Subgroups — C₃₁×#34772 #21491531

Order 7936.

1944 conjugacy classes of subgroups.

The subgroup lattice has 986 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#2522	C₂	1	2	yes	maximal, complemented
2	C₃₁×#2520	C₂	1	2	yes	maximal, complemented
3	C₃₁×#2511	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#2507	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#2505	C₂	1	2	yes	maximal, complemented
6	C₃₁×#2502	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#2497	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#2492	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#2487	C₂	1	1	yes	maximal, characteristic
10	C₃₁×#2450	C₂	1	2	yes	maximal
11	C₃₁×#2440	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#2417	C₂	1	1	yes	maximal, characteristic
13	C₃₁×#2402	C₂	1	2	yes	maximal, complemented
14	C₃₁×#2396	C₂	1	2	yes	maximal, complemented
15	C₄×C₃₁×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×C₃₁×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄×C₃₁×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
18	C₄×C₃₁×C₂²⋊Q₈	C₂	1	2	yes	maximal, complemented
19	C₃₁×#2295	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃₁×#2290	C₂	1	2	yes	maximal
21	C₃₁×#2285	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄²×D₄×C₃₁	C₂	1	1	yes	maximal, characteristic
23	C₂×C₄×C₄⋊C₄×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
25	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
26	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
27	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	—
28	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
29	C₂×C₄×Q₈×C₃₁	C₂²	1	2	yes	—
30	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
31	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
32	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
33	C₂×C₃₁×#117	C₂²	1	2	yes	—
34	C₂²×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
35	C₂²×C₄⋊C₄×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×#400	C₂²	1	2	yes	—
40	C₃₁×#400	C₂²	1	2	yes	—
41	C₃₁×#400	C₂²	1	2	yes	—
42	C₃₁×#400	C₂²	1	2	yes	—
43	C₃₁×#400	C₂²	1	2	yes	—
44	C₃₁×#399	C₂²	1	2	yes	—
45	C₃₁×#398	C₂²	1	2	yes	—
46	C₃₁×#398	C₂²	1	2	yes	—
47	C₃₁×#398	C₂²	1	2	yes	—
48	C₃₁×#398	C₂²	1	2	yes	—
49	C₃₁×#398	C₂²	1	2	yes	—
50	C₃₁×#398	C₂²	1	2	yes	—
51	C₃₁×#396	C₂²	1	2	yes	—
52	C₃₁×#396	C₂²	1	2	yes	—
53	C₃₁×#395	C₂²	1	2	yes	—
54	C₃₁×#393	C₂²	1	2	yes	—
55	C₃₁×#391	C₂²	1	2	yes	—
56	C₃₁×#391	C₂²	1	1	yes	characteristic
57	C₃₁×#391	C₂²	1	1	yes	characteristic
58	C₃₁×#391	C₂²	1	1	yes	characteristic
59	C₃₁×#391	C₂²	1	2	yes	—
60	C₃₁×#391	C₂²	1	1	yes	characteristic
61	C₃₁×#389	C₂²	1	1	yes	characteristic
62	C₃₁×#389	C₂²	1	1	yes	characteristic
63	C₃₁×#389	C₂²	1	2	yes	—
64	C₃₁×#389	C₂²	1	1	yes	characteristic
65	C₃₁×#389	C₂²	1	1	yes	characteristic
66	C₃₁×#389	C₂²	1	1	yes	characteristic
67	C₃₁×#389	C₂²	1	1	yes	characteristic
68	C₃₁×#389	C₂²	1	2	yes	—
69	C₃₁×#388	C₂²	1	2	yes	—
70	C₃₁×#388	C₂²	1	2	yes	—
71	C₃₁×#387	C₂²	1	2	yes	—
72	C₃₁×#387	C₂²	1	2	yes	—
73	C₃₁×#387	C₂²	1	2	yes	—
74	C₃₁×#387	C₂²	1	2	yes	—
75	C₃₁×#387	C₂²	1	2	yes	—
76	C₃₁×#387	C₂²	1	2	yes	—
77	C₃₁×#387	C₂²	1	2	yes	—
78	C₃₁×#387	C₂²	1	2	yes	—
79	C₃₁×#386	C₂²	1	2	yes	—
80	C₃₁×#386	C₂²	1	2	yes	—
81	C₃₁×#385	C₂²	1	2	yes	—
82	C₃₁×#385	C₂²	1	2	yes	—
83	C₃₁×#385	C₂²	1	2	yes	—
84	C₃₁×#385	C₂²	1	2	yes	—
85	C₃₁×#385	C₂²	1	2	yes	—
86	C₃₁×#385	C₂²	1	2	yes	—
87	C₃₁×#384	C₂²	1	1	yes	characteristic
88	C₃₁×#384	C₂²	1	1	yes	characteristic
89	C₃₁×#384	C₂²	1	1	yes	characteristic
90	C₃₁×#382	C₂²	1	2	yes	—
91	C₃₁×#380	C₂²	1	1	yes	characteristic
92	C₃₁×#380	C₂²	1	2	yes	—
93	C₃₁×#380	C₂²	1	1	yes	characteristic
94	C₃₁×#380	C₂²	1	2	yes	—
95	C₃₁×#380	C₂²	1	1	yes	characteristic
96	C₃₁×#380	C₂²	1	1	yes	characteristic
97	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
98	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
99	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
100	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
101	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
102	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
103	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
104	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
105	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
106	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
107	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
108	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
109	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
110	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
111	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
112	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
113	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
114	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
115	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
116	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
117	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
118	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
119	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
120	C₃₁×#376	C₂²	1	2	yes	—
121	C₂×C₃₁×#95	C₂²	1	2	yes	—
122	C₄³×C₃₁	C₂²	1	1	yes	characteristic
123	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
124	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
125	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
126	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
127	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
128	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
129	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
130	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
131	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
132	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
133	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
134	C₃₁×C₄⋊Q₈	—	2	4	no	—
135	C₃₁×C₂²⋊Q₈	—	2	4	no	—
136	C₃₁×C₂²⋊Q₈	—	2	4	no	—
137	C₃₁×C₂²⋊Q₈	—	2	8	no	—
138	C₄×Q₈×C₃₁	—	2	4	no	—
139	C₄×Q₈×C₃₁	—	4	4	no	—
140	C₄×D₄×C₃₁	—	2	4	no	—
141	C₄×D₄×C₃₁	—	2	4	no	—
142	C₄×D₄×C₃₁	Q₈	1	8	yes	complemented
143	C₃₁×#117	—	4	4	no	—
144	C₂×C₄⋊C₄×C₃₁	—	2	4	no	—
145	C₂×C₄⋊C₄×C₃₁	—	2	4	no	—
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	1	yes	characteristic
152	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
153	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
154	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
155	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
156	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
157	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
158	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
159	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
160	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
161	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
162	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
163	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
164	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
165	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
166	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
167	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
168	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
169	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
170	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
171	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
172	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
173	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
174	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
175	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
176	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
177	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
178	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
179	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
180	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
181	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
182	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
183	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
184	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
185	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
186	C₂×C₄²×C₃₁	—	2	4	no	—
187	C₂×C₄²×C₃₁	—	2	4	no	—
188	C₂×C₄²×C₃₁	—	4	4	no	—
189	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
190	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
191	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
192	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
193	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
194	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
195	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
196	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
197	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
198	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
199	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
200	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
201	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
202	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
203	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
204	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
205	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
206	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
207	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
208	C₃₁×#95	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
214	C₃₁×#95	C₂³	1	1	yes	characteristic
215	C₃₁×#95	C₂³	1	2	yes	—
216	C₃₁×#95	C₂³	1	2	yes	—
217	C₃₁×#95	C₂³	1	2	yes	—
218	C₃₁×#95	C₂³	1	2	yes	—
219	C₃₁×#95	C₂³	1	2	yes	—
220	C₃₁×#95	C₂³	1	2	yes	—
221	C₃₁×#95	C₂³	1	2	yes	—
222	C₃₁×#95	C₂³	1	2	yes	—
223	C₃₁×#95	C₂³	1	2	yes	—
224	C₃₁×#95	C₂³	1	2	yes	—
225	C₃₁×#95	C₂³	1	1	yes	characteristic
226	C₃₁×#95	C₂³	1	2	yes	—
227	C₃₁×#95	C₂³	1	2	yes	—
228	C₃₁×#95	C₂³	1	2	yes	—
229	C₃₁×#95	C₂³	1	2	yes	—
230	C₃₁×#95	C₂³	1	2	yes	—
231	C₃₁×#95	C₂³	1	2	yes	—
232	C₃₁×#95	C₂³	1	1	yes	characteristic
233	C₃₁×#95	C₂³	1	1	yes	characteristic
234	C₃₁×#95	C₂³	1	2	yes	—
235	C₃₁×#95	C₂³	1	2	yes	—
236	C₃₁×#95	C₂³	1	2	yes	—
237	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
238	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
239	C₂×Q₈×C₃₁	—	2	2	no	—
240	C₂×Q₈×C₃₁	—	2	4	no	—
241	C₂×Q₈×C₃₁	—	2	2	no	—
242	C₂×Q₈×C₃₁	—	2	2	no	—
243	C₂×Q₈×C₃₁	—	2	4	no	—
244	C₂×Q₈×C₃₁	—	4	2	no	—
245	C₂×D₄×C₃₁	—	2	2	no	—
246	C₂×D₄×C₃₁	—	2	2	no	—
247	C₂×D₄×C₃₁	C₂×Q₈	1	4	yes	—
248	C₂²×C₄×C₃₁	—	2	2	no	—
249	C₂²×C₄×C₃₁	—	2	2	no	—
250	C₂²×C₄×C₃₁	—	2	2	no	—
251	C₂²×C₄×C₃₁	—	2	2	no	—
252	C₂²×C₄×C₃₁	—	2	2	no	—
253	C₂²×C₄×C₃₁	—	2	2	no	—
254	C₂²×C₄×C₃₁	—	2	4	no	—
255	C₂²×C₄×C₃₁	—	2	2	no	—
256	C₂²×C₄×C₃₁	—	2	4	no	—
257	C₂²×C₄×C₃₁	—	2	2	no	—
258	C₂²×C₄×C₃₁	—	2	2	no	—
259	C₂²×C₄×C₃₁	—	2	2	no	—
260	C₂²×C₄×C₃₁	—	2	4	no	—
261	C₂²×C₄×C₃₁	—	2	2	no	—
262	C₂²×C₄×C₃₁	—	2	2	no	—
263	C₂²×C₄×C₃₁	—	2	2	no	—
264	C₂²×C₄×C₃₁	—	4	2	no	—
265	C₂²×C₄×C₃₁	—	4	2	no	—
266	C₂²×C₄×C₃₁	—	4	1	no	—
267	C₂²×C₄×C₃₁	—	4	1	no	—
268	C₂²×C₄×C₃₁	—	4	2	no	—
269	C₂²×C₄×C₃₁	C₂×Q₈	1	4	yes	—
270	C₂²×C₄×C₃₁	C₂×Q₈	1	4	yes	—
271	C₂²×C₄×C₃₁	#41	1	4	yes	—
272	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
273	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
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	2	yes	—
278	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
279	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
280	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
281	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
282	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
283	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
284	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
285	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
286	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
287	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
288	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
289	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
290	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
291	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
292	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
293	C₄⋊C₄×C₃₁	—	2	4	no	—
294	C₄⋊C₄×C₃₁	—	2	4	no	—
295	C₄⋊C₄×C₃₁	—	2	2	no	—
296	C₄⋊C₄×C₃₁	—	2	2	no	—
297	C₄⋊C₄×C₃₁	—	2	2	no	—
298	C₄⋊C₄×C₃₁	—	2	2	no	—
299	C₄⋊C₄×C₃₁	—	2	2	no	—
300	C₄⋊C₄×C₃₁	—	2	2	no	—
301	C₄⋊C₄×C₃₁	—	2	4	no	—
302	C₄⋊C₄×C₃₁	—	2	4	no	—
303	C₄⋊C₄×C₃₁	—	2	2	no	—
304	C₄⋊C₄×C₃₁	—	2	4	no	—
305	C₄⋊C₄×C₃₁	—	2	4	no	—
306	C₄⋊C₄×C₃₁	—	2	4	no	—
307	C₄⋊C₄×C₃₁	—	2	4	no	—
308	C₄⋊C₄×C₃₁	—	2	4	no	—
309	C₄⋊C₄×C₃₁	—	2	2	no	—
310	C₄⋊C₄×C₃₁	—	4	2	no	—
311	C₄⋊C₄×C₃₁	—	4	2	no	—
312	C₄⋊C₄×C₃₁	—	4	2	no	—
313	C₄⋊C₄×C₃₁	—	4	2	no	—
314	C₄⋊C₄×C₃₁	—	4	2	no	—
315	C₄⋊C₄×C₃₁	—	4	2	no	—
316	C₄⋊C₄×C₃₁	—	4	2	no	—
317	C₄⋊C₄×C₃₁	—	4	2	no	—
318	C₄⋊C₄×C₃₁	—	4	2	no	—
319	C₄⋊C₄×C₃₁	C₂×Q₈	1	4	yes	—
320	C₄⋊C₄×C₃₁	#41	1	4	yes	—
321	C₂²⋊C₄×C₃₁	—	2	2	no	—
322	C₂²⋊C₄×C₃₁	—	2	4	no	—
323	C₂²⋊C₄×C₃₁	—	2	4	no	—
324	C₂²⋊C₄×C₃₁	—	2	2	no	—
325	C₂²⋊C₄×C₃₁	—	2	2	no	—
326	C₂²⋊C₄×C₃₁	—	2	4	no	—
327	C₂²⋊C₄×C₃₁	—	4	2	no	—
328	C₂²⋊C₄×C₃₁	—	4	2	no	—
329	C₂²⋊C₄×C₃₁	—	4	2	no	—
330	C₂²⋊C₄×C₃₁	C₂×Q₈	1	4	yes	—
331	C₂²⋊C₄×C₃₁	C₂×Q₈	1	4	yes	—
332	C₂²⋊C₄×C₃₁	#41	1	4	yes	—
333	C₄²×C₃₁	—	2	2	no	—
334	C₄²×C₃₁	—	2	2	no	—
335	C₄²×C₃₁	—	2	2	no	—
336	C₄²×C₃₁	—	2	2	no	—
337	C₄²×C₃₁	—	2	2	no	—
338	C₄²×C₃₁	—	2	2	no	—
339	C₄²×C₃₁	—	2	2	no	—
340	C₄²×C₃₁	—	2	2	no	—
341	C₄²×C₃₁	—	2	4	no	—
342	C₄²×C₃₁	—	2	2	no	—
343	C₄²×C₃₁	—	2	4	no	—
344	C₄²×C₃₁	—	2	4	no	—
345	C₄²×C₃₁	—	2	4	no	—
346	C₄²×C₃₁	—	2	2	no	—
347	C₄²×C₃₁	—	4	2	no	—
348	C₄²×C₃₁	—	4	2	no	—
349	C₄²×C₃₁	—	4	1	no	—
350	C₄²×C₃₁	C₂×Q₈	1	4	yes	—
351	C₄²×C₃₁	#41	1	4	yes	—
352	#34772	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
353	C₂³×C₃₁	—	2	1	no	—
354	C₂³×C₃₁	—	2	1	no	—
355	C₂³×C₃₁	—	2	1	no	—
356	C₂³×C₃₁	—	2	1	no	—
357	C₂³×C₃₁	—	2	1	no	—
358	C₂³×C₃₁	—	2	1	no	—
359	C₂³×C₃₁	—	2	1	no	—
360	C₂³×C₃₁	—	2	1	no	—
361	C₂³×C₃₁	—	2	1	no	—
362	C₂³×C₃₁	—	2	1	no	—
363	C₂³×C₃₁	C₂²×Q₈	1	2	yes	—
364	C₂³×C₃₁	C₂²×Q₈	1	2	yes	—
365	C₂³×C₃₁	C₂×#41	1	2	yes	—
366	C₂³×C₃₁	C₂×#41	1	2	yes	—
367	C₂³×C₃₁	C₂⁵	1	1	yes	characteristic
368	Q₈×C₃₁	—	4	8	no	—
369	Q₈×C₃₁	—	4	4	no	—
370	D₄×C₃₁	—	2	8	no	—
371	C₂×C₄×C₃₁	—	2	1	no	—
372	C₂×C₄×C₃₁	—	2	1	no	—
373	C₂×C₄×C₃₁	—	2	1	no	—
374	C₂×C₄×C₃₁	—	2	1	no	—
375	C₂×C₄×C₃₁	—	2	1	no	—
376	C₂×C₄×C₃₁	—	2	1	no	—
377	C₂×C₄×C₃₁	—	2	1	no	—
378	C₂×C₄×C₃₁	—	2	1	no	—
379	C₂×C₄×C₃₁	—	2	1	no	—
380	C₂×C₄×C₃₁	—	2	1	no	—
381	C₂×C₄×C₃₁	—	2	2	no	—
382	C₂×C₄×C₃₁	—	2	2	no	—
383	C₂×C₄×C₃₁	—	2	1	no	—
384	C₂×C₄×C₃₁	—	2	1	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	1	no	—
389	C₂×C₄×C₃₁	—	2	8	no	—
390	C₂×C₄×C₃₁	—	2	8	no	—
391	C₂×C₄×C₃₁	—	2	8	no	—
392	C₂×C₄×C₃₁	—	2	1	no	—
393	C₂×C₄×C₃₁	—	2	1	no	—
394	C₂×C₄×C₃₁	—	2	1	no	—
395	C₂×C₄×C₃₁	—	2	2	no	—
396	C₂×C₄×C₃₁	—	2	2	no	—
397	C₂×C₄×C₃₁	—	2	2	no	—
398	C₂×C₄×C₃₁	—	2	2	no	—
399	C₂×C₄×C₃₁	—	2	1	no	—
400	C₂×C₄×C₃₁	—	2	1	no	—
401	C₂×C₄×C₃₁	—	2	2	no	—
402	C₂×C₄×C₃₁	—	2	2	no	—
403	C₂×C₄×C₃₁	—	2	2	no	—
404	C₂×C₄×C₃₁	—	2	1	no	—
405	C₂×C₄×C₃₁	—	2	2	no	—
406	C₂×C₄×C₃₁	—	2	2	no	—
407	C₂×C₄×C₃₁	—	2	2	no	—
408	C₂×C₄×C₃₁	—	2	2	no	—
409	C₂×C₄×C₃₁	—	2	2	no	—
410	C₂×C₄×C₃₁	—	2	2	no	—
411	C₂×C₄×C₃₁	—	2	2	no	—
412	C₂×C₄×C₃₁	—	2	2	no	—
413	C₂×C₄×C₃₁	—	2	2	no	—
414	C₂×C₄×C₃₁	—	2	2	no	—
415	C₂×C₄×C₃₁	—	2	1	no	—
416	C₂×C₄×C₃₁	—	2	1	no	—
417	C₂×C₄×C₃₁	—	2	2	no	—
418	C₂×C₄×C₃₁	—	2	2	no	—
419	C₂×C₄×C₃₁	—	2	2	no	—
420	C₂×C₄×C₃₁	—	2	2	no	—
421	C₂×C₄×C₃₁	—	2	1	no	—
422	C₂×C₄×C₃₁	—	4	4	no	—
423	C₂×C₄×C₃₁	—	4	4	no	—
424	C₂×C₄×C₃₁	—	4	8	no	—
425	C₂×C₄×C₃₁	—	4	8	no	—
426	C₂×C₄×C₃₁	—	4	4	no	—
427	C₂×C₄×C₃₁	C₂²×Q₈	1	2	yes	—
428	C₂×C₄×C₃₁	C₂²×Q₈	1	2	yes	—
429	C₂×C₄×C₃₁	C₂²×Q₈	1	2	yes	—
430	C₂×C₄×C₃₁	C₂²×Q₈	1	2	yes	—
431	C₂×C₄×C₃₁	C₂²×Q₈	1	2	yes	—
432	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
433	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
434	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
435	C₂×C₄×C₃₁	C₂×#41	1	4	yes	—
436	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
437	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
438	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
439	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
440	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
441	C₂×C₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
442	#2522	C₂×C₃₁	1	2	yes	complemented
443	#2520	C₂×C₃₁	1	2	yes	complemented
444	#2511	C₂×C₃₁	1	1	yes	characteristic, complemented
445	#2507	C₂×C₃₁	1	1	yes	characteristic, complemented
446	#2505	C₂×C₃₁	1	2	yes	complemented
447	#2502	C₂×C₃₁	1	1	yes	characteristic, complemented
448	#2497	C₂×C₃₁	1	1	yes	characteristic, complemented
449	#2492	C₂×C₃₁	1	1	yes	characteristic, complemented
450	#2487	C₂×C₃₁	1	1	yes	characteristic
451	#2450	C₂×C₃₁	1	2	yes	—
452	#2440	C₂×C₃₁	1	1	yes	characteristic, complemented
453	#2417	C₂×C₃₁	1	1	yes	characteristic
454	#2402	C₂×C₃₁	1	2	yes	complemented
455	#2396	C₂×C₃₁	1	2	yes	complemented
456	C₄×C₄⋊Q₈	C₂×C₃₁	1	1	yes	characteristic, complemented
457	C₄×C₂²⋊Q₈	C₂×C₃₁	1	1	yes	characteristic, complemented
458	C₄×C₂²⋊Q₈	C₂×C₃₁	1	1	yes	characteristic, complemented
459	C₄×C₂²⋊Q₈	C₂×C₃₁	1	2	yes	complemented
460	#2295	C₂×C₃₁	1	1	yes	characteristic, complemented
461	#2290	C₂×C₃₁	1	2	yes	—
462	#2285	C₂×C₃₁	1	1	yes	characteristic, complemented
463	C₄²×D₄	C₂×C₃₁	1	1	yes	characteristic
464	C₂×C₄×C₄⋊C₄	C₂×C₃₁	1	1	yes	characteristic, complemented
465	C₂²×C₃₁	—	2	2	no	—
466	C₂²×C₃₁	—	2	2	no	—
467	C₂²×C₃₁	—	2	2	no	—
468	C₂²×C₃₁	—	2	2	no	—
469	C₂²×C₃₁	—	2	2	no	—
470	C₂²×C₃₁	—	2	2	no	—
471	C₂²×C₃₁	—	2	2	no	—
472	C₂²×C₃₁	—	2	2	no	—
473	C₂²×C₃₁	—	2	2	no	—
474	C₂²×C₃₁	—	4	1	no	—
475	C₂²×C₃₁	—	4	1	no	—
476	C₂²×C₃₁	—	4	1	no	—
477	C₂²×C₃₁	—	4	1	no	—
478	C₂²×C₃₁	#533	1	4	yes	—
479	C₂²×C₃₁	C₂³×Q₈	1	1	yes	characteristic
480	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
481	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
482	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
483	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
484	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
485	C₂²×C₃₁	#585	1	1	yes	characteristic
486	C₄×C₃₁	—	2	2	no	—
487	C₄×C₃₁	—	2	2	no	—
488	C₄×C₃₁	—	2	2	no	—
489	C₄×C₃₁	—	2	2	no	—
490	C₄×C₃₁	—	2	2	no	—
491	C₄×C₃₁	—	2	2	no	—
492	C₄×C₃₁	—	2	2	no	—
493	C₄×C₃₁	—	2	4	no	—
494	C₄×C₃₁	—	2	2	no	—
495	C₄×C₃₁	—	4	1	no	—
496	C₄×C₃₁	—	4	2	no	—
497	C₄×C₃₁	—	4	1	no	—
498	C₄×C₃₁	—	4	2	no	—
499	C₄×C₃₁	—	4	2	no	—
500	C₄×C₃₁	—	4	2	no	—
501	C₄×C₃₁	—	4	2	no	—
502	C₄×C₃₁	—	4	1	no	—
503	C₄×C₃₁	—	4	2	no	—
504	C₄×C₃₁	—	4	2	no	—
505	C₄×C₃₁	#529	1	4	yes	—
506	C₄×C₃₁	#554	1	4	yes	—
507	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
508	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
509	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
510	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	—
511	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
512	C₂×C₄×Q₈	C₂²×C₃₁	1	2	yes	—
513	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
514	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
515	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
516	C₂×#117	C₂²×C₃₁	1	2	yes	—
517	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
518	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
519	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
520	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
521	C₂²×C₄²	C₂²×C₃₁	1	2	yes	—
522	#400	C₂²×C₃₁	1	2	yes	—
523	#400	C₂²×C₃₁	1	2	yes	—
524	#400	C₂²×C₃₁	1	2	yes	—
525	#400	C₂²×C₃₁	1	2	yes	—
526	#400	C₂²×C₃₁	1	2	yes	—
527	#399	C₂²×C₃₁	1	2	yes	—
528	#398	C₂²×C₃₁	1	2	yes	—
529	#398	C₂²×C₃₁	1	2	yes	—
530	#398	C₂²×C₃₁	1	2	yes	—
531	#398	C₂²×C₃₁	1	2	yes	—
532	#398	C₂²×C₃₁	1	2	yes	—
533	#398	C₂²×C₃₁	1	2	yes	—
534	#396	C₂²×C₃₁	1	2	yes	—
535	#396	C₂²×C₃₁	1	2	yes	—
536	#395	C₂²×C₃₁	1	2	yes	—
537	#393	C₂²×C₃₁	1	2	yes	—
538	#391	C₂²×C₃₁	1	2	yes	—
539	#391	C₂²×C₃₁	1	1	yes	characteristic
540	#391	C₂²×C₃₁	1	1	yes	characteristic
541	#391	C₂²×C₃₁	1	1	yes	characteristic
542	#391	C₂²×C₃₁	1	2	yes	—
543	#391	C₂²×C₃₁	1	1	yes	characteristic
544	#389	C₂²×C₃₁	1	1	yes	characteristic
545	#389	C₂²×C₃₁	1	1	yes	characteristic
546	#389	C₂²×C₃₁	1	2	yes	—
547	#389	C₂²×C₃₁	1	1	yes	characteristic
548	#389	C₂²×C₃₁	1	1	yes	characteristic
549	#389	C₂²×C₃₁	1	1	yes	characteristic
550	#389	C₂²×C₃₁	1	1	yes	characteristic
551	#389	C₂²×C₃₁	1	2	yes	—
552	#388	C₂²×C₃₁	1	2	yes	—
553	#388	C₂²×C₃₁	1	2	yes	—
554	#387	C₂²×C₃₁	1	2	yes	—
555	#387	C₂²×C₃₁	1	2	yes	—
556	#387	C₂²×C₃₁	1	2	yes	—
557	#387	C₂²×C₃₁	1	2	yes	—
558	#387	C₂²×C₃₁	1	2	yes	—
559	#387	C₂²×C₃₁	1	2	yes	—
560	#387	C₂²×C₃₁	1	2	yes	—
561	#387	C₂²×C₃₁	1	2	yes	—
562	#386	C₂²×C₃₁	1	2	yes	—
563	#386	C₂²×C₃₁	1	2	yes	—
564	#385	C₂²×C₃₁	1	2	yes	—
565	#385	C₂²×C₃₁	1	2	yes	—
566	#385	C₂²×C₃₁	1	2	yes	—
567	#385	C₂²×C₃₁	1	2	yes	—
568	#385	C₂²×C₃₁	1	2	yes	—
569	#385	C₂²×C₃₁	1	2	yes	—
570	#384	C₂²×C₃₁	1	1	yes	characteristic
571	#384	C₂²×C₃₁	1	1	yes	characteristic
572	#384	C₂²×C₃₁	1	1	yes	characteristic
573	#382	C₂²×C₃₁	1	2	yes	—
574	#380	C₂²×C₃₁	1	1	yes	characteristic
575	#380	C₂²×C₃₁	1	2	yes	—
576	#380	C₂²×C₃₁	1	1	yes	characteristic
577	#380	C₂²×C₃₁	1	2	yes	—
578	#380	C₂²×C₃₁	1	1	yes	characteristic
579	#380	C₂²×C₃₁	1	1	yes	characteristic
580	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
581	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
582	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
583	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
584	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
585	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
586	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
587	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
588	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
589	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
590	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
591	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
592	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
593	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
594	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
595	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
596	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
597	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
598	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
599	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
600	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
601	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
602	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
603	#376	C₂²×C₃₁	1	2	yes	—
604	C₂×#95	C₂²×C₃₁	1	2	yes	—
605	C₄³	C₂²×C₃₁	1	1	yes	characteristic
606	C₂×C₃₁	—	2	4	no	—
607	C₂×C₃₁	—	4	2	no	—
608	C₂×C₃₁	C₂×#529	1	1	yes	characteristic
609	C₂×C₃₁	C₂×#533	1	1	yes	characteristic
610	C₂×C₃₁	#3460	1	1	yes	characteristic
611	C₂×C₃₁	C₂×#554	1	1	yes	characteristic
612	C₂×C₃₁	#3475	1	1	yes	characteristic
613	C₂×C₃₁	Q₈×#41	1	1	yes	characteristic
614	C₂×C₃₁	#3481	1	1	yes	characteristic
615	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
616	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
617	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
618	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
619	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
620	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
621	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
622	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
623	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
624	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
625	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
626	C₄⋊Q₈	—	2	4	no	—
627	C₂²⋊Q₈	—	2	4	no	—
628	C₂²⋊Q₈	—	2	4	no	—
629	C₂²⋊Q₈	—	2	8	no	—
630	C₄×Q₈	—	2	4	no	—
631	C₄×Q₈	—	4	4	no	—
632	C₄×D₄	—	2	4	no	—
633	C₄×D₄	—	2	4	no	—
634	C₄×D₄	Q₈×C₃₁	1	8	yes	complemented
635	#117	—	4	4	no	—
636	C₂×C₄⋊C₄	—	2	4	no	—
637	C₂×C₄⋊C₄	—	2	4	no	—
638	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
639	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
640	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
641	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
642	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
643	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
644	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
645	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
646	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
647	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
648	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
649	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
650	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
651	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
652	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
653	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
654	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
655	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
656	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
657	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
658	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
659	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
660	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
661	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
662	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
663	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
664	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
665	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
666	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
667	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
668	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
669	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
670	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
671	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
672	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
673	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
674	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
675	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
676	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
677	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
678	C₂×C₄²	—	2	4	no	—
679	C₂×C₄²	—	2	4	no	—
680	C₂×C₄²	—	4	4	no	—
681	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
682	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
683	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
684	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
685	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
686	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
687	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
688	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
689	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
690	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
691	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
692	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
693	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
694	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
695	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
696	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
697	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
698	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
699	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
700	#95	C₂³×C₃₁	1	2	yes	—
701	#95	C₂³×C₃₁	1	2	yes	—
702	#95	C₂³×C₃₁	1	2	yes	—
703	#95	C₂³×C₃₁	1	2	yes	—
704	#95	C₂³×C₃₁	1	2	yes	—
705	#95	C₂³×C₃₁	1	2	yes	—
706	#95	C₂³×C₃₁	1	2	yes	—
707	#95	C₂³×C₃₁	1	2	yes	—
708	#95	C₂³×C₃₁	1	1	yes	characteristic
709	#95	C₂³×C₃₁	1	1	yes	characteristic
710	#95	C₂³×C₃₁	1	1	yes	characteristic
711	#95	C₂³×C₃₁	1	1	yes	characteristic
712	#95	C₂³×C₃₁	1	1	yes	characteristic
713	#95	C₂³×C₃₁	1	1	yes	characteristic
714	#95	C₂³×C₃₁	1	2	yes	—
715	#95	C₂³×C₃₁	1	2	yes	—
716	#95	C₂³×C₃₁	1	2	yes	—
717	#95	C₂³×C₃₁	1	2	yes	—
718	#95	C₂³×C₃₁	1	2	yes	—
719	#95	C₂³×C₃₁	1	2	yes	—
720	#95	C₂³×C₃₁	1	2	yes	—
721	#95	C₂³×C₃₁	1	2	yes	—
722	#95	C₂³×C₃₁	1	2	yes	—
723	#95	C₂³×C₃₁	1	2	yes	—
724	#95	C₂³×C₃₁	1	2	yes	—
725	#95	C₂³×C₃₁	1	2	yes	—
726	#95	C₂³×C₃₁	1	2	yes	—
727	#95	C₂³×C₃₁	1	2	yes	—
728	#95	C₂³×C₃₁	1	2	yes	—
729	C₃₁	#34772	1	1	yes	characteristic, direct product factor, Sylow
730	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
731	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
732	C₂×Q₈	—	2	2	no	—
733	C₂×Q₈	—	2	4	no	—
734	C₂×Q₈	—	2	2	no	—
735	C₂×Q₈	—	2	2	no	—
736	C₂×Q₈	—	2	4	no	—
737	C₂×Q₈	—	4	2	no	—
738	C₂×D₄	—	2	2	no	—
739	C₂×D₄	—	2	2	no	—
740	C₂×D₄	C₂×Q₈×C₃₁	1	4	yes	—
741	C₂²×C₄	—	2	2	no	—
742	C₂²×C₄	—	2	2	no	—
743	C₂²×C₄	—	2	2	no	—
744	C₂²×C₄	—	2	2	no	—
745	C₂²×C₄	—	2	2	no	—
746	C₂²×C₄	—	2	2	no	—
747	C₂²×C₄	—	2	4	no	—
748	C₂²×C₄	—	2	2	no	—
749	C₂²×C₄	—	2	4	no	—
750	C₂²×C₄	—	2	2	no	—
751	C₂²×C₄	—	2	2	no	—
752	C₂²×C₄	—	2	2	no	—
753	C₂²×C₄	—	2	4	no	—
754	C₂²×C₄	—	2	2	no	—
755	C₂²×C₄	—	2	2	no	—
756	C₂²×C₄	—	2	2	no	—
757	C₂²×C₄	—	4	2	no	—
758	C₂²×C₄	—	4	2	no	—
759	C₂²×C₄	—	4	1	no	—
760	C₂²×C₄	—	4	1	no	—
761	C₂²×C₄	—	4	2	no	—
762	C₂²×C₄	C₂×Q₈×C₃₁	1	4	yes	—
763	C₂²×C₄	C₂×Q₈×C₃₁	1	4	yes	—
764	C₂²×C₄	#41×C₃₁	1	4	yes	—
765	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
766	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
767	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
768	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
769	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
770	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
771	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
772	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
773	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
774	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
775	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
776	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
777	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
778	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
779	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
780	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
781	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
782	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
783	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
784	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
785	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
786	C₄⋊C₄	—	2	4	no	—
787	C₄⋊C₄	—	2	4	no	—
788	C₄⋊C₄	—	2	2	no	—
789	C₄⋊C₄	—	2	2	no	—
790	C₄⋊C₄	—	2	2	no	—
791	C₄⋊C₄	—	2	2	no	—
792	C₄⋊C₄	—	2	2	no	—
793	C₄⋊C₄	—	2	2	no	—
794	C₄⋊C₄	—	2	4	no	—
795	C₄⋊C₄	—	2	4	no	—
796	C₄⋊C₄	—	2	2	no	—
797	C₄⋊C₄	—	2	4	no	—
798	C₄⋊C₄	—	2	4	no	—
799	C₄⋊C₄	—	2	4	no	—
800	C₄⋊C₄	—	2	4	no	—
801	C₄⋊C₄	—	2	4	no	—
802	C₄⋊C₄	—	2	2	no	—
803	C₄⋊C₄	—	4	2	no	—
804	C₄⋊C₄	—	4	2	no	—
805	C₄⋊C₄	—	4	2	no	—
806	C₄⋊C₄	—	4	2	no	—
807	C₄⋊C₄	—	4	2	no	—
808	C₄⋊C₄	—	4	2	no	—
809	C₄⋊C₄	—	4	2	no	—
810	C₄⋊C₄	—	4	2	no	—
811	C₄⋊C₄	—	4	2	no	—
812	C₄⋊C₄	C₂×Q₈×C₃₁	1	4	yes	—
813	C₄⋊C₄	#41×C₃₁	1	4	yes	—
814	C₂²⋊C₄	—	2	2	no	—
815	C₂²⋊C₄	—	2	4	no	—
816	C₂²⋊C₄	—	2	4	no	—
817	C₂²⋊C₄	—	2	2	no	—
818	C₂²⋊C₄	—	2	2	no	—
819	C₂²⋊C₄	—	2	4	no	—
820	C₂²⋊C₄	—	4	2	no	—
821	C₂²⋊C₄	—	4	2	no	—
822	C₂²⋊C₄	—	4	2	no	—
823	C₂²⋊C₄	C₂×Q₈×C₃₁	1	4	yes	—
824	C₂²⋊C₄	C₂×Q₈×C₃₁	1	4	yes	—
825	C₂²⋊C₄	#41×C₃₁	1	4	yes	—
826	C₄²	—	2	2	no	—
827	C₄²	—	2	2	no	—
828	C₄²	—	2	2	no	—
829	C₄²	—	2	2	no	—
830	C₄²	—	2	2	no	—
831	C₄²	—	2	2	no	—
832	C₄²	—	2	2	no	—
833	C₄²	—	2	2	no	—
834	C₄²	—	2	4	no	—
835	C₄²	—	2	2	no	—
836	C₄²	—	2	4	no	—
837	C₄²	—	2	4	no	—
838	C₄²	—	2	4	no	—
839	C₄²	—	2	2	no	—
840	C₄²	—	4	2	no	—
841	C₄²	—	4	2	no	—
842	C₄²	—	4	1	no	—
843	C₄²	C₂×Q₈×C₃₁	1	4	yes	—
844	C₄²	#41×C₃₁	1	4	yes	—
845	C₂³	—	2	1	no	—
846	C₂³	—	2	1	no	—
847	C₂³	—	2	1	no	—
848	C₂³	—	2	1	no	—
849	C₂³	—	2	1	no	—
850	C₂³	—	2	1	no	—
851	C₂³	—	2	1	no	—
852	C₂³	—	2	1	no	—
853	C₂³	—	2	1	no	—
854	C₂³	—	2	1	no	—
855	C₂³	C₂²×Q₈×C₃₁	1	2	yes	—
856	C₂³	C₂²×Q₈×C₃₁	1	2	yes	—
857	C₂³	C₂×#41×C₃₁	1	2	yes	—
858	C₂³	C₂×#41×C₃₁	1	2	yes	—
859	C₂³	C₂⁵×C₃₁	1	1	yes	characteristic
860	Q₈	—	4	8	no	—
861	Q₈	—	4	4	no	—
862	D₄	—	2	8	no	—
863	C₂×C₄	—	2	1	no	—
864	C₂×C₄	—	2	1	no	—
865	C₂×C₄	—	2	1	no	—
866	C₂×C₄	—	2	1	no	—
867	C₂×C₄	—	2	1	no	—
868	C₂×C₄	—	2	1	no	—
869	C₂×C₄	—	2	1	no	—
870	C₂×C₄	—	2	1	no	—
871	C₂×C₄	—	2	1	no	—
872	C₂×C₄	—	2	1	no	—
873	C₂×C₄	—	2	2	no	—
874	C₂×C₄	—	2	2	no	—
875	C₂×C₄	—	2	1	no	—
876	C₂×C₄	—	2	1	no	—
877	C₂×C₄	—	2	1	no	—
878	C₂×C₄	—	2	1	no	—
879	C₂×C₄	—	2	1	no	—
880	C₂×C₄	—	2	1	no	—
881	C₂×C₄	—	2	8	no	—
882	C₂×C₄	—	2	8	no	—
883	C₂×C₄	—	2	8	no	—
884	C₂×C₄	—	2	1	no	—
885	C₂×C₄	—	2	1	no	—
886	C₂×C₄	—	2	1	no	—
887	C₂×C₄	—	2	2	no	—
888	C₂×C₄	—	2	2	no	—
889	C₂×C₄	—	2	2	no	—
890	C₂×C₄	—	2	2	no	—
891	C₂×C₄	—	2	1	no	—
892	C₂×C₄	—	2	1	no	—
893	C₂×C₄	—	2	2	no	—
894	C₂×C₄	—	2	2	no	—
895	C₂×C₄	—	2	2	no	—
896	C₂×C₄	—	2	1	no	—
897	C₂×C₄	—	2	2	no	—
898	C₂×C₄	—	2	2	no	—
899	C₂×C₄	—	2	2	no	—
900	C₂×C₄	—	2	2	no	—
901	C₂×C₄	—	2	2	no	—
902	C₂×C₄	—	2	2	no	—
903	C₂×C₄	—	2	2	no	—
904	C₂×C₄	—	2	2	no	—
905	C₂×C₄	—	2	2	no	—
906	C₂×C₄	—	2	2	no	—
907	C₂×C₄	—	2	1	no	—
908	C₂×C₄	—	2	1	no	—
909	C₂×C₄	—	2	2	no	—
910	C₂×C₄	—	2	2	no	—
911	C₂×C₄	—	2	2	no	—
912	C₂×C₄	—	2	2	no	—
913	C₂×C₄	—	2	1	no	—
914	C₂×C₄	—	4	4	no	—
915	C₂×C₄	—	4	4	no	—
916	C₂×C₄	—	4	8	no	—
917	C₂×C₄	—	4	8	no	—
918	C₂×C₄	—	4	4	no	—
919	C₂×C₄	C₂²×Q₈×C₃₁	1	2	yes	—
920	C₂×C₄	C₂²×Q₈×C₃₁	1	2	yes	—
921	C₂×C₄	C₂²×Q₈×C₃₁	1	2	yes	—
922	C₂×C₄	C₂²×Q₈×C₃₁	1	2	yes	—
923	C₂×C₄	C₂²×Q₈×C₃₁	1	2	yes	—
924	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
925	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
926	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
927	C₂×C₄	C₂×#41×C₃₁	1	4	yes	—
928	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
929	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
930	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
931	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
932	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
933	C₂×C₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
934	C₂²	—	2	2	no	—
935	C₂²	—	2	2	no	—
936	C₂²	—	2	2	no	—
937	C₂²	—	2	2	no	—
938	C₂²	—	2	2	no	—
939	C₂²	—	2	2	no	—
940	C₂²	—	2	2	no	—
941	C₂²	—	2	2	no	—
942	C₂²	—	2	2	no	—
943	C₂²	—	4	1	no	—
944	C₂²	—	4	1	no	—
945	C₂²	—	4	1	no	—
946	C₂²	—	4	1	no	—
947	C₂²	C₃₁×#533	1	4	yes	—
948	C₂²	C₂³×Q₈×C₃₁	1	1	yes	characteristic
949	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
950	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
951	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
952	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
953	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
954	C₂²	C₃₁×#585	1	1	yes	characteristic
955	C₄	—	2	2	no	—
956	C₄	—	2	2	no	—
957	C₄	—	2	2	no	—
958	C₄	—	2	2	no	—
959	C₄	—	2	2	no	—
960	C₄	—	2	2	no	—
961	C₄	—	2	2	no	—
962	C₄	—	2	4	no	—
963	C₄	—	2	2	no	—
964	C₄	—	4	1	no	—
965	C₄	—	4	2	no	—
966	C₄	—	4	2	no	—
967	C₄	—	4	2	no	—
968	C₄	—	4	1	no	—
969	C₄	—	4	2	no	—
970	C₄	—	4	1	no	—
971	C₄	—	4	2	no	—
972	C₄	—	4	2	no	—
973	C₄	—	4	2	no	—
974	C₄	C₃₁×#529	1	4	yes	—
975	C₄	C₃₁×#554	1	4	yes	—
976	C₂	—	2	4	no	—
977	C₂	—	4	2	no	—
978	C₂	C₂×C₃₁×#529	1	1	yes	characteristic
979	C₂	C₂×C₃₁×#533	1	1	yes	characteristic
980	C₂	C₃₁×#3460	1	1	yes	characteristic
981	C₂	C₂×C₃₁×#554	1	1	yes	characteristic
982	C₂	C₃₁×#3475	1	1	yes	characteristic
983	C₂	Q₈×#41×C₃₁	1	1	yes	characteristic
984	C₂	C₃₁×#3481	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₃₁	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₃₁
socle	C₂³×C₃₁	C₂⁵
prime radical	C₂²×D₄×C₃₁	C₂³
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#2522	C₂	semidirect
2. C₃₁×#2520	C₂	semidirect
3. C₃₁×#2511	C₂	semidirect
4. C₃₁×#2507	C₂	semidirect
5. C₃₁×#2505	C₂	semidirect
6. C₃₁×#2502	C₂	semidirect
7. C₃₁×#2497	C₂	semidirect
8. C₃₁×#2492	C₂	semidirect
11. C₃₁×#2440	C₂	semidirect
13. C₃₁×#2402	C₂	semidirect
14. C₃₁×#2396	C₂	semidirect
15. C₄×C₃₁×C₄⋊Q₈	C₂	semidirect
16. C₄×C₃₁×C₂²⋊Q₈	C₂	semidirect
17. C₄×C₃₁×C₂²⋊Q₈	C₂	semidirect
18. C₄×C₃₁×C₂²⋊Q₈	C₂	semidirect
19. C₃₁×#2295	C₂	semidirect
21. C₃₁×#2285	C₂	semidirect
23. C₂×C₄×C₄⋊C₄×C₃₁	C₂	semidirect
142. C₄×D₄×C₃₁	Q₈	semidirect
352. #34772	C₃₁	direct (N × H)
442. #2522	C₂×C₃₁	semidirect
443. #2520	C₂×C₃₁	semidirect
444. #2511	C₂×C₃₁	semidirect
445. #2507	C₂×C₃₁	semidirect
446. #2505	C₂×C₃₁	semidirect
447. #2502	C₂×C₃₁	semidirect
448. #2497	C₂×C₃₁	semidirect
449. #2492	C₂×C₃₁	semidirect
452. #2440	C₂×C₃₁	semidirect
454. #2402	C₂×C₃₁	semidirect
455. #2396	C₂×C₃₁	semidirect
456. C₄×C₄⋊Q₈	C₂×C₃₁	semidirect
457. C₄×C₂²⋊Q₈	C₂×C₃₁	semidirect
458. C₄×C₂²⋊Q₈	C₂×C₃₁	semidirect
459. C₄×C₂²⋊Q₈	C₂×C₃₁	semidirect
460. #2295	C₂×C₃₁	semidirect
462. #2285	C₂×C₃₁	semidirect
464. C₂×C₄×C₄⋊C₄	C₂×C₃₁	semidirect
634. C₄×D₄	Q₈×C₃₁	semidirect
729. C₃₁	#34772	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃₁×#2522	2
C₃₁×#2520	2
C₃₁×#2511	2
C₃₁×#2507	2
C₃₁×#2505	2
C₃₁×#2502	2
C₃₁×#2497	2
C₃₁×#2492	2
C₃₁×#2487	2
C₃₁×#2450	2
C₃₁×#2440	2
C₃₁×#2417	2
C₃₁×#2402	2
C₃₁×#2396	2
C₄×C₃₁×C₄⋊Q₈	2
C₄×C₃₁×C₂²⋊Q₈	2
C₃₁×#2295	2
C₃₁×#2290	2
C₃₁×#2285	2
C₄²×D₄×C₃₁	2
C₂×C₄×C₄⋊C₄×C₃₁	2
#34772	31

Subgroups — C31×#34772 #21491531

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#34772 #21491531