	no	—
704	C₄²	—	2	4	no	—
705	C₄²	—	2	2	no	—
706	C₄²	—	2	8	no	—
707	C₄²	—	4	4	no	—
708	C₄²	C₂²×C₄×C₃₁	1	8	yes	—
709	C₄²	C₂×D₄×C₃₁	1	8	yes	—
710	C₂³	—	2	1	no	—
711	C₂³	—	2	1	no	—
712	C₂³	—	2	2	no	—
713	C₂³	—	2	2	no	—
714	C₂³	—	2	2	no	—
715	C₂³	—	2	8	no	—
716	C₂³	—	2	8	no	—
717	C₂³	—	2	1	no	—
718	C₂³	—	2	2	no	—
719	C₂³	—	2	2	no	—
720	C₂³	—	2	4	no	—
721	C₂³	—	2	1	no	—
722	C₂³	—	2	2	no	—
723	C₂³	—	2	4	no	—
724	C₂³	—	2	2	no	—
725	C₂³	—	4	4	no	—
726	C₂³	—	4	8	no	—
727	C₂³	—	4	8	no	—
728	C₂³	C₂³×C₄×C₃₁	1	2	yes	—
729	C₂³	C₂³×C₄×C₃₁	1	4	yes	—
730	C₂³	C₂³×C₄×C₃₁	1	2	yes	—
731	C₂³	C₂³×C₄×C₃₁	1	2	yes	—
732	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
733	C₂³	C₂×#41×C₃₁	1	2	yes	—
734	C₂³	C₂×#41×C₃₁	1	4	yes	—
735	C₂³	C₂⁵×C₃₁	1	1	yes	characteristic
736	Q₈	—	2	8	no	—
737	D₄	—	2	16	no	—
738	D₄	—	2	16	no	—
739	D₄	—	2	8	no	—
740	D₄	—	4	8	no	—
741	C₂×C₄	—	2	8	no	—
742	C₂×C₄	—	2	1	no	—
743	C₂×C₄	—	2	2	no	—
744	C₂×C₄	—	2	2	no	—
745	C₂×C₄	—	2	1	no	—
746	C₂×C₄	—	2	2	no	—
747	C₂×C₄	—	2	4	no	—
748	C₂×C₄	—	2	4	no	—
749	C₂×C₄	—	2	1	no	—
750	C₂×C₄	—	2	1	no	—
751	C₂×C₄	—	2	2	no	—
752	C₂×C₄	—	2	2	no	—
753	C₂×C₄	—	2	4	no	—
754	C₂×C₄	—	2	4	no	—
755	C₂×C₄	—	2	2	no	—
756	C₂×C₄	—	2	8	no	—
757	C₂×C₄	—	2	8	no	—
758	C₂×C₄	—	2	8	no	—
759	C₂×C₄	—	2	8	no	—
760	C₂×C₄	—	2	16	no	—
761	C₂×C₄	—	2	4	no	—
762	C₂×C₄	—	2	2	no	—
763	C₂×C₄	—	2	2	no	—
764	C₂×C₄	—	2	2	no	—
765	C₂×C₄	—	2	2	no	—
766	C₂×C₄	—	2	4	no	—
767	C₂×C₄	—	2	2	no	—
768	C₂×C₄	—	2	4	no	—
769	C₂×C₄	—	2	2	no	—
770	C₂×C₄	—	4	16	no	—
771	C₂×C₄	—	4	8	no	—
772	C₂×C₄	—	4	16	no	—
773	C₂×C₄	—	4	8	no	—
774	C₂×C₄	C₄×D₄×C₃₁	1	16	yes	complemented
775	C₂×C₄	C₂³×C₄×C₃₁	1	4	yes	—
776	C₂×C₄	C₂³×C₄×C₃₁	1	4	yes	—
777	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
778	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
779	C₂×C₄	C₂³×C₄×C₃₁	1	4	yes	—
780	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
781	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
782	C₂×C₄	C₂²×D₄×C₃₁	1	8	yes	—
783	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
784	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
785	C₂×C₄	C₂×#41×C₃₁	1	4	yes	—
786	C₂×C₄	C₂×#41×C₃₁	1	4	yes	—
787	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
788	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
789	C₂²	—	2	2	no	—
790	C₂²	—	2	2	no	—
791	C₂²	—	2	2	no	—
792	C₂²	—	2	2	no	—
793	C₂²	—	2	4	no	—
794	C₂²	—	2	4	no	—
795	C₂²	—	2	4	no	—
796	C₂²	—	2	4	no	—
797	C₂²	—	2	2	no	—
798	C₂²	—	2	4	no	—
799	C₂²	—	2	4	no	—
800	C₂²	—	2	2	no	—
801	C₂²	—	2	2	no	—
802	C₂²	—	2	4	no	—
803	C₂²	—	4	16	no	—
804	C₂²	—	4	4	no	—
805	C₂²	—	4	2	no	—
806	C₂²	—	4	2	no	—
807	C₂²	—	4	4	no	—
808	C₂²	C₂×C₄×D₄×C₃₁	1	4	yes	—
809	C₂²	C₄×#41×C₃₁	1	4	yes	complemented
810	C₂²	C₂⁴×C₄×C₃₁	1	1	yes	characteristic
811	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
812	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
813	C₂²	C₂²×#41×C₃₁	1	2	yes	—
814	C₂²	C₃₁×#585	1	2	yes	—
815	C₄	—	2	2	no	—
816	C₄	—	2	2	no	—
817	C₄	—	2	4	no	—
818	C₄	—	2	4	no	—
819	C₄	—	2	4	no	—
820	C₄	—	2	4	no	—
821	C₄	—	2	8	no	—
822	C₄	—	2	4	no	—
823	C₄	—	4	2	no	—
824	C₄	—	4	4	no	—
825	C₄	—	4	2	no	—
826	C₄	C₂×C₄×D₄×C₃₁	1	4	yes	—
827	C₄	C₂×C₄×D₄×C₃₁	1	4	yes	—
828	C₂	—	2	4	no	—
829	C₂	—	2	4	no	—
830	C₂	—	4	2	no	—
831	C₂	—	4	4	no	—
832	C₂	C₂²×C₄×D₄×C₃₁	1	1	yes	characteristic
833	C₂	C₂×C₄×#41×C₃₁	1	1	yes	characteristic
834	C₂	C₃₁×#3428	1	1	yes	characteristic
835	C₂	D₄×#41×C₃₁	1	2	yes	—
836	C₂	C₃₁×#3475	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₃₁	C₂⁴
commutator	C₂²	C₂⁴×C₄×C₃₁
Frattini, cosocle	C₂³	C₂⁵×C₃₁
socle	C₂³×C₃₁	C₂⁵
prime radical	C₂×C₃₁×#525	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×#41×C₃₁	C₂	semidirect
3. C₂²×C₃₁×#117	C₂	semidirect
4. C₃₁×#2363	C₂	semidirect
5. C₃₁×#2362	C₂	semidirect
6. C₃₁×#2361	C₂	semidirect
7. C₃₁×#2360	C₂	semidirect
8. C₃₁×#2359	C₂	semidirect
9. C₃₁×#2358	C₂	semidirect
10. C₃₁×#2297	C₂	semidirect
11. C₃₁×#2296	C₂	semidirect
12. C₃₁×#2293	C₂	semidirect
13. C₃₁×#2290	C₂	semidirect
14. C₃₁×#2290	C₂	semidirect
15. C₄²×D₄×C₃₁	C₂	semidirect
16. C₄×C₃₁×#117	C₂	semidirect
17. C₂×C₄×C₂²⋊C₄×C₃₁	C₂	semidirect
20. C₃₁×#525	C₄	semidirect
28. C₂×C₄×Q₈×C₃₁	C₂²	semidirect
33. C₂×C₄×D₄×C₃₁	C₂²	semidirect
41. C₂×C₃₁×#117	C₂²	semidirect
48. C₂²×C₄²×C₃₁	C₂²	semidirect
49. C₃₁×#391	C₂²	semidirect
51. C₃₁×#390	C₂²	semidirect
52. C₃₁×#389	C₂²	semidirect
53. C₃₁×#389	C₂²	semidirect
54. C₃₁×#389	C₂²	semidirect
57. C₃₁×#388	C₂²	semidirect
58. C₃₁×#388	C₂²	semidirect
59. C₃₁×#387	C₂²	semidirect
60. C₃₁×#387	C₂²	semidirect
66. C₃₁×#385	C₂²	semidirect
67. C₄×C₄⋊C₄×C₃₁	C₂²	semidirect
68. C₄×C₄⋊C₄×C₃₁	C₂²	semidirect
69. C₄×C₄⋊C₄×C₃₁	C₂²	semidirect
70. C₄×C₄⋊C₄×C₃₁	C₂²	semidirect
71. C₄×C₄⋊C₄×C₃₁	C₂²	semidirect
80. C₄×C₂²⋊C₄×C₃₁	C₂²	semidirect
81. C₄×C₂²⋊C₄×C₃₁	C₂²	semidirect
82. C₄×C₂²⋊C₄×C₃₁	C₂²	semidirect
83. C₃₁×#376	C₂²	semidirect
85. C₄³×C₃₁	C₂²	semidirect
89. C₂×#41×C₃₁	C₂×C₄	semidirect
97. C₂³×C₄×C₃₁	C₂×C₄	semidirect
109. C₃₁×#123	C₂×C₄	semidirect
110. C₃₁×C₂²⋊Q₈	C₂×C₄	semidirect
111. C₃₁×C₂²⋊Q₈	C₂×C₄	semidirect
112. C₃₁×#121	C₂×C₄	semidirect
113. C₃₁×#121	C₂×C₄	semidirect
114. C₃₁×#120	C₂×C₄	semidirect
119. C₄×D₄×C₃₁	C₂×C₄	semidirect
120. C₄×D₄×C₃₁	C₂×C₄	semidirect
126. C₃₁×#117	C₂×C₄	semidirect
127. C₃₁×#117	D₄	semidirect
277. C₂²⋊C₄×C₃₁	#41	semidirect
291. #34136	C₃₁	direct (N × H)
356. C₂×C₄×C₃₁	C₄×D₄	semidirect
372. C₂×C₄×#41	C₂×C₃₁	semidirect
373. C₂²×#117	C₂×C₃₁	semidirect
374. #2363	C₂×C₃₁	semidirect
375. #2362	C₂×C₃₁	semidirect
376. #2361	C₂×C₃₁	semidirect
377. #2360	C₂×C₃₁	semidirect
378. #2359	C₂×C₃₁	semidirect
379. #2358	C₂×C₃₁	semidirect
380. #2297	C₂×C₃₁	semidirect
381. #2296	C₂×C₃₁	semidirect
382. #2293	C₂×C₃₁	semidirect
383. #2290	C₂×C₃₁	semidirect
384. #2290	C₂×C₃₁	semidirect
385. C₄²×D₄	C₂×C₃₁	semidirect
386. C₄×#117	C₂×C₃₁	semidirect
387. C₂×C₄×C₂²⋊C₄	C₂×C₃₁	semidirect
408. C₂²×C₃₁	C₄×#41	semidirect
429. #525	C₄×C₃₁	semidirect
437. C₂×C₄×Q₈	C₂²×C₃₁	semidirect
442. C₂×C₄×D₄	C₂²×C₃₁	semidirect
450. C₂×#117	C₂²×C₃₁	semidirect
457. C₂²×C₄²	C₂²×C₃₁	semidirect
458. #391	C₂²×C₃₁	semidirect
460. #390	C₂²×C₃₁	semidirect
461. #389	C₂²×C₃₁	semidirect
462. #389	C₂²×C₃₁	semidirect
463. #389	C₂²×C₃₁	semidirect
466. #388	C₂²×C₃₁	semidirect
467. #388	C₂²×C₃₁	semidirect
468. #387	C₂²×C₃₁	semidirect
469. #387	C₂²×C₃₁	semidirect
475. #385	C₂²×C₃₁	semidirect
476. C₄×C₄⋊C₄	C₂²×C₃₁	semidirect
477. C₄×C₄⋊C₄	C₂²×C₃₁	semidirect
478. C₄×C₄⋊C₄	C₂²×C₃₁	semidirect
479. C₄×C₄⋊C₄	C₂²×C₃₁	semidirect
480. C₄×C₄⋊C₄	C₂²×C₃₁	semidirect
489. C₄×C₂²⋊C₄	C₂²×C₃₁	semidirect
490. C₄×C₂²⋊C₄	C₂²×C₃₁	semidirect
491. C₄×C₂²⋊C₄	C₂²×C₃₁	semidirect
492. #376	C₂²×C₃₁	semidirect
494. C₄³	C₂²×C₃₁	semidirect
507. C₂×#41	C₂×C₄×C₃₁	semidirect
515. C₂³×C₄	C₂×C₄×C₃₁	semidirect
527. #123	C₂×C₄×C₃₁	semidirect
528. C₂²⋊Q₈	C₂×C₄×C₃₁	semidirect
529. C₂²⋊Q₈	C₂×C₄×C₃₁	semidirect
530. #121	C₂×C₄×C₃₁	semidirect
531. #121	C₂×C₄×C₃₁	semidirect
532. #120	C₂×C₄×C₃₁	semidirect
537. C₄×D₄	C₂×C₄×C₃₁	semidirect
538. C₄×D₄	C₂×C₄×C₃₁	semidirect
544. #117	C₂×C₄×C₃₁	semidirect
545. #117	D₄×C₃₁	semidirect
601. C₃₁	#34136	direct (N × H)
696. C₂²⋊C₄	#41×C₃₁	semidirect
774. C₂×C₄	C₄×D₄×C₃₁	semidirect
809. C₂²	C₄×#41×C₃₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃₁×#525	2
C₂×C₄×#41×C₃₁	2
C₂²×C₃₁×#117	2
C₃₁×#2363	2
C₃₁×#2362	2
C₃₁×#2361	2
C₃₁×#2360	2
C₃₁×#2359	2
C₃₁×#2358	2
C₃₁×#2297	2
C₃₁×#2296	2
C₃₁×#2293	2
C₃₁×#2290	2
C₄²×D₄×C₃₁	2
C₄×C₃₁×#117	2
C₂×C₄×C₂²⋊C₄×C₃₁	2
#34136	31

Subgroups — C31×#34136 #21490895

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#34136 #21490895