Subgroups — C₄×C₃₁×#551 #21490921

Order 7936.

2732 conjugacy classes of subgroups.

The subgroup lattice has 914 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#551	C₂	1	1	yes	maximal, characteristic
2	C₃₁×#2374	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#2373	C₂	1	2	yes	maximal, complemented
4	C₃₁×#2372	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#2368	C₂	1	2	yes	maximal, complemented
6	C₃₁×#2359	C₂	1	2	yes	maximal, complemented
7	C₃₁×#2358	C₂	1	1	yes	maximal, characteristic
8	C₃₁×#2353	C₂	1	2	yes	maximal, complemented
9	C₃₁×#2343	C₂	1	2	yes	maximal, complemented
10	C₃₁×#2342	C₂	1	2	yes	maximal, complemented
11	C₄×C₃₁×#126	C₂	1	2	yes	maximal, complemented
12	C₄×C₃₁×#124	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄×C₃₁×C₂²⋊Q₈	C₂	1	2	yes	maximal, complemented
14	C₄×C₃₁×#123	C₂	1	2	yes	maximal, complemented
15	C₄×C₃₁×#123	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×C₃₁×#120	C₂	1	1	yes	maximal, characteristic
17	C₄²×D₄×C₃₁	C₂	1	2	yes	maximal, complemented
18	C₄×C₃₁×#117	C₂	1	2	yes	maximal, complemented
19	C₂×C₄×C₂²⋊C₄×C₃₁	C₂	1	2	yes	maximal, complemented
20	C₂⁴×C₄×C₃₁	C₂²	1	1	yes	characteristic
21	C₃₁×#551	C₄	1	16	yes	direct product factor
22	C₂×C₃₁×#126	C₂²	1	2	yes	—
23	C₂×C₃₁×#124	C₂²	1	1	yes	characteristic
24	C₂×C₃₁×#123	C₂²	1	2	yes	—
25	C₂×C₃₁×#123	C₂²	1	1	yes	characteristic
26	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	—
27	C₂×C₃₁×#120	C₂²	1	1	yes	characteristic
28	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
30	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
31	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
32	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
33	C₂×C₃₁×#117	C₂²	1	2	yes	—
34	C₂×C₃₁×#117	C₂²	1	2	yes	—
35	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
36	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
37	C₂²×C₄²×C₃₁	C₂²	1	2	yes	—
38	C₂²×C₄²×C₃₁	C₂²	1	2	yes	—
39	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic, complemented
40	C₃₁×#391	C₂²	1	1	yes	characteristic, complemented
41	C₃₁×#391	C₂²	1	2	yes	complemented
42	C₃₁×#390	C₂²	1	1	yes	characteristic
43	C₃₁×#389	C₂²	1	2	yes	complemented
44	C₃₁×#388	C₂²	1	2	yes	—
45	C₃₁×#388	C₂²	1	2	yes	—
46	C₃₁×#388	C₂²	1	2	yes	—
47	C₃₁×#388	C₂²	1	2	yes	—
48	C₃₁×#388	C₂²	1	2	yes	—
49	C₃₁×#388	C₂²	1	2	yes	complemented
50	C₃₁×#388	C₂²	1	2	yes	complemented
51	C₃₁×#388	C₂²	1	2	yes	complemented
52	C₃₁×#387	C₂²	1	2	yes	complemented
53	C₃₁×#387	C₂²	1	2	yes	complemented
54	C₃₁×#387	C₂²	1	2	yes	complemented
55	C₃₁×#387	C₂²	1	2	yes	complemented
56	C₃₁×#387	C₂²	1	2	yes	complemented
57	C₃₁×#387	C₂²	1	2	yes	complemented
58	C₃₁×#387	C₂²	1	2	yes	complemented
59	C₃₁×#387	C₂²	1	2	yes	complemented
60	C₃₁×#386	C₂²	1	2	yes	—
61	C₃₁×#386	C₂²	1	2	yes	—
62	C₃₁×#386	C₂²	1	1	yes	characteristic
63	C₃₁×#386	C₂²	1	1	yes	characteristic
64	C₃₁×#385	C₂²	1	2	yes	—
65	C₃₁×#385	C₂²	1	2	yes	—
66	C₃₁×#385	C₂²	1	2	yes	—
67	C₃₁×#385	C₂²	1	2	yes	—
68	C₃₁×#385	C₂²	1	1	yes	characteristic
69	C₃₁×#385	C₂²	1	1	yes	characteristic, complemented
70	C₃₁×#383	C₂²	1	2	yes	complemented
71	C₃₁×#382	C₂²	1	1	yes	characteristic, complemented
72	C₃₁×#381	C₂²	1	2	yes	—
73	C₃₁×#381	C₂²	1	1	yes	characteristic, complemented
74	C₃₁×#380	C₂²	1	2	yes	—
75	C₃₁×#379	C₂²	1	1	yes	characteristic
76	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	complemented
77	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	complemented
78	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	complemented
79	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	complemented
80	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	complemented
81	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	complemented
82	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	complemented
83	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	complemented
84	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
85	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
86	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
87	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
88	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
89	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
90	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
91	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
92	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
93	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
94	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
95	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
96	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
97	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
98	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	complemented
99	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	complemented
100	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	complemented
101	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
102	C₃₁×#376	C₂²	1	2	yes	complemented
103	C₃₁×#376	C₂²	1	2	yes	complemented
104	C₂×C₃₁×#95	C₂²	1	2	yes	—
105	C₂×C₃₁×#95	C₂²	1	2	yes	—
106	C₄³×C₃₁	C₂²	1	1	yes	characteristic, complemented
107	C₄³×C₃₁	C₂²	1	2	yes	complemented
108	C₂⁵×C₃₁	C₂³	1	1	yes	characteristic
109	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
110	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
111	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
112	C₂³×C₄×C₃₁	—	2	8	no	—
113	C₂³×C₄×C₃₁	—	4	2	no	—
114	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
115	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
116	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
117	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
118	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
119	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
120	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
121	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
122	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
123	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
124	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
125	C₃₁×#126	C₂×C₄	1	16	yes	complemented
126	C₃₁×#124	C₂×C₄	1	8	yes	complemented
127	C₃₁×#123	C₂×C₄	1	8	yes	complemented
128	C₃₁×#123	C₂×C₄	1	16	yes	complemented
129	C₃₁×C₂²⋊Q₈	C₂×C₄	1	16	yes	complemented
130	C₃₁×#120	C₂×C₄	1	8	yes	—
131	C₄×Q₈×C₃₁	—	4	2	no	—
132	C₄×D₄×C₃₁	—	2	8	no	—
133	C₄×D₄×C₃₁	—	2	8	no	—
134	C₄×D₄×C₃₁	—	4	2	no	—
135	C₄×D₄×C₃₁	C₂×C₄	1	16	yes	complemented
136	C₃₁×#117	—	2	8	no	—
137	C₃₁×#117	C₂×C₄	1	16	yes	complemented
138	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
139	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
140	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
141	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
142	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
143	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
144	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
145	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
146	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
147	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
148	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
149	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
150	C₂×C₂²⋊C₄×C₃₁	—	2	8	no	—
151	C₂×C₂²⋊C₄×C₃₁	C₂×C₄	1	16	yes	complemented
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×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
157	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
158	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
159	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
160	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
161	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
162	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
163	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
164	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
165	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
166	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
167	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
168	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
169	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
170	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
171	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
172	C₂×C₄²×C₃₁	—	2	8	no	—
173	C₂×C₄²×C₃₁	—	4	4	no	—
174	C₂×C₄²×C₃₁	—	4	2	no	—
175	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
176	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
177	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
178	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
179	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
180	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
181	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
182	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
183	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
184	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
185	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
186	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
187	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
188	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
189	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
190	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
191	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
192	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
193	C₃₁×#95	C₂³	1	2	yes	—
194	C₃₁×#95	C₂³	1	2	yes	—
195	C₃₁×#95	C₂³	1	2	yes	—
196	C₃₁×#95	C₂³	1	2	yes	—
197	C₃₁×#95	C₂³	1	2	yes	—
198	C₃₁×#95	C₂³	1	2	yes	—
199	C₃₁×#95	C₂³	1	2	yes	—
200	C₃₁×#95	C₂³	1	2	yes	—
201	C₃₁×#95	C₂³	1	2	yes	—
202	C₃₁×#95	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	2	yes	—
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	2	yes	—
211	C₃₁×#95	C₂³	1	2	yes	—
212	C₃₁×#95	C₂³	1	2	yes	—
213	C₃₁×#95	C₂³	1	2	yes	—
214	C₃₁×#95	C₂³	1	2	yes	—
215	C₂⁴×C₃₁	—	2	4	no	—
216	C₂⁴×C₃₁	—	2	4	no	—
217	C₂⁴×C₃₁	—	4	1	no	—
218	C₂⁴×C₃₁	—	4	1	no	—
219	C₂⁴×C₃₁	C₂²×C₄	1	4	yes	—
220	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
221	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
222	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
223	C₂×Q₈×C₃₁	—	4	1	no	—
224	C₂×Q₈×C₃₁	—	4	1	no	—
225	C₂×Q₈×C₃₁	C₂²×C₄	1	4	yes	complemented
226	C₂×D₄×C₃₁	—	2	4	no	—
227	C₂×D₄×C₃₁	—	2	4	no	—
228	C₂×D₄×C₃₁	—	4	1	no	—
229	C₂×D₄×C₃₁	—	4	1	no	—
230	C₂×D₄×C₃₁	C₂²×C₄	1	8	yes	—
231	C₂×D₄×C₃₁	C₂²×C₄	1	4	yes	—
232	C₂²×C₄×C₃₁	—	2	4	no	—
233	C₂²×C₄×C₃₁	—	2	4	no	—
234	C₂²×C₄×C₃₁	—	2	4	no	—
235	C₂²×C₄×C₃₁	—	2	4	no	—
236	C₂²×C₄×C₃₁	—	2	4	no	—
237	C₂²×C₄×C₃₁	—	2	4	no	—
238	C₂²×C₄×C₃₁	—	2	4	no	—
239	C₂²×C₄×C₃₁	—	2	4	no	—
240	C₂²×C₄×C₃₁	—	2	4	no	—
241	C₂²×C₄×C₃₁	—	2	4	no	—
242	C₂²×C₄×C₃₁	—	2	4	no	—
243	C₂²×C₄×C₃₁	—	2	4	no	—
244	C₂²×C₄×C₃₁	—	2	4	no	—
245	C₂²×C₄×C₃₁	—	2	4	no	—
246	C₂²×C₄×C₃₁	—	2	2	no	—
247	C₂²×C₄×C₃₁	—	2	2	no	—
248	C₂²×C₄×C₃₁	—	4	1	no	—
249	C₂²×C₄×C₃₁	—	4	1	no	—
250	C₂²×C₄×C₃₁	—	4	2	no	—
251	C₂²×C₄×C₃₁	—	4	2	no	—
252	C₂²×C₄×C₃₁	—	4	1	no	—
253	C₂²×C₄×C₃₁	—	4	2	no	—
254	C₂²×C₄×C₃₁	—	4	2	no	—
255	C₂²×C₄×C₃₁	—	4	1	no	—
256	C₂²×C₄×C₃₁	—	4	2	no	—
257	C₂²×C₄×C₃₁	—	4	16	no	—
258	C₂²×C₄×C₃₁	C₂²×C₄	1	8	yes	—
259	C₂²×C₄×C₃₁	C₂²×C₄	1	8	yes	—
260	C₂²×C₄×C₃₁	C₂²×C₄	1	4	yes	complemented
261	C₂²×C₄×C₃₁	#41	1	8	yes	—
262	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
263	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
264	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
265	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
266	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
267	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
268	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
269	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
270	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
271	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
272	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
273	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
274	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
275	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
276	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
277	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
278	C₄⋊C₄×C₃₁	—	2	4	no	—
279	C₄⋊C₄×C₃₁	—	2	4	no	—
280	C₄⋊C₄×C₃₁	—	2	4	no	—
281	C₄⋊C₄×C₃₁	—	2	4	no	—
282	C₄⋊C₄×C₃₁	—	4	2	no	—
283	C₄⋊C₄×C₃₁	—	4	1	no	—
284	C₄⋊C₄×C₃₁	—	4	2	no	—
285	C₄⋊C₄×C₃₁	—	4	1	no	—
286	C₄⋊C₄×C₃₁	C₂²×C₄	1	8	yes	complemented
287	C₄⋊C₄×C₃₁	C₂²×C₄	1	8	yes	complemented
288	C₄⋊C₄×C₃₁	C₂²×C₄	1	8	yes	complemented
289	C₄⋊C₄×C₃₁	C₂²×C₄	1	8	yes	complemented
290	C₂²⋊C₄×C₃₁	—	2	4	no	—
291	C₂²⋊C₄×C₃₁	—	2	4	no	—
292	C₂²⋊C₄×C₃₁	—	2	4	no	—
293	C₂²⋊C₄×C₃₁	—	2	4	no	—
294	C₂²⋊C₄×C₃₁	—	2	4	no	—
295	C₂²⋊C₄×C₃₁	—	2	4	no	—
296	C₂²⋊C₄×C₃₁	—	2	4	no	—
297	C₂²⋊C₄×C₃₁	—	4	1	no	—
298	C₂²⋊C₄×C₃₁	—	4	1	no	—
299	C₂²⋊C₄×C₃₁	—	4	1	no	—
300	C₂²⋊C₄×C₃₁	—	4	1	no	—
301	C₂²⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
302	C₂²⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
303	C₂²⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
304	C₂²⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
305	C₂²⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
306	C₂²⋊C₄×C₃₁	C₂²×C₄	1	4	yes	—
307	C₂²⋊C₄×C₃₁	C₂²×C₄	1	8	yes	complemented
308	C₂²⋊C₄×C₃₁	C₂²×C₄	1	4	yes	complemented
309	C₂²⋊C₄×C₃₁	#41	1	8	yes	—
310	C₄²×C₃₁	—	2	4	no	—
311	C₄²×C₃₁	—	2	4	no	—
312	C₄²×C₃₁	—	2	4	no	—
313	C₄²×C₃₁	—	2	4	no	—
314	C₄²×C₃₁	—	2	4	no	—
315	C₄²×C₃₁	—	2	4	no	—
316	C₄²×C₃₁	—	2	4	no	—
317	C₄²×C₃₁	—	2	4	no	—
318	C₄²×C₃₁	—	2	4	no	—
319	C₄²×C₃₁	—	2	4	no	—
320	C₄²×C₃₁	—	2	2	no	—
321	C₄²×C₃₁	—	4	2	no	—
322	C₄²×C₃₁	—	4	2	no	—
323	C₄²×C₃₁	—	4	2	no	—
324	C₄²×C₃₁	—	4	1	no	—
325	C₄²×C₃₁	—	4	2	no	—
326	C₄²×C₃₁	C₂²×C₄	1	4	yes	complemented
327	C₄²×C₃₁	C₂²×C₄	1	8	yes	complemented
328	C₄×#551	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
329	C₂³×C₃₁	—	2	2	no	—
330	C₂³×C₃₁	—	2	2	no	—
331	C₂³×C₃₁	—	2	2	no	—
332	C₂³×C₃₁	—	2	2	no	—
333	C₂³×C₃₁	—	2	16	no	—
334	C₂³×C₃₁	—	2	2	no	—
335	C₂³×C₃₁	—	2	2	no	—
336	C₂³×C₃₁	—	2	2	no	—
337	C₂³×C₃₁	—	2	2	no	—
338	C₂³×C₃₁	—	2	1	no	—
339	C₂³×C₃₁	—	2	1	no	—
340	C₂³×C₃₁	—	2	1	no	—
341	C₂³×C₃₁	—	2	1	no	—
342	C₂³×C₃₁	—	4	4	no	—
343	C₂³×C₃₁	—	4	4	no	—
344	C₂³×C₃₁	—	4	8	no	—
345	C₂³×C₃₁	—	4	4	no	—
346	C₂³×C₃₁	C₂³×C₄	1	2	yes	—
347	C₂³×C₃₁	C₂³×C₄	1	2	yes	—
348	C₂³×C₃₁	C₂³×C₄	1	4	yes	—
349	C₂³×C₃₁	C₂×#41	1	4	yes	—
350	C₂³×C₃₁	C₂×#41	1	4	yes	—
351	C₂³×C₃₁	C₂⁵	1	1	yes	characteristic
352	Q₈×C₃₁	—	4	4	no	—
353	D₄×C₃₁	—	2	16	no	—
354	D₄×C₃₁	—	4	4	no	—
355	C₂×C₄×C₃₁	—	2	16	no	—
356	C₂×C₄×C₃₁	—	2	2	no	—
357	C₂×C₄×C₃₁	—	2	2	no	—
358	C₂×C₄×C₃₁	—	2	2	no	—
359	C₂×C₄×C₃₁	—	2	2	no	—
360	C₂×C₄×C₃₁	—	2	2	no	—
361	C₂×C₄×C₃₁	—	2	2	no	—
362	C₂×C₄×C₃₁	—	2	2	no	—
363	C₂×C₄×C₃₁	—	2	2	no	—
364	C₂×C₄×C₃₁	—	2	2	no	—
365	C₂×C₄×C₃₁	—	2	2	no	—
366	C₂×C₄×C₃₁	—	2	2	no	—
367	C₂×C₄×C₃₁	—	2	2	no	—
368	C₂×C₄×C₃₁	—	2	1	no	—
369	C₂×C₄×C₃₁	—	2	2	no	—
370	C₂×C₄×C₃₁	—	2	2	no	—
371	C₂×C₄×C₃₁	—	2	2	no	—
372	C₂×C₄×C₃₁	—	2	1	no	—
373	C₂×C₄×C₃₁	—	2	2	no	—
374	C₂×C₄×C₃₁	—	2	16	no	—
375	C₂×C₄×C₃₁	—	2	2	no	—
376	C₂×C₄×C₃₁	—	2	2	no	—
377	C₂×C₄×C₃₁	—	2	2	no	—
378	C₂×C₄×C₃₁	—	2	2	no	—
379	C₂×C₄×C₃₁	—	2	2	no	—
380	C₂×C₄×C₃₁	—	2	2	no	—
381	C₂×C₄×C₃₁	—	2	2	no	—
382	C₂×C₄×C₃₁	—	2	2	no	—
383	C₂×C₄×C₃₁	—	2	2	no	—
384	C₂×C₄×C₃₁	—	2	2	no	—
385	C₂×C₄×C₃₁	—	2	1	no	—
386	C₂×C₄×C₃₁	—	2	1	no	—
387	C₂×C₄×C₃₁	—	2	1	no	—
388	C₂×C₄×C₃₁	—	2	2	no	—
389	C₂×C₄×C₃₁	—	2	2	no	—
390	C₂×C₄×C₃₁	—	4	8	no	—
391	C₂×C₄×C₃₁	—	4	4	no	—
392	C₂×C₄×C₃₁	—	4	4	no	—
393	C₂×C₄×C₃₁	—	4	4	no	—
394	C₂×C₄×C₃₁	—	4	8	no	—
395	C₂×C₄×C₃₁	—	4	8	no	—
396	C₂×C₄×C₃₁	—	4	8	no	—
397	C₂×C₄×C₃₁	—	4	4	no	—
398	C₂×C₄×C₃₁	—	4	4	no	—
399	C₂×C₄×C₃₁	C₂³×C₄	1	4	yes	—
400	C₂×C₄×C₃₁	C₂³×C₄	1	4	yes	—
401	C₂×C₄×C₃₁	C₂³×C₄	1	4	yes	—
402	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
403	C₂×C₄×C₃₁	C₂³×C₄	1	4	yes	—
404	C₂×C₄×C₃₁	C₂³×C₄	1	4	yes	—
405	C₂×C₄×C₃₁	C₂×#41	1	4	yes	—
406	C₂×C₄×C₃₁	C₂×#41	1	4	yes	—
407	C₂×C₄×C₃₁	C₂×#41	1	4	yes	—
408	C₂×C₄×C₃₁	C₂×#41	1	4	yes	—
409	C₂×C₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
410	C₂×#551	C₂×C₃₁	1	1	yes	characteristic
411	#2374	C₂×C₃₁	1	1	yes	characteristic, complemented
412	#2373	C₂×C₃₁	1	2	yes	complemented
413	#2372	C₂×C₃₁	1	1	yes	characteristic, complemented
414	#2368	C₂×C₃₁	1	2	yes	complemented
415	#2359	C₂×C₃₁	1	2	yes	complemented
416	#2358	C₂×C₃₁	1	1	yes	characteristic
417	#2353	C₂×C₃₁	1	2	yes	complemented
418	#2343	C₂×C₃₁	1	2	yes	complemented
419	#2342	C₂×C₃₁	1	2	yes	complemented
420	C₄×#126	C₂×C₃₁	1	2	yes	complemented
421	C₄×#124	C₂×C₃₁	1	1	yes	characteristic, complemented
422	C₄×C₂²⋊Q₈	C₂×C₃₁	1	2	yes	complemented
423	C₄×#123	C₂×C₃₁	1	1	yes	characteristic, complemented
424	C₄×#123	C₂×C₃₁	1	2	yes	complemented
425	C₄×#120	C₂×C₃₁	1	1	yes	characteristic
426	C₄²×D₄	C₂×C₃₁	1	2	yes	complemented
427	C₄×#117	C₂×C₃₁	1	2	yes	complemented
428	C₂×C₄×C₂²⋊C₄	C₂×C₃₁	1	2	yes	complemented
429	C₂²×C₃₁	—	2	4	no	—
430	C₂²×C₃₁	—	2	4	no	—
431	C₂²×C₃₁	—	2	4	no	—
432	C₂²×C₃₁	—	2	4	no	—
433	C₂²×C₃₁	—	2	4	no	—
434	C₂²×C₃₁	—	2	4	no	—
435	C₂²×C₃₁	—	2	4	no	—
436	C₂²×C₃₁	—	2	4	no	—
437	C₂²×C₃₁	—	2	2	no	—
438	C₂²×C₃₁	—	2	2	no	—
439	C₂²×C₃₁	—	4	16	no	—
440	C₂²×C₃₁	—	4	1	no	—
441	C₂²×C₃₁	—	4	1	no	—
442	C₂²×C₃₁	—	4	2	no	—
443	C₂²×C₃₁	—	4	2	no	—
444	C₂²×C₃₁	—	4	1	no	—
445	C₂²×C₃₁	—	4	1	no	—
446	C₂²×C₃₁	C₄×#41	1	8	yes	—
447	C₂²×C₃₁	C₂⁴×C₄	1	1	yes	characteristic
448	C₂²×C₃₁	C₂²×#41	1	2	yes	—
449	C₂²×C₃₁	C₂²×#41	1	2	yes	—
450	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
451	C₂²×C₃₁	#585	1	1	yes	characteristic
452	C₄×C₃₁	—	2	4	no	—
453	C₄×C₃₁	—	2	4	no	—
454	C₄×C₃₁	—	2	4	no	—
455	C₄×C₃₁	—	2	4	no	—
456	C₄×C₃₁	—	2	4	no	—
457	C₄×C₃₁	—	2	2	no	—
458	C₄×C₃₁	—	2	4	no	—
459	C₄×C₃₁	—	2	4	no	—
460	C₄×C₃₁	—	2	4	no	—
461	C₄×C₃₁	—	4	1	no	—
462	C₄×C₃₁	—	4	1	no	—
463	C₄×C₃₁	—	4	2	no	—
464	C₄×C₃₁	—	4	2	no	—
465	C₄×C₃₁	—	4	1	no	—
466	C₄×C₃₁	—	4	2	no	—
467	C₄×C₃₁	#551	1	4	yes	direct product factor
468	C₂⁴×C₄	C₂²×C₃₁	1	1	yes	characteristic
469	#551	C₄×C₃₁	1	16	yes	direct product factor
470	C₂×#126	C₂²×C₃₁	1	2	yes	—
471	C₂×#124	C₂²×C₃₁	1	1	yes	characteristic
472	C₂×#123	C₂²×C₃₁	1	2	yes	—
473	C₂×#123	C₂²×C₃₁	1	1	yes	characteristic
474	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	—
475	C₂×#120	C₂²×C₃₁	1	1	yes	characteristic
476	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
477	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
478	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
479	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
480	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
481	C₂×#117	C₂²×C₃₁	1	2	yes	—
482	C₂×#117	C₂²×C₃₁	1	2	yes	—
483	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
484	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
485	C₂²×C₄²	C₂²×C₃₁	1	2	yes	—
486	C₂²×C₄²	C₂²×C₃₁	1	2	yes	—
487	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic, complemented
488	#391	C₂²×C₃₁	1	1	yes	characteristic, complemented
489	#391	C₂²×C₃₁	1	2	yes	complemented
490	#390	C₂²×C₃₁	1	1	yes	characteristic
491	#389	C₂²×C₃₁	1	2	yes	complemented
492	#388	C₂²×C₃₁	1	2	yes	—
493	#388	C₂²×C₃₁	1	2	yes	—
494	#388	C₂²×C₃₁	1	2	yes	—
495	#388	C₂²×C₃₁	1	2	yes	—
496	#388	C₂²×C₃₁	1	2	yes	—
497	#388	C₂²×C₃₁	1	2	yes	complemented
498	#388	C₂²×C₃₁	1	2	yes	complemented
499	#388	C₂²×C₃₁	1	2	yes	complemented
500	#387	C₂²×C₃₁	1	2	yes	complemented
501	#387	C₂²×C₃₁	1	2	yes	complemented
502	#387	C₂²×C₃₁	1	2	yes	complemented
503	#387	C₂²×C₃₁	1	2	yes	complemented
504	#387	C₂²×C₃₁	1	2	yes	complemented
505	#387	C₂²×C₃₁	1	2	yes	complemented
506	#387	C₂²×C₃₁	1	2	yes	complemented
507	#387	C₂²×C₃₁	1	2	yes	complemented
508	#386	C₂²×C₃₁	1	2	yes	—
509	#386	C₂²×C₃₁	1	2	yes	—
510	#386	C₂²×C₃₁	1	1	yes	characteristic
511	#386	C₂²×C₃₁	1	1	yes	characteristic
512	#385	C₂²×C₃₁	1	2	yes	—
513	#385	C₂²×C₃₁	1	2	yes	—
514	#385	C₂²×C₃₁	1	2	yes	—
515	#385	C₂²×C₃₁	1	2	yes	—
516	#385	C₂²×C₃₁	1	1	yes	characteristic
517	#385	C₂²×C₃₁	1	1	yes	characteristic, complemented
518	#383	C₂²×C₃₁	1	2	yes	complemented
519	#382	C₂²×C₃₁	1	1	yes	characteristic, complemented
520	#381	C₂²×C₃₁	1	2	yes	—
521	#381	C₂²×C₃₁	1	1	yes	characteristic, complemented
522	#380	C₂²×C₃₁	1	2	yes	—
523	#379	C₂²×C₃₁	1	1	yes	characteristic
524	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	complemented
525	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	complemented
526	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	complemented
527	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	complemented
528	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	complemented
529	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	complemented
530	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	complemented
531	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	complemented
532	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
533	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
534	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
535	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
536	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
537	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
538	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
539	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
540	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
541	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
542	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
543	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
544	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
545	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
546	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	complemented
547	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	complemented
548	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	complemented
549	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
550	#376	C₂²×C₃₁	1	2	yes	complemented
551	#376	C₂²×C₃₁	1	2	yes	complemented
552	C₂×#95	C₂²×C₃₁	1	2	yes	—
553	C₂×#95	C₂²×C₃₁	1	2	yes	—
554	C₄³	C₂²×C₃₁	1	2	yes	complemented
555	C₄³	C₂²×C₃₁	1	1	yes	characteristic, complemented
556	C₂×C₃₁	—	2	8	no	—
557	C₂×C₃₁	—	4	2	no	—
558	C₂×C₃₁	—	4	2	no	—
559	C₂×C₃₁	C₂×C₄×#41	1	2	yes	—
560	C₂×C₃₁	C₄×H(5,𝔽₂)	1	1	yes	characteristic
561	C₂×C₃₁	C₂×#551	1	1	yes	characteristic
562	C₂×C₃₁	#3475	1	2	yes	—
563	C₂×C₃₁	#3481	1	1	yes	characteristic
564	C₂⁵	C₂³×C₃₁	1	1	yes	characteristic
565	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
566	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
567	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
568	C₂³×C₄	—	2	8	no	—
569	C₂³×C₄	—	4	2	no	—
570	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
571	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
572	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
573	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
574	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
575	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
576	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
577	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
578	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
579	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
580	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
581	#126	C₂×C₄×C₃₁	1	16	yes	complemented
582	#124	C₂×C₄×C₃₁	1	8	yes	complemented
583	#123	C₂×C₄×C₃₁	1	8	yes	complemented
584	#123	C₂×C₄×C₃₁	1	16	yes	complemented
585	C₂²⋊Q₈	C₂×C₄×C₃₁	1	16	yes	complemented
586	#120	C₂×C₄×C₃₁	1	8	yes	—
587	C₄×Q₈	—	4	2	no	—
588	C₄×D₄	—	2	8	no	—
589	C₄×D₄	—	2	8	no	—
590	C₄×D₄	—	4	2	no	—
591	C₄×D₄	C₂×C₄×C₃₁	1	16	yes	complemented
592	#117	—	2	8	no	—
593	#117	C₂×C₄×C₃₁	1	16	yes	complemented
594	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
595	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
596	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
597	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
598	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
599	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
600	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
601	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
602	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
603	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
604	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
605	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
606	C₂×C₂²⋊C₄	—	2	8	no	—
607	C₂×C₂²⋊C₄	C₂×C₄×C₃₁	1	16	yes	complemented
608	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
609	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
610	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
611	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
612	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
613	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
614	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
615	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
616	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
617	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
618	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
619	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
620	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
621	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
622	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
623	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
624	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
625	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
626	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
627	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
628	C₂×C₄²	—	2	8	no	—
629	C₂×C₄²	—	4	4	no	—
630	C₂×C₄²	—	4	2	no	—
631	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
632	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
633	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
634	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
635	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
636	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
637	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
638	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
639	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
640	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
641	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
642	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
643	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
644	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
645	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
646	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
647	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
648	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
649	#95	C₂³×C₃₁	1	2	yes	—
650	#95	C₂³×C₃₁	1	2	yes	—
651	#95	C₂³×C₃₁	1	2	yes	—
652	#95	C₂³×C₃₁	1	2	yes	—
653	#95	C₂³×C₃₁	1	2	yes	—
654	#95	C₂³×C₃₁	1	2	yes	—
655	#95	C₂³×C₃₁	1	2	yes	—
656	#95	C₂³×C₃₁	1	2	yes	—
657	#95	C₂³×C₃₁	1	2	yes	—
658	#95	C₂³×C₃₁	1	2	yes	—
659	#95	C₂³×C₃₁	1	2	yes	—
660	#95	C₂³×C₃₁	1	2	yes	—
661	#95	C₂³×C₃₁	1	2	yes	—
662	#95	C₂³×C₃₁	1	2	yes	—
663	#95	C₂³×C₃₁	1	2	yes	—
664	#95	C₂³×C₃₁	1	2	yes	—
665	#95	C₂³×C₃₁	1	2	yes	—
666	#95	C₂³×C₃₁	1	2	yes	—
667	#95	C₂³×C₃₁	1	2	yes	—
668	#95	C₂³×C₃₁	1	2	yes	—
669	#95	C₂³×C₃₁	1	2	yes	—
670	#95	C₂³×C₃₁	1	2	yes	—
671	C₃₁	C₄×#551	1	1	yes	characteristic, direct product factor, Sylow
672	C₂⁴	—	2	4	no	—
673	C₂⁴	—	2	4	no	—
674	C₂⁴	—	4	1	no	—
675	C₂⁴	—	4	1	no	—
676	C₂⁴	C₂²×C₄×C₃₁	1	4	yes	—
677	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
678	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
679	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
680	C₂×Q₈	—	4	1	no	—
681	C₂×Q₈	—	4	1	no	—
682	C₂×Q₈	C₂²×C₄×C₃₁	1	4	yes	complemented
683	C₂×D₄	—	2	4	no	—
684	C₂×D₄	—	2	4	no	—
685	C₂×D₄	—	4	1	no	—
686	C₂×D₄	—	4	1	no	—
687	C₂×D₄	C₂²×C₄×C₃₁	1	8	yes	—
688	C₂×D₄	C₂²×C₄×C₃₁	1	4	yes	—
689	C₂²×C₄	—	2	4	no	—
690	C₂²×C₄	—	2	4	no	—
691	C₂²×C₄	—	2	4	no	—
692	C₂²×C₄	—	2	4	no	—
693	C₂²×C₄	—	2	4	no	—
694	C₂²×C₄	—	2	4	no	—
695	C₂²×C₄	—	2	4	no	—
696	C₂²×C₄	—	2	4	no	—
697	C₂²×C₄	—	2	4	no	—
698	C₂²×C₄	—	2	4	no	—
699	C₂²×C₄	—	2	4	no	—
700	C₂²×C₄	—	2	4	no	—
701	C₂²×C₄	—	2	4	no	—
702	C₂²×C₄	—	2	4	no	—
703	C₂²×C₄	—	2	2	no	—
704	C₂²×C₄	—	2	2	no	—
705	C₂²×C₄	—	4	1	no	—
706	C₂²×C₄	—	4	1	no	—
707	C₂²×C₄	—	4	2	no	—
708	C₂²×C₄	—	4	2	no	—
709	C₂²×C₄	—	4	1	no	—
710	C₂²×C₄	—	4	2	no	—
711	C₂²×C₄	—	4	2	no	—
712	C₂²×C₄	—	4	1	no	—
713	C₂²×C₄	—	4	2	no	—
714	C₂²×C₄	—	4	16	no	—
715	C₂²×C₄	C₂²×C₄×C₃₁	1	8	yes	—
716	C₂²×C₄	C₂²×C₄×C₃₁	1	8	yes	—
717	C₂²×C₄	C₂²×C₄×C₃₁	1	4	yes	complemented
718	C₂²×C₄	#41×C₃₁	1	8	yes	—
719	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
720	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
721	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
722	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
723	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
724	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
725	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
726	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
727	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
728	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
729	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
730	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
731	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
732	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
733	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
734	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
735	C₄⋊C₄	—	2	4	no	—
736	C₄⋊C₄	—	2	4	no	—
737	C₄⋊C₄	—	2	4	no	—
738	C₄⋊C₄	—	2	4	no	—
739	C₄⋊C₄	—	4	2	no	—
740	C₄⋊C₄	—	4	1	no	—
741	C₄⋊C₄	—	4	2	no	—
742	C₄⋊C₄	—	4	1	no	—
743	C₄⋊C₄	C₂²×C₄×C₃₁	1	8	yes	complemented
744	C₄⋊C₄	C₂²×C₄×C₃₁	1	8	yes	complemented
745	C₄⋊C₄	C₂²×C₄×C₃₁	1	8	yes	complemented
746	C₄⋊C₄	C₂²×C₄×C₃₁	1	8	yes	complemented
747	C₂²⋊C₄	—	2	4	no	—
748	C₂²⋊C₄	—	2	4	no	—
749	C₂²⋊C₄	—	2	4	no	—
750	C₂²⋊C₄	—	2	4	no	—
751	C₂²⋊C₄	—	2	4	no	—
752	C₂²⋊C₄	—	2	4	no	—
753	C₂²⋊C₄	—	2	4	no	—
754	C₂²⋊C₄	—	4	1	no	—
755	C₂²⋊C₄	—	4	1	no	—
756	C₂²⋊C₄	—	4	1	no	—
757	C₂²⋊C₄	—	4	1	no	—
758	C₂²⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
759	C₂²⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
760	C₂²⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
761	C₂²⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
762	C₂²⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
763	C₂²⋊C₄	C₂²×C₄×C₃₁	1	4	yes	—
764	C₂²⋊C₄	C₂²×C₄×C₃₁	1	8	yes	complemented
765	C₂²⋊C₄	C₂²×C₄×C₃₁	1	4	yes	complemented
766	C₂²⋊C₄	#41×C₃₁	1	8	yes	—
767	C₄²	—	2	4	no	—
768	C₄²	—	2	4	no	—
769	C₄²	—	2	4	no	—
770	C₄²	—	2	4	no	—
771	C₄²	—	2	4	no	—
772	C₄²	—	2	4	no	—
773	C₄²	—	2	4	no	—
774	C₄²	—	2	4	no	—
775	C₄²	—	2	4	no	—
776	C₄²	—	2	4	no	—
777	C₄²	—	2	2	no	—
778	C₄²	—	4	2	no	—
779	C₄²	—	4	2	no	—
780	C₄²	—	4	2	no	—
781	C₄²	—	4	1	no	—
782	C₄²	—	4	2	no	—
783	C₄²	C₂²×C₄×C₃₁	1	4	yes	complemented
784	C₄²	C₂²×C₄×C₃₁	1	8	yes	complemented
785	C₂³	—	2	2	no	—
786	C₂³	—	2	2	no	—
787	C₂³	—	2	2	no	—
788	C₂³	—	2	2	no	—
789	C₂³	—	2	16	no	—
790	C₂³	—	2	2	no	—
791	C₂³	—	2	2	no	—
792	C₂³	—	2	2	no	—
793	C₂³	—	2	2	no	—
794	C₂³	—	2	1	no	—
795	C₂³	—	2	1	no	—
796	C₂³	—	2	1	no	—
797	C₂³	—	2	1	no	—
798	C₂³	—	4	4	no	—
799	C₂³	—	4	4	no	—
800	C₂³	—	4	8	no	—
801	C₂³	—	4	4	no	—
802	C₂³	C₂³×C₄×C₃₁	1	2	yes	—
803	C₂³	C₂³×C₄×C₃₁	1	2	yes	—
804	C₂³	C₂³×C₄×C₃₁	1	4	yes	—
805	C₂³	C₂×#41×C₃₁	1	4	yes	—
806	C₂³	C₂×#41×C₃₁	1	4	yes	—
807	C₂³	C₂⁵×C₃₁	1	1	yes	characteristic
808	Q₈	—	4	4	no	—
809	D₄	—	2	16	no	—
810	D₄	—	4	4	no	—
811	C₂×C₄	—	2	16	no	—
812	C₂×C₄	—	2	2	no	—
813	C₂×C₄	—	2	2	no	—
814	C₂×C₄	—	2	2	no	—
815	C₂×C₄	—	2	2	no	—
816	C₂×C₄	—	2	2	no	—
817	C₂×C₄	—	2	2	no	—
818	C₂×C₄	—	2	2	no	—
819	C₂×C₄	—	2	2	no	—
820	C₂×C₄	—	2	2	no	—
821	C₂×C₄	—	2	2	no	—
822	C₂×C₄	—	2	2	no	—
823	C₂×C₄	—	2	2	no	—
824	C₂×C₄	—	2	1	no	—
825	C₂×C₄	—	2	2	no	—
826	C₂×C₄	—	2	2	no	—
827	C₂×C₄	—	2	2	no	—
828	C₂×C₄	—	2	1	no	—
829	C₂×C₄	—	2	2	no	—
830	C₂×C₄	—	2	16	no	—
831	C₂×C₄	—	2	2	no	—
832	C₂×C₄	—	2	2	no	—
833	C₂×C₄	—	2	2	no	—
834	C₂×C₄	—	2	2	no	—
835	C₂×C₄	—	2	2	no	—
836	C₂×C₄	—	2	2	no	—
837	C₂×C₄	—	2	2	no	—
838	C₂×C₄	—	2	2	no	—
839	C₂×C₄	—	2	2	no	—
840	C₂×C₄	—	2	2	no	—
841	C₂×C₄	—	2	1	no	—
842	C₂×C₄	—	2	1	no	—
843	C₂×C₄	—	2	1	no	—
844	C₂×C₄	—	2	2	no	—
845	C₂×C₄	—	2	2	no	—
846	C₂×C₄	—	4	8	no	—
847	C₂×C₄	—	4	4	no	—
848	C₂×C₄	—	4	4	no	—
849	C₂×C₄	—	4	4	no	—
850	C₂×C₄	—	4	8	no	—
851	C₂×C₄	—	4	8	no	—
852	C₂×C₄	—	4	8	no	—
853	C₂×C₄	—	4	4	no	—
854	C₂×C₄	—	4	4	no	—
855	C₂×C₄	C₂³×C₄×C₃₁	1	4	yes	—
856	C₂×C₄	C₂³×C₄×C₃₁	1	4	yes	—
857	C₂×C₄	C₂³×C₄×C₃₁	1	4	yes	—
858	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
859	C₂×C₄	C₂³×C₄×C₃₁	1	4	yes	—
860	C₂×C₄	C₂³×C₄×C₃₁	1	4	yes	—
861	C₂×C₄	C₂×#41×C₃₁	1	4	yes	—
862	C₂×C₄	C₂×#41×C₃₁	1	4	yes	—
863	C₂×C₄	C₂×#41×C₃₁	1	4	yes	—
864	C₂×C₄	C₂×#41×C₃₁	1	4	yes	—
865	C₂×C₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
866	C₂²	—	2	4	no	—
867	C₂²	—	2	4	no	—
868	C₂²	—	2	4	no	—
869	C₂²	—	2	4	no	—
870	C₂²	—	2	4	no	—
871	C₂²	—	2	4	no	—
872	C₂²	—	2	4	no	—
873	C₂²	—	2	4	no	—
874	C₂²	—	2	2	no	—
875	C₂²	—	2	2	no	—
876	C₂²	—	4	16	no	—
877	C₂²	—	4	1	no	—
878	C₂²	—	4	1	no	—
879	C₂²	—	4	2	no	—
880	C₂²	—	4	2	no	—
881	C₂²	—	4	1	no	—
882	C₂²	—	4	1	no	—
883	C₂²	C₄×#41×C₃₁	1	8	yes	—
884	C₂²	C₂⁴×C₄×C₃₁	1	1	yes	characteristic
885	C₂²	C₂²×#41×C₃₁	1	2	yes	—
886	C₂²	C₂²×#41×C₃₁	1	2	yes	—
887	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
888	C₂²	C₃₁×#585	1	1	yes	characteristic
889	C₄	—	2	4	no	—
890	C₄	—	2	4	no	—
891	C₄	—	2	4	no	—
892	C₄	—	2	4	no	—
893	C₄	—	2	4	no	—
894	C₄	—	2	2	no	—
895	C₄	—	2	4	no	—
896	C₄	—	2	4	no	—
897	C₄	—	2	4	no	—
898	C₄	—	4	1	no	—
899	C₄	—	4	1	no	—
900	C₄	—	4	2	no	—
901	C₄	—	4	2	no	—
902	C₄	—	4	2	no	—
903	C₄	—	4	1	no	—
904	C₄	C₃₁×#551	1	4	yes	direct product factor
905	C₂	—	2	8	no	—
906	C₂	—	4	2	no	—
907	C₂	—	4	2	no	—
908	C₂	C₂×C₄×#41×C₃₁	1	2	yes	—
909	C₂	C₄×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
910	C₂	C₂×C₃₁×#551	1	1	yes	characteristic
911	C₂	C₃₁×#3475	1	2	yes	—
912	C₂	C₃₁×#3481	1	1	yes	characteristic

	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×#120	C₂²
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. C₃₁×#2374	C₂	semidirect
3. C₃₁×#2373	C₂	semidirect
4. C₃₁×#2372	C₂	semidirect
5. C₃₁×#2368	C₂	semidirect
6. C₃₁×#2359	C₂	semidirect
8. C₃₁×#2353	C₂	semidirect
9. C₃₁×#2343	C₂	semidirect
10. C₃₁×#2342	C₂	semidirect
11. C₄×C₃₁×#126	C₂	semidirect
12. C₄×C₃₁×#124	C₂	semidirect
13. C₄×C₃₁×C₂²⋊Q₈	C₂	semidirect
14. C₄×C₃₁×#123	C₂	semidirect
15. C₄×C₃₁×#123	C₂	semidirect
17. C₄²×D₄×C₃₁	C₂	semidirect
18. C₄×C₃₁×#117	C₂	semidirect
19. C₂×C₄×C₂²⋊C₄×C₃₁	C₂	semidirect
21. C₃₁×#551	C₄	direct (N × H)
28. C₂×C₄×Q₈×C₃₁	C₂²	semidirect
39. C₂²×C₄²×C₃₁	C₂²	semidirect
40. C₃₁×#391	C₂²	semidirect
41. C₃₁×#391	C₂²	semidirect
43. C₃₁×#389	C₂²	semidirect
49. C₃₁×#388	C₂²	semidirect
50. C₃₁×#388	C₂²	semidirect
51. C₃₁×#388	C₂²	semidirect
52. C₃₁×#387	C₂²	semidirect
53. C₃₁×#387	C₂²	semidirect
54. C₃₁×#387	C₂²	semidirect
55. C₃₁×#387	C₂²	semidirect
56. C₃₁×#387	C₂²	semidirect
57. C₃₁×#387	C₂²	semidirect
58. C₃₁×#387	C₂²	semidirect
59. C₃₁×#387	C₂²	semidirect
69. C₃₁×#385	C₂²	semidirect
70. C₃₁×#383	C₂²	semidirect
71. C₃₁×#382	C₂²	semidirect
73. C₃₁×#381	C₂²	semidirect
76. C₄×C₄⋊C₄×C₃₁	C₂²	semidirect
77. C₄×C₄⋊C₄×C₃₁	C₂²	semidirect
78. C₄×C₄⋊C₄×C₃₁	C₂²	semidirect
79. C₄×C₄⋊C₄×C₃₁	C₂²	semidirect
80. C₄×C₄⋊C₄×C₃₁	C₂²	semidirect
81. C₄×C₄⋊C₄×C₃₁	C₂²	semidirect
82. C₄×C₄⋊C₄×C₃₁	C₂²	semidirect
83. C₄×C₄⋊C₄×C₃₁	C₂²	semidirect
98. C₄×C₂²⋊C₄×C₃₁	C₂²	semidirect
99. C₄×C₂²⋊C₄×C₃₁	C₂²	semidirect
100. C₄×C₂²⋊C₄×C₃₁	C₂²	semidirect
101. C₄×C₂²⋊C₄×C₃₁	C₂²	semidirect
102. C₃₁×#376	C₂²	semidirect
103. C₃₁×#376	C₂²	semidirect
106. C₄³×C₃₁	C₂²	semidirect
107. C₄³×C₃₁	C₂²	semidirect
125. C₃₁×#126	C₂×C₄	semidirect
126. C₃₁×#124	C₂×C₄	semidirect
127. C₃₁×#123	C₂×C₄	semidirect
128. C₃₁×#123	C₂×C₄	semidirect
129. C₃₁×C₂²⋊Q₈	C₂×C₄	semidirect
135. C₄×D₄×C₃₁	C₂×C₄	semidirect
137. C₃₁×#117	C₂×C₄	semidirect
151. C₂×C₂²⋊C₄×C₃₁	C₂×C₄	semidirect
225. C₂×Q₈×C₃₁	C₂²×C₄	semidirect
260. C₂²×C₄×C₃₁	C₂²×C₄	semidirect
286. C₄⋊C₄×C₃₁	C₂²×C₄	semidirect
287. C₄⋊C₄×C₃₁	C₂²×C₄	semidirect
288. C₄⋊C₄×C₃₁	C₂²×C₄	semidirect
289. C₄⋊C₄×C₃₁	C₂²×C₄	semidirect
307. C₂²⋊C₄×C₃₁	C₂²×C₄	semidirect
308. C₂²⋊C₄×C₃₁	C₂²×C₄	semidirect
326. C₄²×C₃₁	C₂²×C₄	semidirect
327. C₄²×C₃₁	C₂²×C₄	semidirect
328. C₄×#551	C₃₁	direct (N × H)
411. #2374	C₂×C₃₁	semidirect
412. #2373	C₂×C₃₁	semidirect
413. #2372	C₂×C₃₁	semidirect
414. #2368	C₂×C₃₁	semidirect
415. #2359	C₂×C₃₁	semidirect
417. #2353	C₂×C₃₁	semidirect
418. #2343	C₂×C₃₁	semidirect
419. #2342	C₂×C₃₁	semidirect
420. C₄×#126	C₂×C₃₁	semidirect
421. C₄×#124	C₂×C₃₁	semidirect
422. C₄×C₂²⋊Q₈	C₂×C₃₁	semidirect
423. C₄×#123	C₂×C₃₁	semidirect
424. C₄×#123	C₂×C₃₁	semidirect
426. C₄²×D₄	C₂×C₃₁	semidirect
427. C₄×#117	C₂×C₃₁	semidirect
428. C₂×C₄×C₂²⋊C₄	C₂×C₃₁	semidirect
467. C₄×C₃₁	#551	direct (N × H)
469. #551	C₄×C₃₁	direct (N × H)
476. C₂×C₄×Q₈	C₂²×C₃₁	semidirect
487. C₂²×C₄²	C₂²×C₃₁	semidirect
488. #391	C₂²×C₃₁	semidirect
489. #391	C₂²×C₃₁	semidirect
491. #389	C₂²×C₃₁	semidirect
497. #388	C₂²×C₃₁	semidirect
498. #388	C₂²×C₃₁	semidirect
499. #388	C₂²×C₃₁	semidirect
500. #387	C₂²×C₃₁	semidirect
501. #387	C₂²×C₃₁	semidirect
502. #387	C₂²×C₃₁	semidirect
503. #387	C₂²×C₃₁	semidirect
504. #387	C₂²×C₃₁	semidirect
505. #387	C₂²×C₃₁	semidirect
506. #387	C₂²×C₃₁	semidirect
507. #387	C₂²×C₃₁	semidirect
517. #385	C₂²×C₃₁	semidirect
518. #383	C₂²×C₃₁	semidirect
519. #382	C₂²×C₃₁	semidirect
521. #381	C₂²×C₃₁	semidirect
524. C₄×C₄⋊C₄	C₂²×C₃₁	semidirect
525. C₄×C₄⋊C₄	C₂²×C₃₁	semidirect
526. C₄×C₄⋊C₄	C₂²×C₃₁	semidirect
527. C₄×C₄⋊C₄	C₂²×C₃₁	semidirect
528. C₄×C₄⋊C₄	C₂²×C₃₁	semidirect
529. C₄×C₄⋊C₄	C₂²×C₃₁	semidirect
530. C₄×C₄⋊C₄	C₂²×C₃₁	semidirect
531. C₄×C₄⋊C₄	C₂²×C₃₁	semidirect
546. C₄×C₂²⋊C₄	C₂²×C₃₁	semidirect
547. C₄×C₂²⋊C₄	C₂²×C₃₁	semidirect
548. C₄×C₂²⋊C₄	C₂²×C₃₁	semidirect
549. C₄×C₂²⋊C₄	C₂²×C₃₁	semidirect
550. #376	C₂²×C₃₁	semidirect
551. #376	C₂²×C₃₁	semidirect
554. C₄³	C₂²×C₃₁	semidirect
555. C₄³	C₂²×C₃₁	semidirect
581. #126	C₂×C₄×C₃₁	semidirect
582. #124	C₂×C₄×C₃₁	semidirect
583. #123	C₂×C₄×C₃₁	semidirect
584. #123	C₂×C₄×C₃₁	semidirect
585. C₂²⋊Q₈	C₂×C₄×C₃₁	semidirect
591. C₄×D₄	C₂×C₄×C₃₁	semidirect
593. #117	C₂×C₄×C₃₁	semidirect
607. C₂×C₂²⋊C₄	C₂×C₄×C₃₁	semidirect
671. C₃₁	C₄×#551	direct (N × H)
682. C₂×Q₈	C₂²×C₄×C₃₁	semidirect
717. C₂²×C₄	C₂²×C₄×C₃₁	semidirect
743. C₄⋊C₄	C₂²×C₄×C₃₁	semidirect
744. C₄⋊C₄	C₂²×C₄×C₃₁	semidirect
745. C₄⋊C₄	C₂²×C₄×C₃₁	semidirect
746. C₄⋊C₄	C₂²×C₄×C₃₁	semidirect
764. C₂²⋊C₄	C₂²×C₄×C₃₁	semidirect
765. C₂²⋊C₄	C₂²×C₄×C₃₁	semidirect
783. C₄²	C₂²×C₄×C₃₁	semidirect
784. C₄²	C₂²×C₄×C₃₁	semidirect
904. C₄	C₃₁×#551	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×#551	2
C₃₁×#2374	2
C₃₁×#2373	2
C₃₁×#2372	2
C₃₁×#2368	2
C₃₁×#2359	2
C₃₁×#2358	2
C₃₁×#2353	2
C₃₁×#2343	2
C₃₁×#2342	2
C₄×C₃₁×#126	2
C₄×C₃₁×#124	2
C₄×C₃₁×C₂²⋊Q₈	2
C₄×C₃₁×#123	2
C₄×C₃₁×#120	2
C₄²×D₄×C₃₁	2
C₄×C₃₁×#117	2
C₂×C₄×C₂²⋊C₄×C₃₁	2
C₄×#551	31

Subgroups — C4×C31×#551 #21490921

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₃₁×#551 #21490921