Subgroups — C₄×C₃₁×#539 #21490851

Order 7936.

2330 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#539	C₂	1	1	yes	maximal, characteristic
2	C₃₁×#2336	C₂	1	2	yes	maximal, complemented
3	C₃₁×#2335	C₂	1	2	yes	maximal, complemented
4	C₃₁×#2334	C₂	1	2	yes	maximal, complemented
5	C₃₁×#2332	C₂	1	2	yes	maximal, complemented
6	C₃₁×#2329	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#2325	C₂	1	1	yes	maximal, characteristic
8	C₃₁×#2322	C₂	1	2	yes	maximal, complemented
9	C₃₁×#2318	C₂	1	2	yes	maximal, complemented
10	C₃₁×#2313	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₃₁×#125	C₂	1	2	yes	maximal, complemented
12	C₄×C₃₁×#126	C₂	1	2	yes	maximal, complemented
13	C₄×C₃₁×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×C₃₁×C₂²⋊Q₈	C₂	1	2	yes	maximal, complemented
15	C₄×C₃₁×#123	C₂	1	2	yes	maximal, complemented
16	C₄×C₃₁×#123	C₂	1	2	yes	maximal, complemented
17	C₄×C₃₁×#121	C₂	1	1	yes	maximal, characteristic
18	C₄²×D₄×C₃₁	C₂	1	2	yes	maximal, complemented
19	C₂×C₄×C₄⋊C₄×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃₁×#539	C₄	1	16	yes	direct product factor
21	C₂×C₃₁×#126	C₂²	1	2	yes	—
22	C₂×C₃₁×#125	C₂²	1	2	yes	—
23	C₂×C₃₁×#123	C₂²	1	2	yes	—
24	C₂×C₃₁×#123	C₂²	1	2	yes	—
25	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
26	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	—
27	C₂×C₃₁×#121	C₂²	1	1	yes	characteristic
28	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
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	C₂²×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
34	C₂²×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
35	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
36	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
37	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
38	C₂²×C₄²×C₃₁	C₂²	1	2	yes	—
39	C₃₁×#391	C₂²	1	2	yes	—
40	C₃₁×#391	C₂²	1	1	yes	characteristic
41	C₃₁×#390	C₂²	1	1	yes	characteristic
42	C₃₁×#389	C₂²	1	2	yes	—
43	C₃₁×#389	C₂²	1	2	yes	—
44	C₃₁×#389	C₂²	1	2	yes	—
45	C₃₁×#389	C₂²	1	1	yes	characteristic
46	C₃₁×#389	C₂²	1	1	yes	characteristic
47	C₃₁×#388	C₂²	1	2	yes	—
48	C₃₁×#388	C₂²	1	2	yes	—
49	C₃₁×#388	C₂²	1	2	yes	—
50	C₃₁×#388	C₂²	1	2	yes	—
51	C₃₁×#388	C₂²	1	2	yes	—
52	C₃₁×#388	C₂²	1	2	yes	—
53	C₃₁×#388	C₂²	1	2	yes	—
54	C₃₁×#388	C₂²	1	2	yes	—
55	C₃₁×#387	C₂²	1	2	yes	—
56	C₃₁×#387	C₂²	1	2	yes	—
57	C₃₁×#387	C₂²	1	2	yes	—
58	C₃₁×#387	C₂²	1	2	yes	—
59	C₃₁×#387	C₂²	1	2	yes	—
60	C₃₁×#387	C₂²	1	2	yes	—
61	C₃₁×#387	C₂²	1	2	yes	—
62	C₃₁×#387	C₂²	1	2	yes	—
63	C₃₁×#387	C₂²	1	2	yes	—
64	C₃₁×#387	C₂²	1	2	yes	—
65	C₃₁×#387	C₂²	1	2	yes	—
66	C₃₁×#387	C₂²	1	2	yes	—
67	C₃₁×#387	C₂²	1	2	yes	—
68	C₃₁×#387	C₂²	1	2	yes	—
69	C₃₁×#386	C₂²	1	2	yes	—
70	C₃₁×#386	C₂²	1	2	yes	—
71	C₃₁×#386	C₂²	1	2	yes	—
72	C₃₁×#385	C₂²	1	2	yes	—
73	C₃₁×#385	C₂²	1	2	yes	—
74	C₃₁×#385	C₂²	1	2	yes	—
75	C₃₁×#385	C₂²	1	2	yes	—
76	C₃₁×#385	C₂²	1	2	yes	—
77	C₃₁×#383	C₂²	1	2	yes	—
78	C₃₁×#382	C₂²	1	2	yes	—
79	C₃₁×#381	C₂²	1	2	yes	—
80	C₃₁×#381	C₂²	1	2	yes	—
81	C₃₁×#380	C₂²	1	1	yes	characteristic
82	C₃₁×#380	C₂²	1	1	yes	characteristic
83	C₃₁×#380	C₂²	1	2	yes	—
84	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
85	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
86	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
87	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
88	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
89	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
90	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
91	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
92	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
93	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
94	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
95	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
96	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
97	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
98	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
99	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
100	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
101	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
102	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
103	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
104	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
105	C₂×C₃₁×#95	C₂²	1	1	yes	characteristic
106	C₂×C₃₁×#95	C₂²	1	1	yes	characteristic
107	C₄³×C₃₁	C₂²	1	2	yes	—
108	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
109	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
110	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
111	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
112	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
113	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
114	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
115	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
116	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
117	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
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	C₃₁×#126	C₂×C₄	1	16	yes	complemented
122	C₃₁×#125	C₂×C₄	1	16	yes	complemented
123	C₃₁×#123	C₂×C₄	1	16	yes	complemented
124	C₃₁×#123	C₂×C₄	1	16	yes	complemented
125	C₃₁×C₂²⋊Q₈	C₂×C₄	1	8	yes	complemented
126	C₃₁×C₂²⋊Q₈	C₂×C₄	1	16	yes	complemented
127	C₃₁×#121	C₂×C₄	1	8	yes	—
128	C₄×Q₈×C₃₁	—	4	2	no	—
129	C₄×D₄×C₃₁	—	2	8	no	—
130	C₄×D₄×C₃₁	—	2	8	no	—
131	C₄×D₄×C₃₁	—	4	2	no	—
132	C₄×D₄×C₃₁	C₂×C₄	1	16	yes	complemented
133	C₂×C₄⋊C₄×C₃₁	—	2	4	no	—
134	C₂×C₄⋊C₄×C₃₁	C₂×C₄	1	8	yes	complemented
135	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
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×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
140	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
141	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
142	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
143	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
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×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
151	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
152	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
153	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
154	C₂×C₄⋊C₄×C₃₁	C₂³	1	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	2	yes	—
160	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
161	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
162	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
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×C₄²×C₃₁	—	2	4	no	—
169	C₂×C₄²×C₃₁	—	4	2	no	—
170	C₂×C₄²×C₃₁	—	4	4	no	—
171	C₂×C₄²×C₃₁	—	4	2	no	—
172	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
173	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
174	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
175	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
176	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
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	C₃₁×#95	C₂³	1	2	yes	—
190	C₃₁×#95	C₂³	1	2	yes	—
191	C₃₁×#95	C₂³	1	2	yes	—
192	C₃₁×#95	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	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
214	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
215	C₂×Q₈×C₃₁	—	4	1	no	—
216	C₂×Q₈×C₃₁	—	4	1	no	—
217	C₂×Q₈×C₃₁	C₂²×C₄	1	4	yes	—
218	C₂×D₄×C₃₁	—	2	4	no	—
219	C₂×D₄×C₃₁	—	2	4	no	—
220	C₂×D₄×C₃₁	—	4	1	no	—
221	C₂×D₄×C₃₁	—	4	1	no	—
222	C₂×D₄×C₃₁	C₂²×C₄	1	8	yes	—
223	C₂×D₄×C₃₁	C₂²×C₄	1	4	yes	—
224	C₂²×C₄×C₃₁	—	2	2	no	—
225	C₂²×C₄×C₃₁	—	2	2	no	—
226	C₂²×C₄×C₃₁	—	2	2	no	—
227	C₂²×C₄×C₃₁	—	2	2	no	—
228	C₂²×C₄×C₃₁	—	2	2	no	—
229	C₂²×C₄×C₃₁	—	2	2	no	—
230	C₂²×C₄×C₃₁	—	2	4	no	—
231	C₂²×C₄×C₃₁	—	2	4	no	—
232	C₂²×C₄×C₃₁	—	2	4	no	—
233	C₂²×C₄×C₃₁	—	2	4	no	—
234	C₂²×C₄×C₃₁	—	4	1	no	—
235	C₂²×C₄×C₃₁	—	4	1	no	—
236	C₂²×C₄×C₃₁	—	4	2	no	—
237	C₂²×C₄×C₃₁	—	4	2	no	—
238	C₂²×C₄×C₃₁	—	4	1	no	—
239	C₂²×C₄×C₃₁	—	4	1	no	—
240	C₂²×C₄×C₃₁	—	4	1	no	—
241	C₂²×C₄×C₃₁	—	4	1	no	—
242	C₂²×C₄×C₃₁	—	4	2	no	—
243	C₂²×C₄×C₃₁	—	4	2	no	—
244	C₂²×C₄×C₃₁	—	4	1	no	—
245	C₂²×C₄×C₃₁	—	4	1	no	—
246	C₂²×C₄×C₃₁	—	4	1	no	—
247	C₂²×C₄×C₃₁	—	4	1	no	—
248	C₂²×C₄×C₃₁	C₂²×C₄	1	4	yes	—
249	C₂²×C₄×C₃₁	C₂²×C₄	1	4	yes	—
250	C₂²×C₄×C₃₁	C₂²×C₄	1	4	yes	—
251	C₂²×C₄×C₃₁	C₂²×C₄	1	8	yes	—
252	C₂²×C₄×C₃₁	#41	1	4	yes	—
253	C₂²×C₄×C₃₁	#41	1	4	yes	—
254	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
255	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
256	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
257	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
258	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
259	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
260	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
261	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
262	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
263	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
264	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
265	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
266	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
267	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
268	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
269	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
270	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
271	C₄⋊C₄×C₃₁	—	2	4	no	—
272	C₄⋊C₄×C₃₁	—	2	4	no	—
273	C₄⋊C₄×C₃₁	—	2	4	no	—
274	C₄⋊C₄×C₃₁	—	2	4	no	—
275	C₄⋊C₄×C₃₁	—	4	2	no	—
276	C₄⋊C₄×C₃₁	—	4	2	no	—
277	C₄⋊C₄×C₃₁	—	4	1	no	—
278	C₄⋊C₄×C₃₁	—	4	1	no	—
279	C₄⋊C₄×C₃₁	—	4	2	no	—
280	C₄⋊C₄×C₃₁	—	4	1	no	—
281	C₄⋊C₄×C₃₁	—	4	1	no	—
282	C₄⋊C₄×C₃₁	—	4	2	no	—
283	C₄⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
284	C₄⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
285	C₄⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
286	C₄⋊C₄×C₃₁	C₂²×C₄	1	4	yes	—
287	C₄⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
288	C₄⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
289	C₄⋊C₄×C₃₁	C₂²×C₄	1	4	yes	—
290	C₄⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
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	—	4	2	no	—
296	C₂²⋊C₄×C₃₁	—	4	2	no	—
297	C₂²⋊C₄×C₃₁	—	4	2	no	—
298	C₂²⋊C₄×C₃₁	—	4	2	no	—
299	C₂²⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
300	C₂²⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
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	C₄²×C₃₁	—	2	4	no	—
305	C₄²×C₃₁	—	2	4	no	—
306	C₄²×C₃₁	—	2	4	no	—
307	C₄²×C₃₁	—	2	4	no	—
308	C₄²×C₃₁	—	2	4	no	—
309	C₄²×C₃₁	—	2	2	no	—
310	C₄²×C₃₁	—	2	4	no	—
311	C₄²×C₃₁	—	2	2	no	—
312	C₄²×C₃₁	—	2	4	no	—
313	C₄²×C₃₁	—	4	2	no	—
314	C₄²×C₃₁	—	4	2	no	—
315	C₄²×C₃₁	—	4	2	no	—
316	C₄²×C₃₁	—	4	1	no	—
317	C₄²×C₃₁	—	4	1	no	—
318	C₄²×C₃₁	—	4	2	no	—
319	C₄²×C₃₁	—	4	2	no	—
320	C₄²×C₃₁	C₂²×C₄	1	8	yes	—
321	C₄×#539	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
322	C₂³×C₃₁	—	2	1	no	—
323	C₂³×C₃₁	—	2	1	no	—
324	C₂³×C₃₁	—	2	1	no	—
325	C₂³×C₃₁	—	2	1	no	—
326	C₂³×C₃₁	—	2	2	no	—
327	C₂³×C₃₁	—	2	2	no	—
328	C₂³×C₃₁	—	2	2	no	—
329	C₂³×C₃₁	—	2	2	no	—
330	C₂³×C₃₁	—	2	2	no	—
331	C₂³×C₃₁	—	2	2	no	—
332	C₂³×C₃₁	C₂³×C₄	1	4	yes	—
333	C₂³×C₃₁	C₂³×C₄	1	2	yes	—
334	C₂³×C₃₁	C₂×#41	1	2	yes	—
335	C₂³×C₃₁	C₂×#41	1	2	yes	—
336	C₂³×C₃₁	C₂⁵	1	1	yes	characteristic
337	Q₈×C₃₁	—	4	4	no	—
338	D₄×C₃₁	—	2	16	no	—
339	D₄×C₃₁	—	4	4	no	—
340	C₂×C₄×C₃₁	—	2	8	no	—
341	C₂×C₄×C₃₁	—	2	2	no	—
342	C₂×C₄×C₃₁	—	2	2	no	—
343	C₂×C₄×C₃₁	—	2	2	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	1	no	—
348	C₂×C₄×C₃₁	—	2	2	no	—
349	C₂×C₄×C₃₁	—	2	1	no	—
350	C₂×C₄×C₃₁	—	2	1	no	—
351	C₂×C₄×C₃₁	—	2	2	no	—
352	C₂×C₄×C₃₁	—	2	1	no	—
353	C₂×C₄×C₃₁	—	2	2	no	—
354	C₂×C₄×C₃₁	—	2	2	no	—
355	C₂×C₄×C₃₁	—	2	2	no	—
356	C₂×C₄×C₃₁	—	2	1	no	—
357	C₂×C₄×C₃₁	—	2	1	no	—
358	C₂×C₄×C₃₁	—	2	2	no	—
359	C₂×C₄×C₃₁	—	2	8	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	1	no	—
366	C₂×C₄×C₃₁	—	2	1	no	—
367	C₂×C₄×C₃₁	—	2	1	no	—
368	C₂×C₄×C₃₁	—	2	2	no	—
369	C₂×C₄×C₃₁	—	2	1	no	—
370	C₂×C₄×C₃₁	—	2	2	no	—
371	C₂×C₄×C₃₁	—	2	2	no	—
372	C₂×C₄×C₃₁	—	2	2	no	—
373	C₂×C₄×C₃₁	—	2	2	no	—
374	C₂×C₄×C₃₁	—	2	2	no	—
375	C₂×C₄×C₃₁	—	2	2	no	—
376	C₂×C₄×C₃₁	—	2	1	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	1	no	—
381	C₂×C₄×C₃₁	—	4	4	no	—
382	C₂×C₄×C₃₁	—	4	8	no	—
383	C₂×C₄×C₃₁	—	4	4	no	—
384	C₂×C₄×C₃₁	—	4	4	no	—
385	C₂×C₄×C₃₁	—	4	8	no	—
386	C₂×C₄×C₃₁	—	4	4	no	—
387	C₂×C₄×C₃₁	—	4	4	no	—
388	C₂×C₄×C₃₁	—	4	8	no	—
389	C₂×C₄×C₃₁	C₂³×C₄	1	4	yes	—
390	C₂×C₄×C₃₁	C₂³×C₄	1	4	yes	—
391	C₂×C₄×C₃₁	C₂³×C₄	1	4	yes	—
392	C₂×C₄×C₃₁	C₂³×C₄	1	4	yes	—
393	C₂×C₄×C₃₁	C₂³×C₄	1	4	yes	—
394	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
395	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
396	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
397	C₂×C₄×C₃₁	C₂×#41	1	4	yes	—
398	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
399	C₂×C₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
400	C₂×C₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
401	C₂×#539	C₂×C₃₁	1	1	yes	characteristic
402	#2336	C₂×C₃₁	1	2	yes	complemented
403	#2335	C₂×C₃₁	1	2	yes	complemented
404	#2334	C₂×C₃₁	1	2	yes	complemented
405	#2332	C₂×C₃₁	1	2	yes	complemented
406	#2329	C₂×C₃₁	1	1	yes	characteristic, complemented
407	#2325	C₂×C₃₁	1	1	yes	characteristic
408	#2322	C₂×C₃₁	1	2	yes	complemented
409	#2318	C₂×C₃₁	1	2	yes	complemented
410	#2313	C₂×C₃₁	1	1	yes	characteristic, complemented
411	C₄×#125	C₂×C₃₁	1	2	yes	complemented
412	C₄×#126	C₂×C₃₁	1	2	yes	complemented
413	C₄×C₂²⋊Q₈	C₂×C₃₁	1	1	yes	characteristic, complemented
414	C₄×C₂²⋊Q₈	C₂×C₃₁	1	2	yes	complemented
415	C₄×#123	C₂×C₃₁	1	2	yes	complemented
416	C₄×#123	C₂×C₃₁	1	2	yes	complemented
417	C₄×#121	C₂×C₃₁	1	1	yes	characteristic
418	C₄²×D₄	C₂×C₃₁	1	2	yes	complemented
419	C₂×C₄×C₄⋊C₄	C₂×C₃₁	1	1	yes	characteristic, complemented
420	C₂²×C₃₁	—	2	2	no	—
421	C₂²×C₃₁	—	2	2	no	—
422	C₂²×C₃₁	—	2	2	no	—
423	C₂²×C₃₁	—	2	2	no	—
424	C₂²×C₃₁	—	2	2	no	—
425	C₂²×C₃₁	—	2	2	no	—
426	C₂²×C₃₁	—	2	4	no	—
427	C₂²×C₃₁	—	2	4	no	—
428	C₂²×C₃₁	—	2	4	no	—
429	C₂²×C₃₁	—	4	2	no	—
430	C₂²×C₃₁	—	4	2	no	—
431	C₂²×C₃₁	—	4	2	no	—
432	C₂²×C₃₁	—	4	2	no	—
433	C₂²×C₃₁	C₄×#41	1	4	yes	—
434	C₂²×C₃₁	C₂⁴×C₄	1	1	yes	characteristic
435	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
436	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
437	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
438	C₂²×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
439	C₂²×C₃₁	#585	1	1	yes	characteristic
440	C₂²×C₃₁	#585	1	1	yes	characteristic
441	C₄×C₃₁	—	2	4	no	—
442	C₄×C₃₁	—	2	4	no	—
443	C₄×C₃₁	—	2	4	no	—
444	C₄×C₃₁	—	2	2	no	—
445	C₄×C₃₁	—	2	4	no	—
446	C₄×C₃₁	—	2	2	no	—
447	C₄×C₃₁	—	2	4	no	—
448	C₄×C₃₁	—	2	2	no	—
449	C₄×C₃₁	—	2	4	no	—
450	C₄×C₃₁	—	4	2	no	—
451	C₄×C₃₁	—	4	2	no	—
452	C₄×C₃₁	—	4	2	no	—
453	C₄×C₃₁	—	4	2	no	—
454	C₄×C₃₁	—	4	1	no	—
455	C₄×C₃₁	—	4	1	no	—
456	C₄×C₃₁	—	4	2	no	—
457	C₄×C₃₁	#539	1	4	yes	direct product factor
458	#539	C₄×C₃₁	1	16	yes	direct product factor
459	C₂×#126	C₂²×C₃₁	1	2	yes	—
460	C₂×#125	C₂²×C₃₁	1	2	yes	—
461	C₂×#123	C₂²×C₃₁	1	2	yes	—
462	C₂×#123	C₂²×C₃₁	1	2	yes	—
463	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
464	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	—
465	C₂×#121	C₂²×C₃₁	1	1	yes	characteristic
466	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
467	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
468	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
469	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
470	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
471	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
472	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
473	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
474	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
475	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
476	C₂²×C₄²	C₂²×C₃₁	1	2	yes	—
477	#391	C₂²×C₃₁	1	2	yes	—
478	#391	C₂²×C₃₁	1	1	yes	characteristic
479	#390	C₂²×C₃₁	1	1	yes	characteristic
480	#389	C₂²×C₃₁	1	2	yes	—
481	#389	C₂²×C₃₁	1	2	yes	—
482	#389	C₂²×C₃₁	1	2	yes	—
483	#389	C₂²×C₃₁	1	1	yes	characteristic
484	#389	C₂²×C₃₁	1	1	yes	characteristic
485	#388	C₂²×C₃₁	1	2	yes	—
486	#388	C₂²×C₃₁	1	2	yes	—
487	#388	C₂²×C₃₁	1	2	yes	—
488	#388	C₂²×C₃₁	1	2	yes	—
489	#388	C₂²×C₃₁	1	2	yes	—
490	#388	C₂²×C₃₁	1	2	yes	—
491	#388	C₂²×C₃₁	1	2	yes	—
492	#388	C₂²×C₃₁	1	2	yes	—
493	#387	C₂²×C₃₁	1	2	yes	—
494	#387	C₂²×C₃₁	1	2	yes	—
495	#387	C₂²×C₃₁	1	2	yes	—
496	#387	C₂²×C₃₁	1	2	yes	—
497	#387	C₂²×C₃₁	1	2	yes	—
498	#387	C₂²×C₃₁	1	2	yes	—
499	#387	C₂²×C₃₁	1	2	yes	—
500	#387	C₂²×C₃₁	1	2	yes	—
501	#387	C₂²×C₃₁	1	2	yes	—
502	#387	C₂²×C₃₁	1	2	yes	—
503	#387	C₂²×C₃₁	1	2	yes	—
504	#387	C₂²×C₃₁	1	2	yes	—
505	#387	C₂²×C₃₁	1	2	yes	—
506	#387	C₂²×C₃₁	1	2	yes	—
507	#386	C₂²×C₃₁	1	2	yes	—
508	#386	C₂²×C₃₁	1	2	yes	—
509	#386	C₂²×C₃₁	1	2	yes	—
510	#385	C₂²×C₃₁	1	2	yes	—
511	#385	C₂²×C₃₁	1	2	yes	—
512	#385	C₂²×C₃₁	1	2	yes	—
513	#385	C₂²×C₃₁	1	2	yes	—
514	#385	C₂²×C₃₁	1	2	yes	—
515	#383	C₂²×C₃₁	1	2	yes	—
516	#382	C₂²×C₃₁	1	2	yes	—
517	#381	C₂²×C₃₁	1	2	yes	—
518	#381	C₂²×C₃₁	1	2	yes	—
519	#380	C₂²×C₃₁	1	1	yes	characteristic
520	#380	C₂²×C₃₁	1	1	yes	characteristic
521	#380	C₂²×C₃₁	1	2	yes	—
522	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
523	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
524	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
525	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
526	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
527	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
528	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
529	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
530	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
531	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
532	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
533	C₄×C₄⋊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	C₂×#95	C₂²×C₃₁	1	1	yes	characteristic
544	C₂×#95	C₂²×C₃₁	1	1	yes	characteristic
545	C₄³	C₂²×C₃₁	1	2	yes	—
546	C₂×C₃₁	—	2	4	no	—
547	C₂×C₃₁	—	4	4	no	—
548	C₂×C₃₁	C₂×C₄×#41	1	1	yes	characteristic
549	C₂×C₃₁	C₄×H(5,𝔽₂)	1	1	yes	characteristic
550	C₂×C₃₁	C₄×2₋¹⁺⁴	1	1	yes	characteristic
551	C₂×C₃₁	C₂×#539	1	1	yes	characteristic
552	C₂×C₃₁	#3455	1	1	yes	characteristic
553	C₂×C₃₁	#3459	1	1	yes	characteristic
554	C₂×C₃₁	#3461	1	1	yes	characteristic
555	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
556	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
557	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
558	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
559	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
560	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
561	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
562	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
563	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
564	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
565	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
566	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
567	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
568	#126	C₂×C₄×C₃₁	1	16	yes	complemented
569	#125	C₂×C₄×C₃₁	1	16	yes	complemented
570	#123	C₂×C₄×C₃₁	1	16	yes	complemented
571	#123	C₂×C₄×C₃₁	1	16	yes	complemented
572	C₂²⋊Q₈	C₂×C₄×C₃₁	1	8	yes	complemented
573	C₂²⋊Q₈	C₂×C₄×C₃₁	1	16	yes	complemented
574	#121	C₂×C₄×C₃₁	1	8	yes	—
575	C₄×Q₈	—	4	2	no	—
576	C₄×D₄	—	2	8	no	—
577	C₄×D₄	—	2	8	no	—
578	C₄×D₄	—	4	2	no	—
579	C₄×D₄	C₂×C₄×C₃₁	1	16	yes	complemented
580	C₂×C₄⋊C₄	—	2	4	no	—
581	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	8	yes	complemented
582	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
583	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
584	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
585	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
586	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
587	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
588	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
589	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
590	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
591	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
592	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
593	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
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	1	yes	characteristic
598	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
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×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
603	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
604	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
605	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
606	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
607	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
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×C₄²	—	2	4	no	—
616	C₂×C₄²	—	4	2	no	—
617	C₂×C₄²	—	4	4	no	—
618	C₂×C₄²	—	4	2	no	—
619	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
620	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
621	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
622	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
623	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
624	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
625	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
626	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
627	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
628	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
629	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
630	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
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	1	yes	characteristic
635	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
636	#95	C₂³×C₃₁	1	2	yes	—
637	#95	C₂³×C₃₁	1	2	yes	—
638	#95	C₂³×C₃₁	1	2	yes	—
639	#95	C₂³×C₃₁	1	2	yes	—
640	#95	C₂³×C₃₁	1	2	yes	—
641	#95	C₂³×C₃₁	1	2	yes	—
642	#95	C₂³×C₃₁	1	2	yes	—
643	#95	C₂³×C₃₁	1	2	yes	—
644	#95	C₂³×C₃₁	1	2	yes	—
645	#95	C₂³×C₃₁	1	2	yes	—
646	#95	C₂³×C₃₁	1	2	yes	—
647	#95	C₂³×C₃₁	1	2	yes	—
648	#95	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	C₃₁	C₄×#539	1	1	yes	characteristic, direct product factor, Sylow
661	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
662	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
663	C₂×Q₈	—	4	1	no	—
664	C₂×Q₈	—	4	1	no	—
665	C₂×Q₈	C₂²×C₄×C₃₁	1	4	yes	—
666	C₂×D₄	—	2	4	no	—
667	C₂×D₄	—	2	4	no	—
668	C₂×D₄	—	4	1	no	—
669	C₂×D₄	—	4	1	no	—
670	C₂×D₄	C₂²×C₄×C₃₁	1	8	yes	—
671	C₂×D₄	C₂²×C₄×C₃₁	1	4	yes	—
672	C₂²×C₄	—	2	2	no	—
673	C₂²×C₄	—	2	2	no	—
674	C₂²×C₄	—	2	2	no	—
675	C₂²×C₄	—	2	2	no	—
676	C₂²×C₄	—	2	2	no	—
677	C₂²×C₄	—	2	2	no	—
678	C₂²×C₄	—	2	4	no	—
679	C₂²×C₄	—	2	4	no	—
680	C₂²×C₄	—	2	4	no	—
681	C₂²×C₄	—	2	4	no	—
682	C₂²×C₄	—	4	1	no	—
683	C₂²×C₄	—	4	1	no	—
684	C₂²×C₄	—	4	2	no	—
685	C₂²×C₄	—	4	2	no	—
686	C₂²×C₄	—	4	1	no	—
687	C₂²×C₄	—	4	1	no	—
688	C₂²×C₄	—	4	1	no	—
689	C₂²×C₄	—	4	1	no	—
690	C₂²×C₄	—	4	2	no	—
691	C₂²×C₄	—	4	2	no	—
692	C₂²×C₄	—	4	1	no	—
693	C₂²×C₄	—	4	1	no	—
694	C₂²×C₄	—	4	1	no	—
695	C₂²×C₄	—	4	1	no	—
696	C₂²×C₄	C₂²×C₄×C₃₁	1	4	yes	—
697	C₂²×C₄	C₂²×C₄×C₃₁	1	4	yes	—
698	C₂²×C₄	C₂²×C₄×C₃₁	1	4	yes	—
699	C₂²×C₄	C₂²×C₄×C₃₁	1	8	yes	—
700	C₂²×C₄	#41×C₃₁	1	4	yes	—
701	C₂²×C₄	#41×C₃₁	1	4	yes	—
702	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
703	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
704	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
705	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
706	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
707	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
708	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
709	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
710	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
711	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
712	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
713	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
714	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
715	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
716	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
717	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
718	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
719	C₄⋊C₄	—	2	4	no	—
720	C₄⋊C₄	—	2	4	no	—
721	C₄⋊C₄	—	2	4	no	—
722	C₄⋊C₄	—	2	4	no	—
723	C₄⋊C₄	—	4	2	no	—
724	C₄⋊C₄	—	4	2	no	—
725	C₄⋊C₄	—	4	1	no	—
726	C₄⋊C₄	—	4	1	no	—
727	C₄⋊C₄	—	4	2	no	—
728	C₄⋊C₄	—	4	1	no	—
729	C₄⋊C₄	—	4	1	no	—
730	C₄⋊C₄	—	4	2	no	—
731	C₄⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
732	C₄⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
733	C₄⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
734	C₄⋊C₄	C₂²×C₄×C₃₁	1	4	yes	—
735	C₄⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
736	C₄⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
737	C₄⋊C₄	C₂²×C₄×C₃₁	1	4	yes	—
738	C₄⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
739	C₂²⋊C₄	—	2	4	no	—
740	C₂²⋊C₄	—	2	4	no	—
741	C₂²⋊C₄	—	2	4	no	—
742	C₂²⋊C₄	—	2	4	no	—
743	C₂²⋊C₄	—	4	2	no	—
744	C₂²⋊C₄	—	4	2	no	—
745	C₂²⋊C₄	—	4	2	no	—
746	C₂²⋊C₄	—	4	2	no	—
747	C₂²⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
748	C₂²⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
749	C₂²⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
750	C₂²⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
751	C₂²⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
752	C₄²	—	2	4	no	—
753	C₄²	—	2	4	no	—
754	C₄²	—	2	4	no	—
755	C₄²	—	2	4	no	—
756	C₄²	—	2	4	no	—
757	C₄²	—	2	2	no	—
758	C₄²	—	2	4	no	—
759	C₄²	—	2	2	no	—
760	C₄²	—	2	4	no	—
761	C₄²	—	4	2	no	—
762	C₄²	—	4	2	no	—
763	C₄²	—	4	2	no	—
764	C₄²	—	4	1	no	—
765	C₄²	—	4	1	no	—
766	C₄²	—	4	2	no	—
767	C₄²	—	4	2	no	—
768	C₄²	C₂²×C₄×C₃₁	1	8	yes	—
769	C₂³	—	2	1	no	—
770	C₂³	—	2	1	no	—
771	C₂³	—	2	1	no	—
772	C₂³	—	2	1	no	—
773	C₂³	—	2	2	no	—
774	C₂³	—	2	2	no	—
775	C₂³	—	2	2	no	—
776	C₂³	—	2	2	no	—
777	C₂³	—	2	2	no	—
778	C₂³	—	2	2	no	—
779	C₂³	C₂³×C₄×C₃₁	1	4	yes	—
780	C₂³	C₂³×C₄×C₃₁	1	2	yes	—
781	C₂³	C₂×#41×C₃₁	1	2	yes	—
782	C₂³	C₂×#41×C₃₁	1	2	yes	—
783	C₂³	C₂⁵×C₃₁	1	1	yes	characteristic
784	Q₈	—	4	4	no	—
785	D₄	—	2	16	no	—
786	D₄	—	4	4	no	—
787	C₂×C₄	—	2	8	no	—
788	C₂×C₄	—	2	2	no	—
789	C₂×C₄	—	2	2	no	—
790	C₂×C₄	—	2	2	no	—
791	C₂×C₄	—	2	2	no	—
792	C₂×C₄	—	2	2	no	—
793	C₂×C₄	—	2	2	no	—
794	C₂×C₄	—	2	1	no	—
795	C₂×C₄	—	2	2	no	—
796	C₂×C₄	—	2	1	no	—
797	C₂×C₄	—	2	1	no	—
798	C₂×C₄	—	2	2	no	—
799	C₂×C₄	—	2	1	no	—
800	C₂×C₄	—	2	2	no	—
801	C₂×C₄	—	2	2	no	—
802	C₂×C₄	—	2	2	no	—
803	C₂×C₄	—	2	1	no	—
804	C₂×C₄	—	2	1	no	—
805	C₂×C₄	—	2	2	no	—
806	C₂×C₄	—	2	8	no	—
807	C₂×C₄	—	2	2	no	—
808	C₂×C₄	—	2	2	no	—
809	C₂×C₄	—	2	2	no	—
810	C₂×C₄	—	2	2	no	—
811	C₂×C₄	—	2	2	no	—
812	C₂×C₄	—	2	1	no	—
813	C₂×C₄	—	2	1	no	—
814	C₂×C₄	—	2	1	no	—
815	C₂×C₄	—	2	2	no	—
816	C₂×C₄	—	2	1	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	1	no	—
824	C₂×C₄	—	2	2	no	—
825	C₂×C₄	—	2	2	no	—
826	C₂×C₄	—	2	2	no	—
827	C₂×C₄	—	2	1	no	—
828	C₂×C₄	—	4	4	no	—
829	C₂×C₄	—	4	8	no	—
830	C₂×C₄	—	4	4	no	—
831	C₂×C₄	—	4	4	no	—
832	C₂×C₄	—	4	8	no	—
833	C₂×C₄	—	4	4	no	—
834	C₂×C₄	—	4	4	no	—
835	C₂×C₄	—	4	8	no	—
836	C₂×C₄	C₂³×C₄×C₃₁	1	4	yes	—
837	C₂×C₄	C₂³×C₄×C₃₁	1	4	yes	—
838	C₂×C₄	C₂³×C₄×C₃₁	1	4	yes	—
839	C₂×C₄	C₂³×C₄×C₃₁	1	4	yes	—
840	C₂×C₄	C₂³×C₄×C₃₁	1	4	yes	—
841	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
842	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
843	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
844	C₂×C₄	C₂×#41×C₃₁	1	4	yes	—
845	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
846	C₂×C₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
847	C₂×C₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
848	C₂²	—	2	2	no	—
849	C₂²	—	2	2	no	—
850	C₂²	—	2	2	no	—
851	C₂²	—	2	2	no	—
852	C₂²	—	2	2	no	—
853	C₂²	—	2	2	no	—
854	C₂²	—	2	4	no	—
855	C₂²	—	2	4	no	—
856	C₂²	—	2	4	no	—
857	C₂²	—	4	2	no	—
858	C₂²	—	4	2	no	—
859	C₂²	—	4	2	no	—
860	C₂²	—	4	2	no	—
861	C₂²	C₄×#41×C₃₁	1	4	yes	—
862	C₂²	C₂⁴×C₄×C₃₁	1	1	yes	characteristic
863	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
864	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
865	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
866	C₂²	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
867	C₂²	C₃₁×#585	1	1	yes	characteristic
868	C₂²	C₃₁×#585	1	1	yes	characteristic
869	C₄	—	2	4	no	—
870	C₄	—	2	4	no	—
871	C₄	—	2	4	no	—
872	C₄	—	2	2	no	—
873	C₄	—	2	4	no	—
874	C₄	—	2	2	no	—
875	C₄	—	2	4	no	—
876	C₄	—	2	2	no	—
877	C₄	—	2	4	no	—
878	C₄	—	4	2	no	—
879	C₄	—	4	2	no	—
880	C₄	—	4	2	no	—
881	C₄	—	4	2	no	—
882	C₄	—	4	1	no	—
883	C₄	—	4	1	no	—
884	C₄	—	4	2	no	—
885	C₄	C₃₁×#539	1	4	yes	direct product factor
886	C₂	—	2	4	no	—
887	C₂	—	4	4	no	—
888	C₂	C₂×C₄×#41×C₃₁	1	1	yes	characteristic
889	C₂	C₄×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
890	C₂	C₄×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
891	C₂	C₂×C₃₁×#539	1	1	yes	characteristic
892	C₂	C₃₁×#3455	1	1	yes	characteristic
893	C₂	C₃₁×#3459	1	1	yes	characteristic
894	C₂	C₃₁×#3461	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×#121	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×#2336	C₂	semidirect
3. C₃₁×#2335	C₂	semidirect
4. C₃₁×#2334	C₂	semidirect
5. C₃₁×#2332	C₂	semidirect
6. C₃₁×#2329	C₂	semidirect
8. C₃₁×#2322	C₂	semidirect
9. C₃₁×#2318	C₂	semidirect
10. C₃₁×#2313	C₂	semidirect
11. C₄×C₃₁×#125	C₂	semidirect
12. C₄×C₃₁×#126	C₂	semidirect
13. C₄×C₃₁×C₂²⋊Q₈	C₂	semidirect
14. C₄×C₃₁×C₂²⋊Q₈	C₂	semidirect
15. C₄×C₃₁×#123	C₂	semidirect
16. C₄×C₃₁×#123	C₂	semidirect
18. C₄²×D₄×C₃₁	C₂	semidirect
19. C₂×C₄×C₄⋊C₄×C₃₁	C₂	semidirect
20. C₃₁×#539	C₄	direct (N × H)
121. C₃₁×#126	C₂×C₄	semidirect
122. C₃₁×#125	C₂×C₄	semidirect
123. C₃₁×#123	C₂×C₄	semidirect
124. C₃₁×#123	C₂×C₄	semidirect
125. C₃₁×C₂²⋊Q₈	C₂×C₄	semidirect
126. C₃₁×C₂²⋊Q₈	C₂×C₄	semidirect
132. C₄×D₄×C₃₁	C₂×C₄	semidirect
134. C₂×C₄⋊C₄×C₃₁	C₂×C₄	semidirect
321. C₄×#539	C₃₁	direct (N × H)
402. #2336	C₂×C₃₁	semidirect
403. #2335	C₂×C₃₁	semidirect
404. #2334	C₂×C₃₁	semidirect
405. #2332	C₂×C₃₁	semidirect
406. #2329	C₂×C₃₁	semidirect
408. #2322	C₂×C₃₁	semidirect
409. #2318	C₂×C₃₁	semidirect
410. #2313	C₂×C₃₁	semidirect
411. C₄×#125	C₂×C₃₁	semidirect
412. C₄×#126	C₂×C₃₁	semidirect
413. C₄×C₂²⋊Q₈	C₂×C₃₁	semidirect
414. C₄×C₂²⋊Q₈	C₂×C₃₁	semidirect
415. C₄×#123	C₂×C₃₁	semidirect
416. C₄×#123	C₂×C₃₁	semidirect
418. C₄²×D₄	C₂×C₃₁	semidirect
419. C₂×C₄×C₄⋊C₄	C₂×C₃₁	semidirect
457. C₄×C₃₁	#539	direct (N × H)
458. #539	C₄×C₃₁	direct (N × H)
568. #126	C₂×C₄×C₃₁	semidirect
569. #125	C₂×C₄×C₃₁	semidirect
570. #123	C₂×C₄×C₃₁	semidirect
571. #123	C₂×C₄×C₃₁	semidirect
572. C₂²⋊Q₈	C₂×C₄×C₃₁	semidirect
573. C₂²⋊Q₈	C₂×C₄×C₃₁	semidirect
579. C₄×D₄	C₂×C₄×C₃₁	semidirect
581. C₂×C₄⋊C₄	C₂×C₄×C₃₁	semidirect
660. C₃₁	C₄×#539	direct (N × H)
885. C₄	C₃₁×#539	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×#539	2
C₃₁×#2336	2
C₃₁×#2335	2
C₃₁×#2334	2
C₃₁×#2332	2
C₃₁×#2329	2
C₃₁×#2325	2
C₃₁×#2322	2
C₃₁×#2318	2
C₃₁×#2313	2
C₄×C₃₁×#125	2
C₄×C₃₁×#126	2
C₄×C₃₁×C₂²⋊Q₈	2
C₄×C₃₁×#123	2
C₄×C₃₁×#121	2
C₄²×D₄×C₃₁	2
C₂×C₄×C₄⋊C₄×C₃₁	2
C₄×#539	31

Subgroups — C4×C31×#539 #21490851

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₃₁×#539 #21490851