Subgroups — C₃₁×#35017 #21491776

Order 7936.

1816 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×#2863	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#2859	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#2857	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#2855	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#2667	C₂	1	2	yes	maximal, complemented
6	C₃₁×#2666	C₂	1	2	yes	maximal, complemented
7	C₃₁×#2585	C₂	1	2	yes	maximal, complemented
8	C₃₁×#2556	C₂	1	2	yes	maximal, complemented
9	C₃₁×#2507	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#2502	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#2497	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#2487	C₂	1	1	yes	maximal, characteristic
13	C₃₁×#2473	C₂	1	2	yes	maximal, complemented
14	C₃₁×#2451	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#2449	C₂	1	2	yes	maximal
16	C₃₁×#2440	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#2423	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃₁×#2417	C₂	1	1	yes	maximal, characteristic
19	C₃₁×#2329	C₂	1	2	yes	maximal, complemented
20	C₃₁×#2318	C₂	1	2	yes	maximal
21	C₄×C₃₁×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×C₃₁×#389	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄²×D₄×C₃₁	C₂	1	1	yes	maximal, characteristic
24	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
25	C₂×C₃₁×#125	C₂²	1	2	yes	—
26	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	—
27	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
28	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
29	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	—
30	C₂×C₄×Q₈×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×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
34	C₂²×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
35	C₂²×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
36	C₂²×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
37	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
38	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
39	C₃₁×#400	C₂²	1	2	yes	—
40	C₃₁×#400	C₂²	1	2	yes	—
41	C₃₁×#399	C₂²	1	2	yes	—
42	C₃₁×#399	C₂²	1	2	yes	—
43	C₃₁×#398	C₂²	1	2	yes	—
44	C₃₁×#398	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×#395	C₂²	1	2	yes	—
55	C₃₁×#391	C₂²	1	2	yes	—
56	C₃₁×#391	C₂²	1	2	yes	—
57	C₃₁×#391	C₂²	1	1	yes	characteristic
58	C₃₁×#391	C₂²	1	1	yes	characteristic
59	C₃₁×#391	C₂²	1	1	yes	characteristic
60	C₃₁×#391	C₂²	1	1	yes	characteristic
61	C₃₁×#389	C₂²	1	2	yes	—
62	C₃₁×#389	C₂²	1	2	yes	—
63	C₃₁×#389	C₂²	1	2	yes	—
64	C₃₁×#389	C₂²	1	2	yes	—
65	C₃₁×#389	C₂²	1	2	yes	—
66	C₃₁×#389	C₂²	1	1	yes	characteristic
67	C₃₁×#389	C₂²	1	1	yes	characteristic
68	C₃₁×#389	C₂²	1	1	yes	characteristic
69	C₃₁×#389	C₂²	1	1	yes	characteristic
70	C₃₁×#389	C₂²	1	1	yes	characteristic
71	C₃₁×#389	C₂²	1	1	yes	characteristic
72	C₃₁×#389	C₂²	1	1	yes	characteristic
73	C₃₁×#389	C₂²	1	1	yes	characteristic
74	C₃₁×#389	C₂²	1	2	yes	—
75	C₃₁×#389	C₂²	1	1	yes	characteristic
76	C₃₁×#389	C₂²	1	1	yes	characteristic
77	C₃₁×#388	C₂²	1	2	yes	—
78	C₃₁×#388	C₂²	1	2	yes	—
79	C₃₁×#387	C₂²	1	2	yes	—
80	C₃₁×#387	C₂²	1	2	yes	—
81	C₃₁×#387	C₂²	1	2	yes	—
82	C₃₁×#387	C₂²	1	2	yes	—
83	C₃₁×#387	C₂²	1	2	yes	—
84	C₃₁×#387	C₂²	1	2	yes	—
85	C₃₁×#387	C₂²	1	2	yes	—
86	C₃₁×#387	C₂²	1	2	yes	—
87	C₃₁×#387	C₂²	1	2	yes	—
88	C₃₁×#387	C₂²	1	2	yes	—
89	C₃₁×#386	C₂²	1	2	yes	—
90	C₃₁×#386	C₂²	1	2	yes	—
91	C₃₁×#385	C₂²	1	2	yes	—
92	C₃₁×#385	C₂²	1	2	yes	—
93	C₃₁×#385	C₂²	1	2	yes	—
94	C₃₁×#385	C₂²	1	2	yes	—
95	C₃₁×#385	C₂²	1	2	yes	—
96	C₃₁×#385	C₂²	1	2	yes	—
97	C₃₁×#384	C₂²	1	1	yes	characteristic
98	C₃₁×#384	C₂²	1	1	yes	characteristic
99	C₃₁×#384	C₂²	1	1	yes	characteristic
100	C₃₁×#383	C₂²	1	2	yes	—
101	C₃₁×#382	C₂²	1	2	yes	—
102	C₃₁×#381	C₂²	1	2	yes	—
103	C₃₁×#380	C₂²	1	2	yes	—
104	C₃₁×#380	C₂²	1	2	yes	—
105	C₃₁×#380	C₂²	1	1	yes	characteristic
106	C₃₁×#380	C₂²	1	1	yes	characteristic
107	C₃₁×#380	C₂²	1	1	yes	characteristic
108	C₃₁×#380	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×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
113	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
114	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
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	1	yes	characteristic
120	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
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	1	yes	characteristic
128	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
129	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
130	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
131	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
132	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
133	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
134	C₃₁×C₄⋊Q₈	—	4	2	no	—
135	C₃₁×#125	—	4	4	no	—
136	C₃₁×C₂²⋊Q₈	—	2	4	no	—
137	C₃₁×C₂²⋊Q₈	—	2	8	no	—
138	C₃₁×C₂²⋊Q₈	—	4	4	no	—
139	C₃₁×C₂²⋊Q₈	—	4	2	no	—
140	C₄×Q₈×C₃₁	—	4	2	no	—
141	C₄×D₄×C₃₁	—	2	4	no	—
142	C₄×D₄×C₃₁	—	2	4	no	—
143	C₄×D₄×C₃₁	Q₈	1	8	yes	complemented
144	C₂×C₄⋊C₄×C₃₁	—	2	4	no	—
145	C₂×C₄⋊C₄×C₃₁	—	4	4	no	—
146	C₂×C₄⋊C₄×C₃₁	—	4	2	no	—
147	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
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	2	yes	—
151	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
152	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
153	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
154	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
155	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
156	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
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	1	yes	characteristic
161	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
162	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
163	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
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	2	yes	—
173	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
174	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
175	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
176	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
177	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
178	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
179	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
180	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
181	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
182	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
183	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
184	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
185	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
186	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
187	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
188	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
189	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
190	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
191	C₂×C₄²×C₃₁	—	4	2	no	—
192	C₂×C₄²×C₃₁	—	4	2	no	—
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	1	yes	characteristic
197	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
198	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
199	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
200	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
201	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
202	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
203	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
204	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
205	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
206	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
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	2	yes	—
214	C₃₁×#95	C₂³	1	2	yes	—
215	C₃₁×#95	C₂³	1	2	yes	—
216	C₃₁×#95	C₂³	1	1	yes	characteristic
217	C₃₁×#95	C₂³	1	1	yes	characteristic
218	C₃₁×#95	C₂³	1	1	yes	characteristic
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	2	yes	—
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	—	4	2	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	4	no	—
251	C₂²×C₄×C₃₁	—	2	2	no	—
252	C₂²×C₄×C₃₁	—	2	4	no	—
253	C₂²×C₄×C₃₁	—	2	2	no	—
254	C₂²×C₄×C₃₁	—	2	2	no	—
255	C₂²×C₄×C₃₁	—	2	2	no	—
256	C₂²×C₄×C₃₁	—	2	2	no	—
257	C₂²×C₄×C₃₁	—	2	2	no	—
258	C₂²×C₄×C₃₁	—	2	2	no	—
259	C₂²×C₄×C₃₁	—	4	1	no	—
260	C₂²×C₄×C₃₁	—	4	1	no	—
261	C₂²×C₄×C₃₁	—	4	1	no	—
262	C₂²×C₄×C₃₁	—	4	1	no	—
263	C₂²×C₄×C₃₁	—	4	2	no	—
264	C₂²×C₄×C₃₁	—	4	1	no	—
265	C₂²×C₄×C₃₁	—	4	1	no	—
266	C₂²×C₄×C₃₁	—	4	2	no	—
267	C₂²×C₄×C₃₁	—	4	2	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	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	2	yes	—
278	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
279	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
280	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
281	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
282	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
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	1	yes	characteristic
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	2	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	4	no	—
300	C₄⋊C₄×C₃₁	—	2	4	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	2	no	—
307	C₄⋊C₄×C₃₁	—	2	2	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	—	4	2	no	—
320	C₄⋊C₄×C₃₁	—	4	2	no	—
321	C₄⋊C₄×C₃₁	—	4	2	no	—
322	C₄⋊C₄×C₃₁	—	4	2	no	—
323	C₄⋊C₄×C₃₁	—	4	2	no	—
324	C₄⋊C₄×C₃₁	C₂×Q₈	1	4	yes	—
325	C₂²⋊C₄×C₃₁	—	2	2	no	—
326	C₂²⋊C₄×C₃₁	—	2	4	no	—
327	C₂²⋊C₄×C₃₁	—	2	4	no	—
328	C₂²⋊C₄×C₃₁	—	2	2	no	—
329	C₂²⋊C₄×C₃₁	—	2	2	no	—
330	C₂²⋊C₄×C₃₁	—	4	2	no	—
331	C₂²⋊C₄×C₃₁	—	4	2	no	—
332	C₂²⋊C₄×C₃₁	—	4	2	no	—
333	C₂²⋊C₄×C₃₁	—	4	2	no	—
334	C₂²⋊C₄×C₃₁	C₂×Q₈	1	4	yes	—
335	C₂²⋊C₄×C₃₁	C₂×Q₈	1	4	yes	—
336	C₂²⋊C₄×C₃₁	#41	1	4	yes	—
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	2	no	—
342	C₄²×C₃₁	—	2	2	no	—
343	C₄²×C₃₁	—	2	2	no	—
344	C₄²×C₃₁	—	4	1	no	—
345	C₄²×C₃₁	—	4	1	no	—
346	C₄²×C₃₁	—	4	1	no	—
347	C₄²×C₃₁	—	4	1	no	—
348	C₄²×C₃₁	—	4	2	no	—
349	C₄²×C₃₁	—	4	1	no	—
350	C₄²×C₃₁	—	4	2	no	—
351	C₄²×C₃₁	C₂×Q₈	1	4	yes	—
352	#35017	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	4	no	—
369	Q₈×C₃₁	—	8	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	1	no	—
382	C₂×C₄×C₃₁	—	2	1	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	1	no	—
391	C₂×C₄×C₃₁	—	2	2	no	—
392	C₂×C₄×C₃₁	—	2	2	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	2	no	—
400	C₂×C₄×C₃₁	—	2	2	no	—
401	C₂×C₄×C₃₁	—	2	1	no	—
402	C₂×C₄×C₃₁	—	2	1	no	—
403	C₂×C₄×C₃₁	—	2	1	no	—
404	C₂×C₄×C₃₁	—	2	2	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	1	no	—
415	C₂×C₄×C₃₁	—	2	2	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	1	no	—
420	C₂×C₄×C₃₁	—	2	2	no	—
421	C₂×C₄×C₃₁	—	2	2	no	—
422	C₂×C₄×C₃₁	—	2	2	no	—
423	C₂×C₄×C₃₁	—	4	4	no	—
424	C₂×C₄×C₃₁	—	4	4	no	—
425	C₂×C₄×C₃₁	—	4	4	no	—
426	C₂×C₄×C₃₁	—	4	4	no	—
427	C₂×C₄×C₃₁	—	4	8	no	—
428	C₂×C₄×C₃₁	—	4	4	no	—
429	C₂×C₄×C₃₁	—	8	4	no	—
430	C₂×C₄×C₃₁	C₂²×Q₈	1	2	yes	—
431	C₂×C₄×C₃₁	C₂²×Q₈	1	2	yes	—
432	C₂×C₄×C₃₁	C₂²×Q₈	1	2	yes	—
433	C₂×C₄×C₃₁	C₂²×Q₈	1	2	yes	—
434	C₂×C₄×C₃₁	C₂²×Q₈	1	2	yes	—
435	C₂×C₄×C₃₁	C₂×#41	1	2	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	H(5,𝔽₂)	1	2	yes	—
440	C₂×C₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
441	C₂×C₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
442	#2863	C₂×C₃₁	1	1	yes	characteristic, complemented
443	#2859	C₂×C₃₁	1	1	yes	characteristic, complemented
444	#2857	C₂×C₃₁	1	1	yes	characteristic, complemented
445	#2855	C₂×C₃₁	1	1	yes	characteristic, complemented
446	#2667	C₂×C₃₁	1	2	yes	complemented
447	#2666	C₂×C₃₁	1	2	yes	complemented
448	#2585	C₂×C₃₁	1	2	yes	complemented
449	#2556	C₂×C₃₁	1	2	yes	complemented
450	#2507	C₂×C₃₁	1	1	yes	characteristic, complemented
451	#2502	C₂×C₃₁	1	1	yes	characteristic, complemented
452	#2497	C₂×C₃₁	1	1	yes	characteristic, complemented
453	#2487	C₂×C₃₁	1	1	yes	characteristic
454	#2473	C₂×C₃₁	1	2	yes	complemented
455	#2451	C₂×C₃₁	1	1	yes	characteristic, complemented
456	#2449	C₂×C₃₁	1	2	yes	—
457	#2440	C₂×C₃₁	1	1	yes	characteristic, complemented
458	#2423	C₂×C₃₁	1	1	yes	characteristic, complemented
459	#2417	C₂×C₃₁	1	1	yes	characteristic
460	#2329	C₂×C₃₁	1	2	yes	complemented
461	#2318	C₂×C₃₁	1	2	yes	—
462	C₄×C₂²⋊Q₈	C₂×C₃₁	1	1	yes	characteristic, complemented
463	C₂×#389	C₂×C₃₁	1	1	yes	characteristic, complemented
464	C₄²×D₄	C₂×C₃₁	1	1	yes	characteristic
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	C₂×H(5,𝔽₂)	1	1	yes	characteristic
483	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
484	C₂²×C₃₁	C₂×2₋¹⁺⁴	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	2	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	—	4	2	no	—
506	C₄×C₃₁	#539	1	4	yes	—
507	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
508	C₂×#125	C₂²×C₃₁	1	2	yes	—
509	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	—
510	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
511	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
512	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	—
513	C₂×C₄×Q₈	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×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
517	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
518	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
519	C₂²×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
520	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
521	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
522	#400	C₂²×C₃₁	1	2	yes	—
523	#400	C₂²×C₃₁	1	2	yes	—
524	#399	C₂²×C₃₁	1	2	yes	—
525	#399	C₂²×C₃₁	1	2	yes	—
526	#398	C₂²×C₃₁	1	2	yes	—
527	#398	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	#395	C₂²×C₃₁	1	2	yes	—
538	#391	C₂²×C₃₁	1	2	yes	—
539	#391	C₂²×C₃₁	1	2	yes	—
540	#391	C₂²×C₃₁	1	1	yes	characteristic
541	#391	C₂²×C₃₁	1	1	yes	characteristic
542	#391	C₂²×C₃₁	1	1	yes	characteristic
543	#391	C₂²×C₃₁	1	1	yes	characteristic
544	#389	C₂²×C₃₁	1	2	yes	—
545	#389	C₂²×C₃₁	1	2	yes	—
546	#389	C₂²×C₃₁	1	2	yes	—
547	#389	C₂²×C₃₁	1	2	yes	—
548	#389	C₂²×C₃₁	1	2	yes	—
549	#389	C₂²×C₃₁	1	1	yes	characteristic
550	#389	C₂²×C₃₁	1	1	yes	characteristic
551	#389	C₂²×C₃₁	1	1	yes	characteristic
552	#389	C₂²×C₃₁	1	1	yes	characteristic
553	#389	C₂²×C₃₁	1	1	yes	characteristic
554	#389	C₂²×C₃₁	1	1	yes	characteristic
555	#389	C₂²×C₃₁	1	1	yes	characteristic
556	#389	C₂²×C₃₁	1	1	yes	characteristic
557	#389	C₂²×C₃₁	1	2	yes	—
558	#389	C₂²×C₃₁	1	1	yes	characteristic
559	#389	C₂²×C₃₁	1	1	yes	characteristic
560	#388	C₂²×C₃₁	1	2	yes	—
561	#388	C₂²×C₃₁	1	2	yes	—
562	#387	C₂²×C₃₁	1	2	yes	—
563	#387	C₂²×C₃₁	1	2	yes	—
564	#387	C₂²×C₃₁	1	2	yes	—
565	#387	C₂²×C₃₁	1	2	yes	—
566	#387	C₂²×C₃₁	1	2	yes	—
567	#387	C₂²×C₃₁	1	2	yes	—
568	#387	C₂²×C₃₁	1	2	yes	—
569	#387	C₂²×C₃₁	1	2	yes	—
570	#387	C₂²×C₃₁	1	2	yes	—
571	#387	C₂²×C₃₁	1	2	yes	—
572	#386	C₂²×C₃₁	1	2	yes	—
573	#386	C₂²×C₃₁	1	2	yes	—
574	#385	C₂²×C₃₁	1	2	yes	—
575	#385	C₂²×C₃₁	1	2	yes	—
576	#385	C₂²×C₃₁	1	2	yes	—
577	#385	C₂²×C₃₁	1	2	yes	—
578	#385	C₂²×C₃₁	1	2	yes	—
579	#385	C₂²×C₃₁	1	2	yes	—
580	#384	C₂²×C₃₁	1	1	yes	characteristic
581	#384	C₂²×C₃₁	1	1	yes	characteristic
582	#384	C₂²×C₃₁	1	1	yes	characteristic
583	#383	C₂²×C₃₁	1	2	yes	—
584	#382	C₂²×C₃₁	1	2	yes	—
585	#381	C₂²×C₃₁	1	2	yes	—
586	#380	C₂²×C₃₁	1	2	yes	—
587	#380	C₂²×C₃₁	1	2	yes	—
588	#380	C₂²×C₃₁	1	1	yes	characteristic
589	#380	C₂²×C₃₁	1	1	yes	characteristic
590	#380	C₂²×C₃₁	1	1	yes	characteristic
591	#380	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×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
596	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
597	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
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	1	yes	characteristic
603	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
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×#533	1	1	yes	characteristic
609	C₂×C₃₁	C₂×#539	1	1	yes	characteristic
610	C₂×C₃₁	#3460	1	1	yes	characteristic
611	C₂×C₃₁	#3501	1	1	yes	characteristic
612	C₂×C₃₁	#3503	1	1	yes	characteristic
613	C₂×C₃₁	#3515	1	1	yes	characteristic
614	C₂×C₃₁	#3519	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	1	yes	characteristic
620	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
621	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
622	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
623	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
624	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
625	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
626	C₄⋊Q₈	—	4	2	no	—
627	#125	—	4	4	no	—
628	C₂²⋊Q₈	—	2	4	no	—
629	C₂²⋊Q₈	—	2	8	no	—
630	C₂²⋊Q₈	—	4	4	no	—
631	C₂²⋊Q₈	—	4	2	no	—
632	C₄×Q₈	—	4	2	no	—
633	C₄×D₄	—	2	4	no	—
634	C₄×D₄	—	2	4	no	—
635	C₄×D₄	Q₈×C₃₁	1	8	yes	complemented
636	C₂×C₄⋊C₄	—	2	4	no	—
637	C₂×C₄⋊C₄	—	4	4	no	—
638	C₂×C₄⋊C₄	—	4	2	no	—
639	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
640	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
641	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
642	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
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	2	yes	—
646	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
647	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
648	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
649	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
650	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
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	2	yes	—
654	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
655	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
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	2	yes	—
665	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
666	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
667	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
668	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
669	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
670	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
671	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
672	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
673	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
674	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
675	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
676	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
677	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
678	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
679	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
680	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
681	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
682	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
683	C₂×C₄²	—	4	2	no	—
684	C₂×C₄²	—	4	2	no	—
685	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
686	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
687	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
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	2	yes	—
693	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
694	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
695	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
696	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
697	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
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	1	yes	characteristic
705	#95	C₂³×C₃₁	1	1	yes	characteristic
706	#95	C₂³×C₃₁	1	1	yes	characteristic
707	#95	C₂³×C₃₁	1	1	yes	characteristic
708	#95	C₂³×C₃₁	1	1	yes	characteristic
709	#95	C₂³×C₃₁	1	1	yes	characteristic
710	#95	C₂³×C₃₁	1	2	yes	—
711	#95	C₂³×C₃₁	1	2	yes	—
712	#95	C₂³×C₃₁	1	2	yes	—
713	#95	C₂³×C₃₁	1	2	yes	—
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	#35017	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	—	4	2	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	4	no	—
744	C₂²×C₄	—	2	2	no	—
745	C₂²×C₄	—	2	4	no	—
746	C₂²×C₄	—	2	2	no	—
747	C₂²×C₄	—	2	2	no	—
748	C₂²×C₄	—	2	2	no	—
749	C₂²×C₄	—	2	2	no	—
750	C₂²×C₄	—	2	2	no	—
751	C₂²×C₄	—	2	2	no	—
752	C₂²×C₄	—	4	1	no	—
753	C₂²×C₄	—	4	1	no	—
754	C₂²×C₄	—	4	1	no	—
755	C₂²×C₄	—	4	1	no	—
756	C₂²×C₄	—	4	2	no	—
757	C₂²×C₄	—	4	1	no	—
758	C₂²×C₄	—	4	1	no	—
759	C₂²×C₄	—	4	2	no	—
760	C₂²×C₄	—	4	2	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	2	yes	—
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	1	yes	characteristic
772	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
773	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
774	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
775	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
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	1	yes	characteristic
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	2	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	4	no	—
793	C₄⋊C₄	—	2	4	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	2	no	—
800	C₄⋊C₄	—	2	2	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	—	4	2	no	—
813	C₄⋊C₄	—	4	2	no	—
814	C₄⋊C₄	—	4	2	no	—
815	C₄⋊C₄	—	4	2	no	—
816	C₄⋊C₄	—	4	2	no	—
817	C₄⋊C₄	C₂×Q₈×C₃₁	1	4	yes	—
818	C₂²⋊C₄	—	2	2	no	—
819	C₂²⋊C₄	—	2	4	no	—
820	C₂²⋊C₄	—	2	4	no	—
821	C₂²⋊C₄	—	2	2	no	—
822	C₂²⋊C₄	—	2	2	no	—
823	C₂²⋊C₄	—	4	2	no	—
824	C₂²⋊C₄	—	4	2	no	—
825	C₂²⋊C₄	—	4	2	no	—
826	C₂²⋊C₄	—	4	2	no	—
827	C₂²⋊C₄	C₂×Q₈×C₃₁	1	4	yes	—
828	C₂²⋊C₄	C₂×Q₈×C₃₁	1	4	yes	—
829	C₂²⋊C₄	#41×C₃₁	1	4	yes	—
830	C₄²	—	2	2	no	—
831	C₄²	—	2	2	no	—
832	C₄²	—	2	2	no	—
833	C₄²	—	2	2	no	—
834	C₄²	—	2	2	no	—
835	C₄²	—	2	2	no	—
836	C₄²	—	2	2	no	—
837	C₄²	—	4	1	no	—
838	C₄²	—	4	1	no	—
839	C₄²	—	4	1	no	—
840	C₄²	—	4	1	no	—
841	C₄²	—	4	2	no	—
842	C₄²	—	4	1	no	—
843	C₄²	—	4	2	no	—
844	C₄²	C₂×Q₈×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	4	no	—
861	Q₈	—	8	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	1	no	—
874	C₂×C₄	—	2	1	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	1	no	—
883	C₂×C₄	—	2	2	no	—
884	C₂×C₄	—	2	2	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	2	no	—
892	C₂×C₄	—	2	2	no	—
893	C₂×C₄	—	2	1	no	—
894	C₂×C₄	—	2	1	no	—
895	C₂×C₄	—	2	1	no	—
896	C₂×C₄	—	2	2	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	1	no	—
907	C₂×C₄	—	2	2	no	—
908	C₂×C₄	—	2	1	no	—
909	C₂×C₄	—	2	2	no	—
910	C₂×C₄	—	2	2	no	—
911	C₂×C₄	—	2	1	no	—
912	C₂×C₄	—	2	2	no	—
913	C₂×C₄	—	2	2	no	—
914	C₂×C₄	—	2	2	no	—
915	C₂×C₄	—	4	4	no	—
916	C₂×C₄	—	4	4	no	—
917	C₂×C₄	—	4	4	no	—
918	C₂×C₄	—	4	4	no	—
919	C₂×C₄	—	4	8	no	—
920	C₂×C₄	—	4	4	no	—
921	C₂×C₄	—	8	4	no	—
922	C₂×C₄	C₂²×Q₈×C₃₁	1	2	yes	—
923	C₂×C₄	C₂²×Q₈×C₃₁	1	2	yes	—
924	C₂×C₄	C₂²×Q₈×C₃₁	1	2	yes	—
925	C₂×C₄	C₂²×Q₈×C₃₁	1	2	yes	—
926	C₂×C₄	C₂²×Q₈×C₃₁	1	2	yes	—
927	C₂×C₄	C₂×#41×C₃₁	1	2	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	C₃₁×H(5,𝔽₂)	1	2	yes	—
932	C₂×C₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
933	C₂×C₄	C₃₁×2₋¹⁺⁴	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	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
952	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
953	C₂²	C₂×C₃₁×2₋¹⁺⁴	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	2	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	2	no	—
971	C₄	—	4	1	no	—
972	C₄	—	4	2	no	—
973	C₄	—	4	2	no	—
974	C₄	—	4	2	no	—
975	C₄	C₃₁×#539	1	4	yes	—
976	C₂	—	2	4	no	—
977	C₂	—	4	2	no	—
978	C₂	C₂×C₃₁×#533	1	1	yes	characteristic
979	C₂	C₂×C₃₁×#539	1	1	yes	characteristic
980	C₂	C₃₁×#3460	1	1	yes	characteristic
981	C₂	C₃₁×#3501	1	1	yes	characteristic
982	C₂	C₃₁×#3503	1	1	yes	characteristic
983	C₂	C₃₁×#3515	1	1	yes	characteristic
984	C₂	C₃₁×#3519	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₃₁×#2863	C₂	semidirect
2. C₃₁×#2859	C₂	semidirect
3. C₃₁×#2857	C₂	semidirect
4. C₃₁×#2855	C₂	semidirect
5. C₃₁×#2667	C₂	semidirect
6. C₃₁×#2666	C₂	semidirect
7. C₃₁×#2585	C₂	semidirect
8. C₃₁×#2556	C₂	semidirect
9. C₃₁×#2507	C₂	semidirect
10. C₃₁×#2502	C₂	semidirect
11. C₃₁×#2497	C₂	semidirect
13. C₃₁×#2473	C₂	semidirect
14. C₃₁×#2451	C₂	semidirect
16. C₃₁×#2440	C₂	semidirect
17. C₃₁×#2423	C₂	semidirect
19. C₃₁×#2329	C₂	semidirect
21. C₄×C₃₁×C₂²⋊Q₈	C₂	semidirect
22. C₂×C₃₁×#389	C₂	semidirect
143. C₄×D₄×C₃₁	Q₈	semidirect
352. #35017	C₃₁	direct (N × H)
442. #2863	C₂×C₃₁	semidirect
443. #2859	C₂×C₃₁	semidirect
444. #2857	C₂×C₃₁	semidirect
445. #2855	C₂×C₃₁	semidirect
446. #2667	C₂×C₃₁	semidirect
447. #2666	C₂×C₃₁	semidirect
448. #2585	C₂×C₃₁	semidirect
449. #2556	C₂×C₃₁	semidirect
450. #2507	C₂×C₃₁	semidirect
451. #2502	C₂×C₃₁	semidirect
452. #2497	C₂×C₃₁	semidirect
454. #2473	C₂×C₃₁	semidirect
455. #2451	C₂×C₃₁	semidirect
457. #2440	C₂×C₃₁	semidirect
458. #2423	C₂×C₃₁	semidirect
460. #2329	C₂×C₃₁	semidirect
462. C₄×C₂²⋊Q₈	C₂×C₃₁	semidirect
463. C₂×#389	C₂×C₃₁	semidirect
635. C₄×D₄	Q₈×C₃₁	semidirect
729. C₃₁	#35017	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×#2863	2
C₃₁×#2859	2
C₃₁×#2857	2
C₃₁×#2855	2
C₃₁×#2667	2
C₃₁×#2666	2
C₃₁×#2585	2
C₃₁×#2556	2
C₃₁×#2507	2
C₃₁×#2502	2
C₃₁×#2497	2
C₃₁×#2487	2
C₃₁×#2473	2
C₃₁×#2451	2
C₃₁×#2449	2
C₃₁×#2440	2
C₃₁×#2423	2
C₃₁×#2417	2
C₃₁×#2329	2
C₃₁×#2318	2
C₄×C₃₁×C₂²⋊Q₈	2
C₂×C₃₁×#389	2
C₄²×D₄×C₃₁	2
#35017	31

Subgroups — C31×#35017 #21491776

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#35017 #21491776