Subgroups — C₃₁×#34308 #21491067

Order 7936.

3124 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#547	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃₁×#520	C₂	1	2	yes	maximal, complemented
3	C₃₁×#2365	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#2361	C₂	1	2	yes	maximal, complemented
5	C₃₁×#2360	C₂	1	2	yes	maximal, complemented
6	C₃₁×#2359	C₂	1	4	yes	maximal, complemented
7	D₄×C₄⋊C₄×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
8	D₄×C₄⋊C₄×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#2344	C₂	1	2	yes	maximal, complemented
10	C₃₁×#2339	C₂	1	2	yes	maximal, complemented
11	C₃₁×#2323	C₂	1	2	yes	maximal, complemented
12	C₃₁×#2322	C₂	1	4	yes	maximal, complemented
13	C₄×C₃₁×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×C₃₁×#121	C₂	1	2	yes	maximal, complemented
15	C₃₁×#2293	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₃₁×#389	C₂	1	2	yes	maximal, complemented
17	C₄²×D₄×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×#41×C₃₁	C₂²	1	2	yes	—
19	C₃₁×#547	C₄	1	16	yes	complemented
20	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
21	C₂×C₃₁×#123	C₂²	1	4	yes	—
22	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	—
23	C₂×C₃₁×#121	C₂²	1	2	yes	—
24	C₃₁×#520	—	2	16	no	—
25	C₂×C₄×Q₈×C₃₁	C₂²	1	2	yes	—
26	C₂×C₄×Q₈×C₃₁	C₂²	1	2	yes	—
27	C₂×C₄×D₄×C₃₁	C₂²	1	4	yes	—
28	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
29	C₂×C₄×D₄×C₃₁	C₂²	1	2	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	1	yes	characteristic
33	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
34	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
35	C₂×C₃₁×#117	C₂²	1	2	yes	—
36	C₂×C₃₁×#117	C₂²	1	4	yes	—
37	C₂²×C₄⋊C₄×C₃₁	C₂²	1	4	yes	—
38	C₂²×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
39	C₂²×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
40	C₂²×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
41	C₂²×C₄²×C₃₁	C₂²	1	2	yes	—
42	C₃₁×#391	C₂²	1	2	yes	—
43	C₃₁×#391	C₂²	1	2	yes	—
44	C₃₁×#390	C₂²	1	1	yes	characteristic
45	C₃₁×#390	C₂²	1	1	yes	characteristic
46	C₃₁×#389	C₂²	1	2	yes	—
47	C₃₁×#389	C₂²	1	2	yes	—
48	C₃₁×#389	C₂²	1	4	yes	—
49	C₃₁×#389	C₂²	1	2	yes	—
50	C₃₁×#389	C₂²	1	1	yes	characteristic
51	C₃₁×#389	C₂²	1	2	yes	—
52	C₃₁×#389	C₂²	1	4	yes	—
53	C₃₁×#389	C₂²	1	2	yes	—
54	C₃₁×#389	C₂²	1	1	yes	characteristic
55	C₃₁×#388	C₂²	1	2	yes	—
56	C₃₁×#388	C₂²	1	4	yes	—
57	C₃₁×#388	C₂²	1	4	yes	—
58	C₃₁×#388	C₂²	1	2	yes	—
59	C₃₁×#387	C₂²	1	4	yes	—
60	C₃₁×#387	C₂²	1	4	yes	—
61	C₃₁×#387	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	—
67	C₃₁×#384	C₂²	1	1	yes	characteristic
68	C₃₁×#381	C₂²	1	4	yes	—
69	C₃₁×#380	C₂²	1	2	yes	—
70	C₃₁×#380	C₂²	1	2	yes	—
71	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
72	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
73	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
74	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
75	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
76	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
77	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
78	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
79	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
80	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
81	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
82	C₄×C₂²⋊C₄×C₃₁	C₂²	1	4	yes	—
83	C₂×C₃₁×#95	C₂²	1	4	yes	—
84	C₄³×C₃₁	C₂²	1	1	yes	characteristic
85	C₂×#41×C₃₁	—	2	8	no	—
86	C₂×#41×C₃₁	—	2	8	no	—
87	C₂×#41×C₃₁	C₂×C₄	1	16	yes	complemented
88	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
89	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
90	C₂²×D₄×C₃₁	C₂³	1	4	yes	—
91	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
92	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
93	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
94	C₂³×C₄×C₃₁	C₂³	1	4	yes	—
95	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
96	C₂³×C₄×C₃₁	C₂³	1	4	yes	—
97	C₂³×C₄×C₃₁	C₂³	1	4	yes	—
98	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
99	C₃₁×C₄⋊Q₈	C₂×C₄	1	8	yes	complemented
100	C₃₁×#123	C₂×C₄	1	32	yes	complemented
101	C₃₁×C₂²⋊Q₈	C₂×C₄	1	16	yes	complemented
102	C₃₁×#121	C₂×C₄	1	16	yes	complemented
103	C₄×Q₈×C₃₁	—	2	8	no	—
104	C₄×Q₈×C₃₁	—	2	8	no	—
105	C₄×D₄×C₃₁	—	2	8	no	—
106	C₄×D₄×C₃₁	—	2	4	no	—
107	C₄×D₄×C₃₁	—	2	16	no	—
108	C₄×D₄×C₃₁	—	2	16	no	—
109	C₄×D₄×C₃₁	—	4	4	no	—
110	C₄×D₄×C₃₁	C₂×C₄	1	8	yes	complemented
111	C₄×D₄×C₃₁	C₂×C₄	1	8	yes	complemented
112	C₄×D₄×C₃₁	D₄	1	8	yes	complemented
113	C₃₁×#117	—	2	16	no	—
114	C₃₁×#117	—	2	8	no	—
115	C₂×C₄⋊C₄×C₃₁	—	2	16	no	—
116	C₂×C₄⋊C₄×C₃₁	—	2	8	no	—
117	C₂×C₄⋊C₄×C₃₁	—	4	4	no	—
118	C₂×C₄⋊C₄×C₃₁	C₂×C₄	1	16	yes	complemented
119	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
120	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
121	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
122	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
123	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
124	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
125	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
126	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
127	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
128	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
132	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	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	2	yes	—
136	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
137	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
138	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
139	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
140	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
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	2	yes	—
148	C₂×C₄²×C₃₁	—	4	4	no	—
149	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
150	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
151	C₂×C₄²×C₃₁	C₂³	1	4	yes	—
152	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
153	C₂×C₄²×C₃₁	C₂³	1	4	yes	—
154	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
155	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
156	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
157	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
158	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
159	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
160	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
161	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
162	C₃₁×#95	C₂³	1	2	yes	—
163	C₃₁×#95	C₂³	1	4	yes	—
164	C₃₁×#95	C₂³	1	4	yes	—
165	C₃₁×#95	C₂³	1	4	yes	—
166	C₃₁×#95	C₂³	1	2	yes	—
167	C₃₁×#95	C₂³	1	2	yes	—
168	C₃₁×#95	C₂³	1	2	yes	—
169	C₃₁×#95	C₂³	1	4	yes	—
170	C₃₁×#95	C₂³	1	2	yes	—
171	C₃₁×#95	C₂³	1	4	yes	—
172	C₃₁×#95	C₂³	1	4	yes	—
173	C₃₁×#95	C₂³	1	2	yes	—
174	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
175	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
176	#41×C₃₁	—	2	64	no	—
177	C₂×Q₈×C₃₁	—	2	4	no	—
178	C₂×Q₈×C₃₁	—	2	4	no	—
179	C₂×Q₈×C₃₁	C₂²×C₄	1	8	yes	—
180	C₂×D₄×C₃₁	—	2	8	no	—
181	C₂×D₄×C₃₁	—	2	8	no	—
182	C₂×D₄×C₃₁	—	2	2	no	—
183	C₂×D₄×C₃₁	—	2	2	no	—
184	C₂×D₄×C₃₁	C₂²×C₄	1	4	yes	—
185	C₂×D₄×C₃₁	C₂²×C₄	1	16	yes	—
186	C₂×D₄×C₃₁	C₂²×C₄	1	4	yes	—
187	C₂×D₄×C₃₁	C₂×D₄	1	4	yes	—
188	C₂×D₄×C₃₁	#41	1	4	yes	—
189	C₂²×C₄×C₃₁	—	2	8	no	—
190	C₂²×C₄×C₃₁	—	2	8	no	—
191	C₂²×C₄×C₃₁	—	2	4	no	—
192	C₂²×C₄×C₃₁	—	2	4	no	—
193	C₂²×C₄×C₃₁	—	2	4	no	—
194	C₂²×C₄×C₃₁	—	2	4	no	—
195	C₂²×C₄×C₃₁	—	2	4	no	—
196	C₂²×C₄×C₃₁	—	2	8	no	—
197	C₂²×C₄×C₃₁	—	2	4	no	—
198	C₂²×C₄×C₃₁	—	2	8	no	—
199	C₂²×C₄×C₃₁	—	4	2	no	—
200	C₂²×C₄×C₃₁	—	4	2	no	—
201	C₂²×C₄×C₃₁	—	4	2	no	—
202	C₂²×C₄×C₃₁	—	4	4	no	—
203	C₂²×C₄×C₃₁	—	4	4	no	—
204	C₂²×C₄×C₃₁	—	4	4	no	—
205	C₂²×C₄×C₃₁	—	4	4	no	—
206	C₂²×C₄×C₃₁	C₂²×C₄	1	8	yes	—
207	C₂²×C₄×C₃₁	C₂²×C₄	1	16	yes	—
208	C₂²×C₄×C₃₁	C₂²×C₄	1	8	yes	—
209	C₂²×C₄×C₃₁	C₂×D₄	1	8	yes	—
210	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
211	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
212	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
213	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
214	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
215	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
216	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
217	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
218	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
219	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
220	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
221	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
222	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
223	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
224	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
225	C₄⋊C₄×C₃₁	—	2	8	no	—
226	C₄⋊C₄×C₃₁	—	2	4	no	—
227	C₄⋊C₄×C₃₁	—	2	8	no	—
228	C₄⋊C₄×C₃₁	—	2	8	no	—
229	C₄⋊C₄×C₃₁	—	2	4	no	—
230	C₄⋊C₄×C₃₁	—	2	4	no	—
231	C₄⋊C₄×C₃₁	—	2	2	no	—
232	C₄⋊C₄×C₃₁	—	2	2	no	—
233	C₄⋊C₄×C₃₁	—	2	4	no	—
234	C₄⋊C₄×C₃₁	—	2	2	no	—
235	C₄⋊C₄×C₃₁	—	4	4	no	—
236	C₄⋊C₄×C₃₁	—	4	2	no	—
237	C₄⋊C₄×C₃₁	C₂²×C₄	1	4	yes	—
238	C₄⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
239	C₄⋊C₄×C₃₁	C₂²×C₄	1	16	yes	—
240	C₄⋊C₄×C₃₁	C₂²×C₄	1	4	yes	—
241	C₄⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
242	C₄⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
243	C₂²⋊C₄×C₃₁	—	2	8	no	—
244	C₂²⋊C₄×C₃₁	—	2	4	no	—
245	C₂²⋊C₄×C₃₁	—	2	4	no	—
246	C₂²⋊C₄×C₃₁	—	2	4	no	—
247	C₂²⋊C₄×C₃₁	—	2	4	no	—
248	C₂²⋊C₄×C₃₁	—	4	2	no	—
249	C₂²⋊C₄×C₃₁	—	4	4	no	—
250	C₂²⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
251	C₂²⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
252	C₂²⋊C₄×C₃₁	C₂²×C₄	1	16	yes	—
253	C₂²⋊C₄×C₃₁	C₂×D₄	1	8	yes	—
254	C₄²×C₃₁	—	2	8	no	—
255	C₄²×C₃₁	—	2	8	no	—
256	C₄²×C₃₁	—	2	4	no	—
257	C₄²×C₃₁	—	2	2	no	—
258	C₄²×C₃₁	—	2	2	no	—
259	C₄²×C₃₁	—	2	4	no	—
260	C₄²×C₃₁	—	2	2	no	—
261	C₄²×C₃₁	—	2	2	no	—
262	C₄²×C₃₁	—	4	2	no	—
263	C₄²×C₃₁	—	4	2	no	—
264	C₄²×C₃₁	—	4	1	no	—
265	C₄²×C₃₁	C₂²×C₄	1	4	yes	—
266	C₄²×C₃₁	C₂×D₄	1	4	yes	—
267	#34308	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
268	C₂³×C₃₁	—	2	2	no	—
269	C₂³×C₃₁	—	2	2	no	—
270	C₂³×C₃₁	—	2	2	no	—
271	C₂³×C₃₁	—	2	2	no	—
272	C₂³×C₃₁	—	2	2	no	—
273	C₂³×C₃₁	—	2	2	no	—
274	C₂³×C₃₁	—	2	2	no	—
275	C₂³×C₃₁	—	2	2	no	—
276	C₂³×C₃₁	—	2	2	no	—
277	C₂³×C₃₁	—	2	2	no	—
278	C₂³×C₃₁	C₂³×C₄	1	4	yes	—
279	C₂³×C₃₁	C₂³×C₄	1	4	yes	—
280	C₂³×C₃₁	C₂²×D₄	1	4	yes	—
281	C₂³×C₃₁	C₂×#41	1	4	yes	—
282	C₂³×C₃₁	C₂⁵	1	1	yes	characteristic
283	Q₈×C₃₁	—	2	16	no	—
284	D₄×C₃₁	—	2	32	no	—
285	D₄×C₃₁	—	2	8	no	—
286	D₄×C₃₁	C₄×D₄	1	16	yes	complemented
287	C₂×C₄×C₃₁	—	2	32	no	—
288	C₂×C₄×C₃₁	—	2	4	no	—
289	C₂×C₄×C₃₁	—	2	2	no	—
290	C₂×C₄×C₃₁	—	2	1	no	—
291	C₂×C₄×C₃₁	—	2	2	no	—
292	C₂×C₄×C₃₁	—	2	4	no	—
293	C₂×C₄×C₃₁	—	2	1	no	—
294	C₂×C₄×C₃₁	—	2	1	no	—
295	C₂×C₄×C₃₁	—	2	2	no	—
296	C₂×C₄×C₃₁	—	2	2	no	—
297	C₂×C₄×C₃₁	—	2	1	no	—
298	C₂×C₄×C₃₁	—	2	1	no	—
299	C₂×C₄×C₃₁	—	2	1	no	—
300	C₂×C₄×C₃₁	—	2	2	no	—
301	C₂×C₄×C₃₁	—	2	1	no	—
302	C₂×C₄×C₃₁	—	2	1	no	—
303	C₂×C₄×C₃₁	—	2	2	no	—
304	C₂×C₄×C₃₁	—	2	16	no	—
305	C₂×C₄×C₃₁	—	2	16	no	—
306	C₂×C₄×C₃₁	—	2	2	no	—
307	C₂×C₄×C₃₁	—	2	4	no	—
308	C₂×C₄×C₃₁	—	2	2	no	—
309	C₂×C₄×C₃₁	—	2	1	no	—
310	C₂×C₄×C₃₁	—	2	2	no	—
311	C₂×C₄×C₃₁	—	2	2	no	—
312	C₂×C₄×C₃₁	—	2	4	no	—
313	C₂×C₄×C₃₁	—	2	2	no	—
314	C₂×C₄×C₃₁	—	2	1	no	—
315	C₂×C₄×C₃₁	—	2	2	no	—
316	C₂×C₄×C₃₁	—	2	2	no	—
317	C₂×C₄×C₃₁	—	2	2	no	—
318	C₂×C₄×C₃₁	—	2	1	no	—
319	C₂×C₄×C₃₁	—	2	2	no	—
320	C₂×C₄×C₃₁	—	2	4	no	—
321	C₂×C₄×C₃₁	—	4	8	no	—
322	C₂×C₄×C₃₁	—	4	8	no	—
323	C₂×C₄×C₃₁	—	8	8	no	—
324	C₂×C₄×C₃₁	—	8	8	no	—
325	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
326	C₂×C₄×C₃₁	C₂³×C₄	1	4	yes	—
327	C₂×C₄×C₃₁	C₂³×C₄	1	4	yes	—
328	C₂×C₄×C₃₁	C₂³×C₄	1	8	yes	—
329	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
330	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
331	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
332	C₂×C₄×C₃₁	C₂²×D₄	1	4	yes	—
333	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
334	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
335	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
336	C₂×C₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
337	C₂×C₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
338	C₂×C₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
339	C₂×#547	C₂×C₃₁	1	1	yes	characteristic
340	C₂×#520	C₂×C₃₁	1	2	yes	complemented
341	#2365	C₂×C₃₁	1	1	yes	characteristic, complemented
342	#2361	C₂×C₃₁	1	2	yes	complemented
343	#2360	C₂×C₃₁	1	2	yes	complemented
344	#2359	C₂×C₃₁	1	4	yes	complemented
345	D₄×C₄⋊C₄	C₂×C₃₁	1	1	yes	characteristic, complemented
346	D₄×C₄⋊C₄	C₂×C₃₁	1	1	yes	characteristic, complemented
347	#2344	C₂×C₃₁	1	2	yes	complemented
348	#2339	C₂×C₃₁	1	2	yes	complemented
349	#2323	C₂×C₃₁	1	2	yes	complemented
350	#2322	C₂×C₃₁	1	4	yes	complemented
351	C₄×C₄⋊Q₈	C₂×C₃₁	1	1	yes	characteristic, complemented
352	C₄×#121	C₂×C₃₁	1	2	yes	complemented
353	#2293	C₂×C₃₁	1	1	yes	characteristic, complemented
354	C₂×#389	C₂×C₃₁	1	2	yes	complemented
355	C₄²×D₄	C₂×C₃₁	1	1	yes	characteristic, complemented
356	C₂²×C₃₁	—	2	4	no	—
357	C₂²×C₃₁	—	2	4	no	—
358	C₂²×C₃₁	—	2	4	no	—
359	C₂²×C₃₁	—	2	4	no	—
360	C₂²×C₃₁	—	2	4	no	—
361	C₂²×C₃₁	—	2	4	no	—
362	C₂²×C₃₁	—	2	4	no	—
363	C₂²×C₃₁	—	2	4	no	—
364	C₂²×C₃₁	—	2	4	no	—
365	C₂²×C₃₁	—	4	2	no	—
366	C₂²×C₃₁	—	4	2	no	—
367	C₂²×C₃₁	—	4	2	no	—
368	C₂²×C₃₁	—	4	2	no	—
369	C₂²×C₃₁	C₂×C₄×D₄	1	8	yes	—
370	C₂²×C₃₁	C₂⁴×C₄	1	1	yes	characteristic
371	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
372	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
373	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
374	C₂²×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
375	C₂²×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
376	C₂²×C₃₁	#585	1	1	yes	characteristic
377	C₄×C₃₁	—	2	4	no	—
378	C₄×C₃₁	—	2	8	no	—
379	C₄×C₃₁	—	2	4	no	—
380	C₄×C₃₁	—	2	2	no	—
381	C₄×C₃₁	—	2	2	no	—
382	C₄×C₃₁	—	2	4	no	—
383	C₄×C₃₁	—	2	2	no	—
384	C₄×C₃₁	—	2	2	no	—
385	C₄×C₃₁	—	4	4	no	—
386	C₄×C₃₁	—	4	2	no	—
387	C₄×C₃₁	—	4	2	no	—
388	C₄×C₃₁	—	4	1	no	—
389	C₄×C₃₁	—	4	2	no	—
390	C₄×C₃₁	C₂×C₄×D₄	1	4	yes	—
391	C₄×C₃₁	#520	1	4	yes	complemented
392	C₂²×#41	C₂²×C₃₁	1	2	yes	—
393	#547	C₄×C₃₁	1	16	yes	complemented
394	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
395	C₂×#123	C₂²×C₃₁	1	4	yes	—
396	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	—
397	C₂×#121	C₂²×C₃₁	1	2	yes	—
398	#520	—	2	16	no	—
399	C₂×C₄×Q₈	C₂²×C₃₁	1	2	yes	—
400	C₂×C₄×Q₈	C₂²×C₃₁	1	2	yes	—
401	C₂×C₄×D₄	C₂²×C₃₁	1	4	yes	—
402	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
403	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
404	C₂×C₄×D₄	C₂²×C₃₁	1	4	yes	—
405	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
406	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
407	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
408	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
409	C₂×#117	C₂²×C₃₁	1	2	yes	—
410	C₂×#117	C₂²×C₃₁	1	4	yes	—
411	C₂²×C₄⋊C₄	C₂²×C₃₁	1	4	yes	—
412	C₂²×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
413	C₂²×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
414	C₂²×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
415	C₂²×C₄²	C₂²×C₃₁	1	2	yes	—
416	#391	C₂²×C₃₁	1	2	yes	—
417	#391	C₂²×C₃₁	1	2	yes	—
418	#390	C₂²×C₃₁	1	1	yes	characteristic
419	#390	C₂²×C₃₁	1	1	yes	characteristic
420	#389	C₂²×C₃₁	1	2	yes	—
421	#389	C₂²×C₃₁	1	2	yes	—
422	#389	C₂²×C₃₁	1	4	yes	—
423	#389	C₂²×C₃₁	1	2	yes	—
424	#389	C₂²×C₃₁	1	1	yes	characteristic
425	#389	C₂²×C₃₁	1	2	yes	—
426	#389	C₂²×C₃₁	1	4	yes	—
427	#389	C₂²×C₃₁	1	2	yes	—
428	#389	C₂²×C₃₁	1	1	yes	characteristic
429	#388	C₂²×C₃₁	1	2	yes	—
430	#388	C₂²×C₃₁	1	4	yes	—
431	#388	C₂²×C₃₁	1	4	yes	—
432	#388	C₂²×C₃₁	1	2	yes	—
433	#387	C₂²×C₃₁	1	4	yes	—
434	#387	C₂²×C₃₁	1	4	yes	—
435	#387	C₂²×C₃₁	1	4	yes	—
436	#386	C₂²×C₃₁	1	4	yes	—
437	#386	C₂²×C₃₁	1	4	yes	—
438	#385	C₂²×C₃₁	1	4	yes	—
439	#385	C₂²×C₃₁	1	4	yes	—
440	#385	C₂²×C₃₁	1	4	yes	—
441	#384	C₂²×C₃₁	1	1	yes	characteristic
442	#381	C₂²×C₃₁	1	4	yes	—
443	#380	C₂²×C₃₁	1	2	yes	—
444	#380	C₂²×C₃₁	1	2	yes	—
445	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
446	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
447	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
448	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
449	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
450	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
451	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
452	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
453	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
454	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
455	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
456	C₄×C₂²⋊C₄	C₂²×C₃₁	1	4	yes	—
457	C₂×#95	C₂²×C₃₁	1	4	yes	—
458	C₄³	C₂²×C₃₁	1	1	yes	characteristic
459	C₂×C₃₁	—	2	8	no	—
460	C₂×C₃₁	—	4	4	no	—
461	C₂×C₃₁	C₂²×C₄×D₄	1	1	yes	characteristic
462	C₂×C₃₁	C₂×#520	1	1	yes	characteristic
463	C₂×C₃₁	C₄×2₋¹⁺⁴	1	1	yes	characteristic
464	C₂×C₃₁	#3496	1	1	yes	characteristic
465	C₂×C₃₁	#3499	1	1	yes	characteristic
466	C₂×C₃₁	#3515	1	1	yes	characteristic
467	C₂×C₃₁	#3520	1	1	yes	characteristic
468	C₂×#41	—	2	8	no	—
469	C₂×#41	—	2	8	no	—
470	C₂×#41	C₂×C₄×C₃₁	1	16	yes	complemented
471	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
472	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
473	C₂²×D₄	C₂³×C₃₁	1	4	yes	—
474	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
475	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
476	C₂³×C₄	C₂³×C₃₁	1	4	yes	—
477	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
478	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
479	C₂³×C₄	C₂³×C₃₁	1	4	yes	—
480	C₂³×C₄	C₂³×C₃₁	1	4	yes	—
481	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
482	C₄⋊Q₈	C₂×C₄×C₃₁	1	8	yes	complemented
483	#123	C₂×C₄×C₃₁	1	32	yes	complemented
484	C₂²⋊Q₈	C₂×C₄×C₃₁	1	16	yes	complemented
485	#121	C₂×C₄×C₃₁	1	16	yes	complemented
486	C₄×Q₈	—	2	8	no	—
487	C₄×Q₈	—	2	8	no	—
488	C₄×D₄	—	2	8	no	—
489	C₄×D₄	—	2	4	no	—
490	C₄×D₄	—	2	16	no	—
491	C₄×D₄	—	2	16	no	—
492	C₄×D₄	—	4	4	no	—
493	C₄×D₄	C₂×C₄×C₃₁	1	8	yes	complemented
494	C₄×D₄	C₂×C₄×C₃₁	1	8	yes	complemented
495	C₄×D₄	D₄×C₃₁	1	8	yes	complemented
496	#117	—	2	16	no	—
497	#117	—	2	8	no	—
498	C₂×C₄⋊C₄	—	2	16	no	—
499	C₂×C₄⋊C₄	—	2	8	no	—
500	C₂×C₄⋊C₄	—	4	4	no	—
501	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	16	yes	complemented
502	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
503	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
504	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
505	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
506	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
507	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
508	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
509	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
510	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
511	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
512	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
513	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
514	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
515	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
516	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
517	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
518	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
519	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
520	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
521	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
522	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
523	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
524	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
525	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
526	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
527	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
528	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
529	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
530	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
531	C₂×C₄²	—	4	4	no	—
532	C₂×C₄²	C₂³×C₃₁	1	4	yes	—
533	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
534	C₂×C₄²	C₂³×C₃₁	1	4	yes	—
535	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
536	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
537	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
538	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
539	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
540	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
541	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
542	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
543	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
544	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
545	#95	C₂³×C₃₁	1	2	yes	—
546	#95	C₂³×C₃₁	1	4	yes	—
547	#95	C₂³×C₃₁	1	4	yes	—
548	#95	C₂³×C₃₁	1	4	yes	—
549	#95	C₂³×C₃₁	1	2	yes	—
550	#95	C₂³×C₃₁	1	2	yes	—
551	#95	C₂³×C₃₁	1	2	yes	—
552	#95	C₂³×C₃₁	1	4	yes	—
553	#95	C₂³×C₃₁	1	2	yes	—
554	#95	C₂³×C₃₁	1	4	yes	—
555	#95	C₂³×C₃₁	1	4	yes	—
556	#95	C₂³×C₃₁	1	2	yes	—
557	C₃₁	#34308	1	1	yes	characteristic, direct product factor, Sylow
558	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
559	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
560	#41	—	2	64	no	—
561	C₂×Q₈	—	2	4	no	—
562	C₂×Q₈	—	2	4	no	—
563	C₂×Q₈	C₂²×C₄×C₃₁	1	8	yes	—
564	C₂×D₄	—	2	8	no	—
565	C₂×D₄	—	2	8	no	—
566	C₂×D₄	—	2	2	no	—
567	C₂×D₄	—	2	2	no	—
568	C₂×D₄	C₂²×C₄×C₃₁	1	4	yes	—
569	C₂×D₄	C₂²×C₄×C₃₁	1	16	yes	—
570	C₂×D₄	C₂²×C₄×C₃₁	1	4	yes	—
571	C₂×D₄	C₂×D₄×C₃₁	1	4	yes	—
572	C₂×D₄	#41×C₃₁	1	4	yes	—
573	C₂²×C₄	—	2	8	no	—
574	C₂²×C₄	—	2	8	no	—
575	C₂²×C₄	—	2	4	no	—
576	C₂²×C₄	—	2	4	no	—
577	C₂²×C₄	—	2	4	no	—
578	C₂²×C₄	—	2	4	no	—
579	C₂²×C₄	—	2	4	no	—
580	C₂²×C₄	—	2	8	no	—
581	C₂²×C₄	—	2	4	no	—
582	C₂²×C₄	—	2	8	no	—
583	C₂²×C₄	—	4	2	no	—
584	C₂²×C₄	—	4	2	no	—
585	C₂²×C₄	—	4	2	no	—
586	C₂²×C₄	—	4	4	no	—
587	C₂²×C₄	—	4	4	no	—
588	C₂²×C₄	—	4	4	no	—
589	C₂²×C₄	—	4	4	no	—
590	C₂²×C₄	C₂²×C₄×C₃₁	1	8	yes	—
591	C₂²×C₄	C₂²×C₄×C₃₁	1	16	yes	—
592	C₂²×C₄	C₂²×C₄×C₃₁	1	8	yes	—
593	C₂²×C₄	C₂×D₄×C₃₁	1	8	yes	—
594	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
595	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
596	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
597	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
598	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
599	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
600	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
601	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
602	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
603	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
604	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
605	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
606	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
607	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
608	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
609	C₄⋊C₄	—	2	8	no	—
610	C₄⋊C₄	—	2	4	no	—
611	C₄⋊C₄	—	2	8	no	—
612	C₄⋊C₄	—	2	8	no	—
613	C₄⋊C₄	—	2	4	no	—
614	C₄⋊C₄	—	2	4	no	—
615	C₄⋊C₄	—	2	2	no	—
616	C₄⋊C₄	—	2	2	no	—
617	C₄⋊C₄	—	2	4	no	—
618	C₄⋊C₄	—	2	2	no	—
619	C₄⋊C₄	—	4	4	no	—
620	C₄⋊C₄	—	4	2	no	—
621	C₄⋊C₄	C₂²×C₄×C₃₁	1	4	yes	—
622	C₄⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
623	C₄⋊C₄	C₂²×C₄×C₃₁	1	16	yes	—
624	C₄⋊C₄	C₂²×C₄×C₃₁	1	4	yes	—
625	C₄⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
626	C₄⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
627	C₂²⋊C₄	—	2	8	no	—
628	C₂²⋊C₄	—	2	4	no	—
629	C₂²⋊C₄	—	2	4	no	—
630	C₂²⋊C₄	—	2	4	no	—
631	C₂²⋊C₄	—	2	4	no	—
632	C₂²⋊C₄	—	4	2	no	—
633	C₂²⋊C₄	—	4	4	no	—
634	C₂²⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
635	C₂²⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
636	C₂²⋊C₄	C₂²×C₄×C₃₁	1	16	yes	—
637	C₂²⋊C₄	C₂×D₄×C₃₁	1	8	yes	—
638	C₄²	—	2	8	no	—
639	C₄²	—	2	8	no	—
640	C₄²	—	2	4	no	—
641	C₄²	—	2	2	no	—
642	C₄²	—	2	2	no	—
643	C₄²	—	2	4	no	—
644	C₄²	—	2	2	no	—
645	C₄²	—	2	2	no	—
646	C₄²	—	4	2	no	—
647	C₄²	—	4	2	no	—
648	C₄²	—	4	1	no	—
649	C₄²	C₂²×C₄×C₃₁	1	4	yes	—
650	C₄²	C₂×D₄×C₃₁	1	4	yes	—
651	C₂³	—	2	2	no	—
652	C₂³	—	2	2	no	—
653	C₂³	—	2	2	no	—
654	C₂³	—	2	2	no	—
655	C₂³	—	2	2	no	—
656	C₂³	—	2	2	no	—
657	C₂³	—	2	2	no	—
658	C₂³	—	2	2	no	—
659	C₂³	—	2	2	no	—
660	C₂³	—	2	2	no	—
661	C₂³	C₂³×C₄×C₃₁	1	4	yes	—
662	C₂³	C₂³×C₄×C₃₁	1	4	yes	—
663	C₂³	C₂²×D₄×C₃₁	1	4	yes	—
664	C₂³	C₂×#41×C₃₁	1	4	yes	—
665	C₂³	C₂⁵×C₃₁	1	1	yes	characteristic
666	Q₈	—	2	16	no	—
667	D₄	—	2	32	no	—
668	D₄	—	2	8	no	—
669	D₄	C₄×D₄×C₃₁	1	16	yes	complemented
670	C₂×C₄	—	2	32	no	—
671	C₂×C₄	—	2	4	no	—
672	C₂×C₄	—	2	2	no	—
673	C₂×C₄	—	2	1	no	—
674	C₂×C₄	—	2	2	no	—
675	C₂×C₄	—	2	4	no	—
676	C₂×C₄	—	2	1	no	—
677	C₂×C₄	—	2	1	no	—
678	C₂×C₄	—	2	2	no	—
679	C₂×C₄	—	2	2	no	—
680	C₂×C₄	—	2	1	no	—
681	C₂×C₄	—	2	1	no	—
682	C₂×C₄	—	2	1	no	—
683	C₂×C₄	—	2	2	no	—
684	C₂×C₄	—	2	1	no	—
685	C₂×C₄	—	2	1	no	—
686	C₂×C₄	—	2	2	no	—
687	C₂×C₄	—	2	16	no	—
688	C₂×C₄	—	2	16	no	—
689	C₂×C₄	—	2	2	no	—
690	C₂×C₄	—	2	4	no	—
691	C₂×C₄	—	2	2	no	—
692	C₂×C₄	—	2	1	no	—
693	C₂×C₄	—	2	2	no	—
694	C₂×C₄	—	2	2	no	—
695	C₂×C₄	—	2	4	no	—
696	C₂×C₄	—	2	2	no	—
697	C₂×C₄	—	2	1	no	—
698	C₂×C₄	—	2	2	no	—
699	C₂×C₄	—	2	2	no	—
700	C₂×C₄	—	2	2	no	—
701	C₂×C₄	—	2	1	no	—
702	C₂×C₄	—	2	2	no	—
703	C₂×C₄	—	2	4	no	—
704	C₂×C₄	—	4	8	no	—
705	C₂×C₄	—	4	8	no	—
706	C₂×C₄	—	8	8	no	—
707	C₂×C₄	—	8	8	no	—
708	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
709	C₂×C₄	C₂³×C₄×C₃₁	1	4	yes	—
710	C₂×C₄	C₂³×C₄×C₃₁	1	4	yes	—
711	C₂×C₄	C₂³×C₄×C₃₁	1	8	yes	—
712	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
713	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
714	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
715	C₂×C₄	C₂²×D₄×C₃₁	1	4	yes	—
716	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
717	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
718	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
719	C₂×C₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
720	C₂×C₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
721	C₂×C₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
722	C₂²	—	2	4	no	—
723	C₂²	—	2	4	no	—
724	C₂²	—	2	4	no	—
725	C₂²	—	2	4	no	—
726	C₂²	—	2	4	no	—
727	C₂²	—	2	4	no	—
728	C₂²	—	2	4	no	—
729	C₂²	—	2	4	no	—
730	C₂²	—	2	4	no	—
731	C₂²	—	4	2	no	—
732	C₂²	—	4	2	no	—
733	C₂²	—	4	2	no	—
734	C₂²	—	4	2	no	—
735	C₂²	C₂×C₄×D₄×C₃₁	1	8	yes	—
736	C₂²	C₂⁴×C₄×C₃₁	1	1	yes	characteristic
737	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
738	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
739	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
740	C₂²	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
741	C₂²	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
742	C₂²	C₃₁×#585	1	1	yes	characteristic
743	C₄	—	2	4	no	—
744	C₄	—	2	8	no	—
745	C₄	—	2	4	no	—
746	C₄	—	2	2	no	—
747	C₄	—	2	2	no	—
748	C₄	—	2	4	no	—
749	C₄	—	2	2	no	—
750	C₄	—	2	2	no	—
751	C₄	—	4	4	no	—
752	C₄	—	4	2	no	—
753	C₄	—	4	2	no	—
754	C₄	—	4	1	no	—
755	C₄	—	4	2	no	—
756	C₄	C₂×C₄×D₄×C₃₁	1	4	yes	—
757	C₄	C₃₁×#520	1	4	yes	complemented
758	C₂	—	2	8	no	—
759	C₂	—	4	4	no	—
760	C₂	C₂²×C₄×D₄×C₃₁	1	1	yes	characteristic
761	C₂	C₂×C₃₁×#520	1	1	yes	characteristic
762	C₂	C₄×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
763	C₂	C₃₁×#3496	1	1	yes	characteristic
764	C₂	C₃₁×#3499	1	1	yes	characteristic
765	C₂	C₃₁×#3515	1	1	yes	characteristic
766	C₂	C₃₁×#3520	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃₁	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₃₁
Frattini, cosocle	C₂³	C₂⁵×C₃₁
prime radical	C₂×C₃₁×#547	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₃₁×#520	C₂	semidirect
3. C₃₁×#2365	C₂	semidirect
4. C₃₁×#2361	C₂	semidirect
5. C₃₁×#2360	C₂	semidirect
6. C₃₁×#2359	C₂	semidirect
7. D₄×C₄⋊C₄×C₃₁	C₂	semidirect
8. D₄×C₄⋊C₄×C₃₁	C₂	semidirect
9. C₃₁×#2344	C₂	semidirect
10. C₃₁×#2339	C₂	semidirect
11. C₃₁×#2323	C₂	semidirect
12. C₃₁×#2322	C₂	semidirect
13. C₄×C₃₁×C₄⋊Q₈	C₂	semidirect
14. C₄×C₃₁×#121	C₂	semidirect
15. C₃₁×#2293	C₂	semidirect
16. C₂×C₃₁×#389	C₂	semidirect
17. C₄²×D₄×C₃₁	C₂	semidirect
19. C₃₁×#547	C₄	semidirect
87. C₂×#41×C₃₁	C₂×C₄	semidirect
99. C₃₁×C₄⋊Q₈	C₂×C₄	semidirect
100. C₃₁×#123	C₂×C₄	semidirect
101. C₃₁×C₂²⋊Q₈	C₂×C₄	semidirect
102. C₃₁×#121	C₂×C₄	semidirect
110. C₄×D₄×C₃₁	C₂×C₄	semidirect
111. C₄×D₄×C₃₁	C₂×C₄	semidirect
112. C₄×D₄×C₃₁	D₄	semidirect
118. C₂×C₄⋊C₄×C₃₁	C₂×C₄	semidirect
267. #34308	C₃₁	direct (N × H)
286. D₄×C₃₁	C₄×D₄	semidirect
340. C₂×#520	C₂×C₃₁	semidirect
341. #2365	C₂×C₃₁	semidirect
342. #2361	C₂×C₃₁	semidirect
343. #2360	C₂×C₃₁	semidirect
344. #2359	C₂×C₃₁	semidirect
345. D₄×C₄⋊C₄	C₂×C₃₁	semidirect
346. D₄×C₄⋊C₄	C₂×C₃₁	semidirect
347. #2344	C₂×C₃₁	semidirect
348. #2339	C₂×C₃₁	semidirect
349. #2323	C₂×C₃₁	semidirect
350. #2322	C₂×C₃₁	semidirect
351. C₄×C₄⋊Q₈	C₂×C₃₁	semidirect
352. C₄×#121	C₂×C₃₁	semidirect
353. #2293	C₂×C₃₁	semidirect
354. C₂×#389	C₂×C₃₁	semidirect
355. C₄²×D₄	C₂×C₃₁	semidirect
391. C₄×C₃₁	#520	semidirect
393. #547	C₄×C₃₁	semidirect
470. C₂×#41	C₂×C₄×C₃₁	semidirect
482. C₄⋊Q₈	C₂×C₄×C₃₁	semidirect
483. #123	C₂×C₄×C₃₁	semidirect
484. C₂²⋊Q₈	C₂×C₄×C₃₁	semidirect
485. #121	C₂×C₄×C₃₁	semidirect
493. C₄×D₄	C₂×C₄×C₃₁	semidirect
494. C₄×D₄	C₂×C₄×C₃₁	semidirect
495. C₄×D₄	D₄×C₃₁	semidirect
501. C₂×C₄⋊C₄	C₂×C₄×C₃₁	semidirect
557. C₃₁	#34308	direct (N × H)
669. D₄	C₄×D₄×C₃₁	semidirect
757. C₄	C₃₁×#520	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃₁×#547	2
C₂×C₃₁×#520	2
C₃₁×#2365	2
C₃₁×#2361	2
C₃₁×#2360	2
C₃₁×#2359	2
D₄×C₄⋊C₄×C₃₁	2
C₃₁×#2344	2
C₃₁×#2339	2
C₃₁×#2323	2
C₃₁×#2322	2
C₄×C₃₁×C₄⋊Q₈	2
C₄×C₃₁×#121	2
C₃₁×#2293	2
C₂×C₃₁×#389	2
C₄²×D₄×C₃₁	2
#34308	31

Subgroups — C31×#34308 #21491067

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#34308 #21491067