Subgroups — C₃₁×#34233 #21490992

Order 7936.

2826 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#525	C₂	1	1	yes	maximal, characteristic
2	C₃₁×#2361	C₂	1	2	yes	maximal, complemented
3	C₃₁×#2360	C₂	1	2	yes	maximal, complemented
4	C₃₁×#2358	C₂	1	4	yes	maximal, complemented
5	C₃₁×#2353	C₂	1	2	yes	maximal, complemented
6	C₃₁×#2349	C₂	1	2	yes	maximal, complemented
7	C₃₁×#2347	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#2346	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#2341	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#2339	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#2335	C₂	1	4	yes	maximal, complemented
12	C₃₁×#2318	C₂	1	2	yes	maximal, complemented
13	C₄×C₃₁×C₂²⋊Q₈	C₂	1	2	yes	maximal, complemented
14	C₄×C₃₁×#121	C₂	1	2	yes	maximal, complemented
15	C₂×C₃₁×#380	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#2275	C₂	1	2	yes	maximal, complemented
17	C₂×C₄×C₂²⋊C₄×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×#41×C₃₁	C₂²	1	1	yes	characteristic
19	C₂⁴×C₄×C₃₁	C₂²	1	1	yes	characteristic
20	C₃₁×#525	C₄	1	16	yes	complemented
21	C₂×C₃₁×#123	C₂²	1	2	yes	—
22	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
23	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
24	C₂×C₃₁×#121	C₂²	1	1	yes	characteristic
25	C₂×C₃₁×#121	C₂²	1	1	yes	characteristic
26	C₂×C₃₁×#120	C₂²	1	2	yes	—
27	C₂×C₄×Q₈×C₃₁	C₂²	1	2	yes	complemented
28	C₂×C₄×D₄×C₃₁	C₂²	1	4	yes	—
29	C₂×C₄×D₄×C₃₁	C₂²	1	4	yes	—
30	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
31	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
32	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	complemented
33	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
34	C₂²×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
35	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
36	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
37	C₂²×C₄²×C₃₁	C₂²	1	2	yes	—
38	C₃₁×#391	C₂²	1	2	yes	complemented
39	C₃₁×#390	C₂²	1	4	yes	—
40	C₃₁×#390	C₂²	1	2	yes	complemented
41	C₃₁×#389	C₂²	1	4	yes	complemented
42	C₃₁×#389	C₂²	1	2	yes	complemented
43	C₃₁×#389	C₂²	1	2	yes	complemented
44	C₃₁×#388	C₂²	1	4	yes	—
45	C₃₁×#388	C₂²	1	4	yes	—
46	C₃₁×#388	C₂²	1	4	yes	complemented
47	C₃₁×#388	C₂²	1	4	yes	complemented
48	C₃₁×#387	C₂²	1	4	yes	complemented
49	C₃₁×#387	C₂²	1	4	yes	complemented
50	C₃₁×#386	C₂²	1	4	yes	—
51	C₃₁×#386	C₂²	1	4	yes	—
52	C₃₁×#386	C₂²	1	4	yes	—
53	C₃₁×#385	C₂²	1	4	yes	—
54	C₃₁×#385	C₂²	1	4	yes	—
55	C₃₁×#385	C₂²	1	4	yes	complemented
56	C₃₁×#383	C₂²	1	2	yes	complemented
57	C₃₁×#382	C₂²	1	2	yes	complemented
58	C₃₁×#381	C₂²	1	2	yes	complemented
59	C₃₁×#380	C₂²	1	2	yes	—
60	C₃₁×#380	C₂²	1	1	yes	characteristic
61	C₃₁×#380	C₂²	1	1	yes	characteristic
62	C₃₁×#380	C₂²	1	2	yes	—
63	C₃₁×#380	C₂²	1	2	yes	—
64	C₃₁×#380	C₂²	1	2	yes	complemented
65	C₄×C₄⋊C₄×C₃₁	C₂²	1	4	yes	complemented
66	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	complemented
67	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	complemented
68	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	complemented
69	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
70	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
71	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
72	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
73	C₄×C₂²⋊C₄×C₃₁	C₂²	1	4	yes	—
74	C₄×C₂²⋊C₄×C₃₁	C₂²	1	4	yes	—
75	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
76	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
77	C₄×C₂²⋊C₄×C₃₁	C₂²	1	4	yes	complemented
78	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	complemented
79	C₃₁×#376	C₂²	1	2	yes	complemented
80	C₂×C₃₁×#95	C₂²	1	2	yes	—
81	C₂×C₃₁×#95	C₂²	1	1	yes	characteristic
82	C₂×C₃₁×#95	C₂²	1	1	yes	characteristic
83	C₂×C₃₁×#95	C₂²	1	2	yes	complemented
84	C₂⁵×C₃₁	C₂³	1	1	yes	characteristic
85	C₂×#41×C₃₁	—	4	4	no	—
86	C₂×#41×C₃₁	C₂×C₄	1	8	yes	complemented
87	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
88	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
89	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
90	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
91	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
92	C₂³×C₄×C₃₁	—	4	4	no	—
93	C₂³×C₄×C₃₁	C₂×C₄	1	8	yes	complemented
94	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
95	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
96	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
97	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
98	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
99	C₂³×C₄×C₃₁	C₂³	1	4	yes	—
100	C₂³×C₄×C₃₁	C₂³	1	4	yes	—
101	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
102	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
103	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
104	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
105	C₃₁×#123	C₂×C₄	1	16	yes	complemented
106	C₃₁×C₂²⋊Q₈	C₂×C₄	1	8	yes	complemented
107	C₃₁×C₂²⋊Q₈	C₂×C₄	1	8	yes	complemented
108	C₃₁×#121	C₂×C₄	1	8	yes	complemented
109	C₃₁×#121	C₂×C₄	1	8	yes	complemented
110	C₃₁×#120	C₂×C₄	1	16	yes	complemented
111	C₄×Q₈×C₃₁	—	4	4	no	—
112	C₄×D₄×C₃₁	—	2	16	no	—
113	C₄×D₄×C₃₁	—	4	4	no	—
114	C₄×D₄×C₃₁	—	4	8	no	—
115	C₄×D₄×C₃₁	C₂×C₄	1	16	yes	complemented
116	C₄×D₄×C₃₁	C₂×C₄	1	16	yes	complemented
117	C₃₁×#117	C₂×C₄	1	8	yes	complemented
118	C₂×C₄⋊C₄×C₃₁	—	4	4	no	—
119	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
120	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
121	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
122	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
123	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
124	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
125	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
126	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
127	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
128	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
129	C₂×C₂²⋊C₄×C₃₁	—	2	8	no	—
130	C₂×C₂²⋊C₄×C₃₁	—	4	4	no	—
131	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
132	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
133	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
134	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
135	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
136	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
137	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
138	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
139	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
140	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
141	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
142	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
143	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
144	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
145	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
146	C₂×C₄²×C₃₁	—	4	4	no	—
147	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
148	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
149	C₂×C₄²×C₃₁	C₂³	1	4	yes	—
150	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
151	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
152	C₂×C₄²×C₃₁	C₂³	1	4	yes	—
153	C₂×C₄²×C₃₁	C₂³	1	4	yes	—
154	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
155	C₃₁×#95	C₂³	1	1	yes	characteristic
156	C₃₁×#95	C₂³	1	2	yes	—
157	C₃₁×#95	C₂³	1	1	yes	characteristic
158	C₃₁×#95	C₂³	1	1	yes	characteristic
159	C₃₁×#95	C₂³	1	1	yes	characteristic
160	C₃₁×#95	C₂³	1	2	yes	—
161	C₃₁×#95	C₂³	1	2	yes	—
162	C₃₁×#95	C₂³	1	2	yes	—
163	C₃₁×#95	C₂³	1	4	yes	—
164	C₃₁×#95	C₂³	1	4	yes	—
165	C₃₁×#95	C₂³	1	4	yes	—
166	C₃₁×#95	C₂³	1	4	yes	—
167	C₃₁×#95	C₂³	1	4	yes	—
168	C₃₁×#95	C₂³	1	4	yes	—
169	C₃₁×#95	C₂³	1	4	yes	—
170	C₂⁴×C₃₁	—	2	4	no	—
171	C₂⁴×C₃₁	—	2	2	no	—
172	C₂⁴×C₃₁	—	2	2	no	—
173	C₂⁴×C₃₁	—	4	2	no	—
174	C₂⁴×C₃₁	C₂²×C₄	1	4	yes	—
175	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
176	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
177	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
178	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
179	#41×C₃₁	—	4	16	no	—
180	C₂×Q₈×C₃₁	—	2	4	no	—
181	C₂×Q₈×C₃₁	C₂²×C₄	1	4	yes	—
182	C₂×D₄×C₃₁	—	2	8	no	—
183	C₂×D₄×C₃₁	—	2	4	no	—
184	C₂×D₄×C₃₁	—	2	4	no	—
185	C₂×D₄×C₃₁	—	2	4	no	—
186	C₂×D₄×C₃₁	—	4	4	no	—
187	C₂×D₄×C₃₁	C₂²×C₄	1	8	yes	—
188	C₂×D₄×C₃₁	C₂²×C₄	1	8	yes	—
189	C₂×D₄×C₃₁	C₂²×C₄	1	4	yes	—
190	C₂×D₄×C₃₁	C₂²×C₄	1	8	yes	—
191	C₂²×C₄×C₃₁	—	2	4	no	—
192	C₂²×C₄×C₃₁	—	2	4	no	—
193	C₂²×C₄×C₃₁	—	2	4	no	—
194	C₂²×C₄×C₃₁	—	2	4	no	—
195	C₂²×C₄×C₃₁	—	2	4	no	—
196	C₂²×C₄×C₃₁	—	2	8	no	—
197	C₂²×C₄×C₃₁	—	2	4	no	—
198	C₂²×C₄×C₃₁	—	2	4	no	—
199	C₂²×C₄×C₃₁	—	2	8	no	—
200	C₂²×C₄×C₃₁	—	4	16	no	—
201	C₂²×C₄×C₃₁	—	4	2	no	—
202	C₂²×C₄×C₃₁	—	4	2	no	—
203	C₂²×C₄×C₃₁	—	4	2	no	—
204	C₂²×C₄×C₃₁	—	4	2	no	—
205	C₂²×C₄×C₃₁	—	4	2	no	—
206	C₂²×C₄×C₃₁	—	4	4	no	—
207	C₂²×C₄×C₃₁	—	4	4	no	—
208	C₂²×C₄×C₃₁	—	4	4	no	—
209	C₂²×C₄×C₃₁	—	4	4	no	—
210	C₂²×C₄×C₃₁	—	4	4	no	—
211	C₂²×C₄×C₃₁	C₂²×C₄	1	4	yes	—
212	C₂²×C₄×C₃₁	C₂²×C₄	1	4	yes	—
213	C₂²×C₄×C₃₁	C₂²×C₄	1	4	yes	—
214	C₂²×C₄×C₃₁	C₂²×C₄	1	4	yes	—
215	C₂²×C₄×C₃₁	C₂²×C₄	1	4	yes	—
216	C₂²×C₄×C₃₁	C₂²×C₄	1	8	yes	—
217	C₂²×C₄×C₃₁	C₂²×C₄	1	4	yes	—
218	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
219	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
220	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
221	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
222	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
223	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
224	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
225	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
226	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
227	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
228	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
229	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
230	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
231	C₄⋊C₄×C₃₁	—	2	8	no	—
232	C₄⋊C₄×C₃₁	—	2	4	no	—
233	C₄⋊C₄×C₃₁	—	2	4	no	—
234	C₄⋊C₄×C₃₁	—	4	4	no	—
235	C₄⋊C₄×C₃₁	—	4	4	no	—
236	C₄⋊C₄×C₃₁	—	4	4	no	—
237	C₄⋊C₄×C₃₁	C₂²×C₄	1	4	yes	—
238	C₄⋊C₄×C₃₁	C₂²×C₄	1	4	yes	—
239	C₄⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
240	C₄⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
241	C₂²⋊C₄×C₃₁	—	2	4	no	—
242	C₂²⋊C₄×C₃₁	—	2	8	no	—
243	C₂²⋊C₄×C₃₁	—	2	4	no	—
244	C₂²⋊C₄×C₃₁	—	2	4	no	—
245	C₂²⋊C₄×C₃₁	—	2	8	no	—
246	C₂²⋊C₄×C₃₁	—	4	2	no	—
247	C₂²⋊C₄×C₃₁	—	4	2	no	—
248	C₂²⋊C₄×C₃₁	—	4	4	no	—
249	C₂²⋊C₄×C₃₁	—	4	4	no	—
250	C₂²⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
251	C₂²⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
252	C₂²⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
253	C₂²⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
254	C₂²⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
255	C₂²⋊C₄×C₃₁	#41	1	8	yes	complemented
256	C₄²×C₃₁	—	2	8	no	—
257	C₄²×C₃₁	—	2	4	no	—
258	C₄²×C₃₁	—	2	4	no	—
259	C₄²×C₃₁	—	4	2	no	—
260	C₄²×C₃₁	—	4	2	no	—
261	C₄²×C₃₁	—	4	4	no	—
262	C₄²×C₃₁	—	4	4	no	—
263	C₄²×C₃₁	C₂²×C₄	1	8	yes	—
264	#34233	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
265	C₂³×C₃₁	—	2	2	no	—
266	C₂³×C₃₁	—	2	2	no	—
267	C₂³×C₃₁	—	2	2	no	—
268	C₂³×C₃₁	—	2	1	no	—
269	C₂³×C₃₁	—	2	1	no	—
270	C₂³×C₃₁	—	2	8	no	—
271	C₂³×C₃₁	—	2	8	no	—
272	C₂³×C₃₁	—	2	2	no	—
273	C₂³×C₃₁	—	2	4	no	—
274	C₂³×C₃₁	—	2	1	no	—
275	C₂³×C₃₁	—	2	2	no	—
276	C₂³×C₃₁	—	2	4	no	—
277	C₂³×C₃₁	—	2	2	no	—
278	C₂³×C₃₁	—	2	2	no	—
279	C₂³×C₃₁	—	2	1	no	—
280	C₂³×C₃₁	—	4	4	no	—
281	C₂³×C₃₁	—	4	8	no	—
282	C₂³×C₃₁	—	4	8	no	—
283	C₂³×C₃₁	C₂³×C₄	1	2	yes	—
284	C₂³×C₃₁	C₂³×C₄	1	4	yes	—
285	C₂³×C₃₁	C₂³×C₄	1	2	yes	—
286	C₂³×C₃₁	C₂³×C₄	1	2	yes	—
287	C₂³×C₃₁	C₂×#41	1	4	yes	—
288	C₂³×C₃₁	H(5,𝔽₂)	1	2	yes	—
289	C₂³×C₃₁	2₋¹⁺⁴	1	2	yes	—
290	C₂³×C₃₁	C₂⁵	1	1	yes	characteristic
291	Q₈×C₃₁	—	2	8	no	—
292	D₄×C₃₁	—	2	16	no	—
293	D₄×C₃₁	—	2	16	no	—
294	D₄×C₃₁	—	2	8	no	—
295	D₄×C₃₁	—	4	8	no	—
296	C₂×C₄×C₃₁	—	2	4	no	—
297	C₂×C₄×C₃₁	—	2	2	no	—
298	C₂×C₄×C₃₁	—	2	2	no	—
299	C₂×C₄×C₃₁	—	2	2	no	—
300	C₂×C₄×C₃₁	—	2	2	no	—
301	C₂×C₄×C₃₁	—	2	2	no	—
302	C₂×C₄×C₃₁	—	2	4	no	—
303	C₂×C₄×C₃₁	—	2	2	no	—
304	C₂×C₄×C₃₁	—	2	2	no	—
305	C₂×C₄×C₃₁	—	2	2	no	—
306	C₂×C₄×C₃₁	—	2	2	no	—
307	C₂×C₄×C₃₁	—	2	8	no	—
308	C₂×C₄×C₃₁	—	2	8	no	—
309	C₂×C₄×C₃₁	—	2	8	no	—
310	C₂×C₄×C₃₁	—	2	4	no	—
311	C₂×C₄×C₃₁	—	2	2	no	—
312	C₂×C₄×C₃₁	—	2	2	no	—
313	C₂×C₄×C₃₁	—	2	4	no	—
314	C₂×C₄×C₃₁	—	2	2	no	—
315	C₂×C₄×C₃₁	—	2	2	no	—
316	C₂×C₄×C₃₁	—	2	4	no	—
317	C₂×C₄×C₃₁	—	2	4	no	—
318	C₂×C₄×C₃₁	—	2	4	no	—
319	C₂×C₄×C₃₁	—	2	2	no	—
320	C₂×C₄×C₃₁	—	2	4	no	—
321	C₂×C₄×C₃₁	—	2	2	no	—
322	C₂×C₄×C₃₁	—	4	4	no	—
323	C₂×C₄×C₃₁	—	4	4	no	—
324	C₂×C₄×C₃₁	—	4	4	no	—
325	C₂×C₄×C₃₁	—	4	8	no	—
326	C₂×C₄×C₃₁	—	4	8	no	—
327	C₂×C₄×C₃₁	—	4	8	no	—
328	C₂×C₄×C₃₁	—	8	8	no	—
329	C₂×C₄×C₃₁	—	8	8	no	—
330	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
331	C₂×C₄×C₃₁	C₂³×C₄	1	4	yes	—
332	C₂×C₄×C₃₁	C₂³×C₄	1	4	yes	—
333	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
334	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
335	C₂×C₄×C₃₁	C₂³×C₄	1	4	yes	—
336	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
337	C₂×C₄×C₃₁	C₂×#41	1	4	yes	—
338	C₂×C₄×C₃₁	C₂×#41	1	4	yes	—
339	C₂×C₄×C₃₁	H(5,𝔽₂)	1	4	yes	—
340	C₂×#525	C₂×C₃₁	1	1	yes	characteristic
341	#2361	C₂×C₃₁	1	2	yes	complemented
342	#2360	C₂×C₃₁	1	2	yes	complemented
343	#2358	C₂×C₃₁	1	4	yes	complemented
344	#2353	C₂×C₃₁	1	2	yes	complemented
345	#2349	C₂×C₃₁	1	2	yes	complemented
346	#2347	C₂×C₃₁	1	1	yes	characteristic, complemented
347	#2346	C₂×C₃₁	1	1	yes	characteristic, complemented
348	#2341	C₂×C₃₁	1	1	yes	characteristic, complemented
349	#2339	C₂×C₃₁	1	1	yes	characteristic, complemented
350	#2335	C₂×C₃₁	1	4	yes	complemented
351	#2318	C₂×C₃₁	1	2	yes	complemented
352	C₄×C₂²⋊Q₈	C₂×C₃₁	1	2	yes	complemented
353	C₄×#121	C₂×C₃₁	1	2	yes	complemented
354	C₂×#380	C₂×C₃₁	1	1	yes	characteristic, complemented
355	#2275	C₂×C₃₁	1	2	yes	complemented
356	C₂×C₄×C₂²⋊C₄	C₂×C₃₁	1	1	yes	characteristic, complemented
357	C₂²×C₃₁	—	2	2	no	—
358	C₂²×C₃₁	—	2	2	no	—
359	C₂²×C₃₁	—	2	2	no	—
360	C₂²×C₃₁	—	2	2	no	—
361	C₂²×C₃₁	—	2	4	no	—
362	C₂²×C₃₁	—	2	4	no	—
363	C₂²×C₃₁	—	2	4	no	—
364	C₂²×C₃₁	—	2	4	no	—
365	C₂²×C₃₁	—	2	4	no	—
366	C₂²×C₃₁	—	2	2	no	—
367	C₂²×C₃₁	—	2	2	no	—
368	C₂²×C₃₁	—	2	4	no	—
369	C₂²×C₃₁	—	2	4	no	—
370	C₂²×C₃₁	—	2	2	no	—
371	C₂²×C₃₁	—	4	16	no	—
372	C₂²×C₃₁	—	4	4	no	—
373	C₂²×C₃₁	—	4	2	no	—
374	C₂²×C₃₁	—	4	4	no	—
375	C₂²×C₃₁	—	4	2	no	—
376	C₂²×C₃₁	C₄×#41	1	4	yes	—
377	C₂²×C₃₁	#520	1	4	yes	—
378	C₂²×C₃₁	C₂⁴×C₄	1	1	yes	characteristic
379	C₂²×C₃₁	C₂²×#41	1	2	yes	—
380	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	2	yes	—
381	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
382	C₂²×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
383	C₄×C₃₁	—	2	4	no	—
384	C₄×C₃₁	—	2	2	no	—
385	C₄×C₃₁	—	2	2	no	—
386	C₄×C₃₁	—	2	2	no	—
387	C₄×C₃₁	—	2	4	no	—
388	C₄×C₃₁	—	2	4	no	—
389	C₄×C₃₁	—	2	4	no	—
390	C₄×C₃₁	—	2	4	no	—
391	C₄×C₃₁	—	4	2	no	—
392	C₄×C₃₁	—	4	4	no	—
393	C₄×C₃₁	—	4	4	no	—
394	C₄×C₃₁	—	4	2	no	—
395	C₄×C₃₁	#518	1	4	yes	—
396	C₂²×#41	C₂²×C₃₁	1	1	yes	characteristic
397	C₂⁴×C₄	C₂²×C₃₁	1	1	yes	characteristic
398	#525	C₄×C₃₁	1	16	yes	complemented
399	C₂×#123	C₂²×C₃₁	1	2	yes	—
400	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
401	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
402	C₂×#121	C₂²×C₃₁	1	1	yes	characteristic
403	C₂×#121	C₂²×C₃₁	1	1	yes	characteristic
404	C₂×#120	C₂²×C₃₁	1	2	yes	—
405	C₂×C₄×Q₈	C₂²×C₃₁	1	2	yes	complemented
406	C₂×C₄×D₄	C₂²×C₃₁	1	4	yes	—
407	C₂×C₄×D₄	C₂²×C₃₁	1	4	yes	—
408	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
409	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
410	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	complemented
411	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
412	C₂²×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
413	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
414	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
415	C₂²×C₄²	C₂²×C₃₁	1	2	yes	—
416	#391	C₂²×C₃₁	1	2	yes	complemented
417	#390	C₂²×C₃₁	1	4	yes	—
418	#390	C₂²×C₃₁	1	2	yes	complemented
419	#389	C₂²×C₃₁	1	4	yes	complemented
420	#389	C₂²×C₃₁	1	2	yes	complemented
421	#389	C₂²×C₃₁	1	2	yes	complemented
422	#388	C₂²×C₃₁	1	4	yes	—
423	#388	C₂²×C₃₁	1	4	yes	—
424	#388	C₂²×C₃₁	1	4	yes	complemented
425	#388	C₂²×C₃₁	1	4	yes	complemented
426	#387	C₂²×C₃₁	1	4	yes	complemented
427	#387	C₂²×C₃₁	1	4	yes	complemented
428	#386	C₂²×C₃₁	1	4	yes	—
429	#386	C₂²×C₃₁	1	4	yes	—
430	#386	C₂²×C₃₁	1	4	yes	—
431	#385	C₂²×C₃₁	1	4	yes	—
432	#385	C₂²×C₃₁	1	4	yes	—
433	#385	C₂²×C₃₁	1	4	yes	complemented
434	#383	C₂²×C₃₁	1	2	yes	complemented
435	#382	C₂²×C₃₁	1	2	yes	complemented
436	#381	C₂²×C₃₁	1	2	yes	complemented
437	#380	C₂²×C₃₁	1	2	yes	—
438	#380	C₂²×C₃₁	1	1	yes	characteristic
439	#380	C₂²×C₃₁	1	1	yes	characteristic
440	#380	C₂²×C₃₁	1	2	yes	—
441	#380	C₂²×C₃₁	1	2	yes	—
442	#380	C₂²×C₃₁	1	2	yes	complemented
443	C₄×C₄⋊C₄	C₂²×C₃₁	1	4	yes	complemented
444	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	complemented
445	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	complemented
446	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	complemented
447	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
448	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
449	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
450	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
451	C₄×C₂²⋊C₄	C₂²×C₃₁	1	4	yes	—
452	C₄×C₂²⋊C₄	C₂²×C₃₁	1	4	yes	—
453	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
454	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
455	C₄×C₂²⋊C₄	C₂²×C₃₁	1	4	yes	complemented
456	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	complemented
457	#376	C₂²×C₃₁	1	2	yes	complemented
458	C₂×#95	C₂²×C₃₁	1	2	yes	—
459	C₂×#95	C₂²×C₃₁	1	1	yes	characteristic
460	C₂×#95	C₂²×C₃₁	1	1	yes	characteristic
461	C₂×#95	C₂²×C₃₁	1	2	yes	complemented
462	C₂×C₃₁	—	2	4	no	—
463	C₂×C₃₁	—	2	4	no	—
464	C₂×C₃₁	—	4	4	no	—
465	C₂×C₃₁	—	4	2	no	—
466	C₂×C₃₁	C₂×C₄×#41	1	1	yes	characteristic
467	C₂×C₃₁	C₂×#518	1	1	yes	characteristic
468	C₂×C₃₁	C₂×#520	1	1	yes	characteristic
469	C₂×C₃₁	#3519	1	2	yes	—
470	C₂×C₃₁	#3520	1	2	yes	—
471	C₂⁵	C₂³×C₃₁	1	1	yes	characteristic
472	C₂×#41	—	4	4	no	—
473	C₂×#41	C₂×C₄×C₃₁	1	8	yes	complemented
474	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
475	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
476	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
477	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
478	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
479	C₂³×C₄	—	4	4	no	—
480	C₂³×C₄	C₂×C₄×C₃₁	1	8	yes	complemented
481	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
482	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
483	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
484	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
485	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
486	C₂³×C₄	C₂³×C₃₁	1	4	yes	—
487	C₂³×C₄	C₂³×C₃₁	1	4	yes	—
488	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
489	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
490	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
491	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
492	#123	C₂×C₄×C₃₁	1	16	yes	complemented
493	C₂²⋊Q₈	C₂×C₄×C₃₁	1	8	yes	complemented
494	C₂²⋊Q₈	C₂×C₄×C₃₁	1	8	yes	complemented
495	#121	C₂×C₄×C₃₁	1	8	yes	complemented
496	#121	C₂×C₄×C₃₁	1	8	yes	complemented
497	#120	C₂×C₄×C₃₁	1	16	yes	complemented
498	C₄×Q₈	—	4	4	no	—
499	C₄×D₄	—	2	16	no	—
500	C₄×D₄	—	4	4	no	—
501	C₄×D₄	—	4	8	no	—
502	C₄×D₄	C₂×C₄×C₃₁	1	16	yes	complemented
503	C₄×D₄	C₂×C₄×C₃₁	1	16	yes	complemented
504	#117	C₂×C₄×C₃₁	1	8	yes	complemented
505	C₂×C₄⋊C₄	—	4	4	no	—
506	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
507	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
508	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
509	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
510	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
511	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
512	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
513	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
514	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
515	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
516	C₂×C₂²⋊C₄	—	2	8	no	—
517	C₂×C₂²⋊C₄	—	4	4	no	—
518	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
519	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
520	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
521	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
522	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
523	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
524	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
525	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
526	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
527	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
528	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
529	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
530	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
531	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
532	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
533	C₂×C₄²	—	4	4	no	—
534	C₂×C₄²	C₂³×C₃₁	1	4	yes	—
535	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
536	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
537	C₂×C₄²	C₂³×C₃₁	1	4	yes	—
538	C₂×C₄²	C₂³×C₃₁	1	4	yes	—
539	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
540	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
541	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
542	#95	C₂³×C₃₁	1	1	yes	characteristic
543	#95	C₂³×C₃₁	1	2	yes	—
544	#95	C₂³×C₃₁	1	1	yes	characteristic
545	#95	C₂³×C₃₁	1	1	yes	characteristic
546	#95	C₂³×C₃₁	1	1	yes	characteristic
547	#95	C₂³×C₃₁	1	2	yes	—
548	#95	C₂³×C₃₁	1	2	yes	—
549	#95	C₂³×C₃₁	1	2	yes	—
550	#95	C₂³×C₃₁	1	4	yes	—
551	#95	C₂³×C₃₁	1	4	yes	—
552	#95	C₂³×C₃₁	1	4	yes	—
553	#95	C₂³×C₃₁	1	4	yes	—
554	#95	C₂³×C₃₁	1	4	yes	—
555	#95	C₂³×C₃₁	1	4	yes	—
556	#95	C₂³×C₃₁	1	4	yes	—
557	C₃₁	#34233	1	1	yes	characteristic, direct product factor, Sylow
558	C₂⁴	—	2	4	no	—
559	C₂⁴	—	2	2	no	—
560	C₂⁴	—	2	2	no	—
561	C₂⁴	—	4	2	no	—
562	C₂⁴	C₂²×C₄×C₃₁	1	4	yes	—
563	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
564	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
565	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
566	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
567	#41	—	4	16	no	—
568	C₂×Q₈	—	2	4	no	—
569	C₂×Q₈	C₂²×C₄×C₃₁	1	4	yes	—
570	C₂×D₄	—	2	8	no	—
571	C₂×D₄	—	2	4	no	—
572	C₂×D₄	—	2	4	no	—
573	C₂×D₄	—	2	4	no	—
574	C₂×D₄	—	4	4	no	—
575	C₂×D₄	C₂²×C₄×C₃₁	1	8	yes	—
576	C₂×D₄	C₂²×C₄×C₃₁	1	8	yes	—
577	C₂×D₄	C₂²×C₄×C₃₁	1	4	yes	—
578	C₂×D₄	C₂²×C₄×C₃₁	1	8	yes	—
579	C₂²×C₄	—	2	4	no	—
580	C₂²×C₄	—	2	4	no	—
581	C₂²×C₄	—	2	4	no	—
582	C₂²×C₄	—	2	4	no	—
583	C₂²×C₄	—	2	4	no	—
584	C₂²×C₄	—	2	8	no	—
585	C₂²×C₄	—	2	4	no	—
586	C₂²×C₄	—	2	4	no	—
587	C₂²×C₄	—	2	8	no	—
588	C₂²×C₄	—	4	16	no	—
589	C₂²×C₄	—	4	2	no	—
590	C₂²×C₄	—	4	2	no	—
591	C₂²×C₄	—	4	2	no	—
592	C₂²×C₄	—	4	2	no	—
593	C₂²×C₄	—	4	2	no	—
594	C₂²×C₄	—	4	4	no	—
595	C₂²×C₄	—	4	4	no	—
596	C₂²×C₄	—	4	4	no	—
597	C₂²×C₄	—	4	4	no	—
598	C₂²×C₄	—	4	4	no	—
599	C₂²×C₄	C₂²×C₄×C₃₁	1	4	yes	—
600	C₂²×C₄	C₂²×C₄×C₃₁	1	4	yes	—
601	C₂²×C₄	C₂²×C₄×C₃₁	1	4	yes	—
602	C₂²×C₄	C₂²×C₄×C₃₁	1	4	yes	—
603	C₂²×C₄	C₂²×C₄×C₃₁	1	4	yes	—
604	C₂²×C₄	C₂²×C₄×C₃₁	1	8	yes	—
605	C₂²×C₄	C₂²×C₄×C₃₁	1	4	yes	—
606	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
607	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
608	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
609	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
610	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
611	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
612	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
613	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
614	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
615	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
616	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
617	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
618	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
619	C₄⋊C₄	—	2	8	no	—
620	C₄⋊C₄	—	2	4	no	—
621	C₄⋊C₄	—	2	4	no	—
622	C₄⋊C₄	—	4	4	no	—
623	C₄⋊C₄	—	4	4	no	—
624	C₄⋊C₄	—	4	4	no	—
625	C₄⋊C₄	C₂²×C₄×C₃₁	1	4	yes	—
626	C₄⋊C₄	C₂²×C₄×C₃₁	1	4	yes	—
627	C₄⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
628	C₄⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
629	C₂²⋊C₄	—	2	4	no	—
630	C₂²⋊C₄	—	2	8	no	—
631	C₂²⋊C₄	—	2	4	no	—
632	C₂²⋊C₄	—	2	4	no	—
633	C₂²⋊C₄	—	2	8	no	—
634	C₂²⋊C₄	—	4	2	no	—
635	C₂²⋊C₄	—	4	2	no	—
636	C₂²⋊C₄	—	4	4	no	—
637	C₂²⋊C₄	—	4	4	no	—
638	C₂²⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
639	C₂²⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
640	C₂²⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
641	C₂²⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
642	C₂²⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
643	C₂²⋊C₄	#41×C₃₁	1	8	yes	complemented
644	C₄²	—	2	8	no	—
645	C₄²	—	2	4	no	—
646	C₄²	—	2	4	no	—
647	C₄²	—	4	2	no	—
648	C₄²	—	4	2	no	—
649	C₄²	—	4	4	no	—
650	C₄²	—	4	4	no	—
651	C₄²	C₂²×C₄×C₃₁	1	8	yes	—
652	C₂³	—	2	2	no	—
653	C₂³	—	2	2	no	—
654	C₂³	—	2	2	no	—
655	C₂³	—	2	1	no	—
656	C₂³	—	2	1	no	—
657	C₂³	—	2	8	no	—
658	C₂³	—	2	8	no	—
659	C₂³	—	2	2	no	—
660	C₂³	—	2	4	no	—
661	C₂³	—	2	1	no	—
662	C₂³	—	2	2	no	—
663	C₂³	—	2	4	no	—
664	C₂³	—	2	2	no	—
665	C₂³	—	2	2	no	—
666	C₂³	—	2	1	no	—
667	C₂³	—	4	4	no	—
668	C₂³	—	4	8	no	—
669	C₂³	—	4	8	no	—
670	C₂³	C₂³×C₄×C₃₁	1	2	yes	—
671	C₂³	C₂³×C₄×C₃₁	1	4	yes	—
672	C₂³	C₂³×C₄×C₃₁	1	2	yes	—
673	C₂³	C₂³×C₄×C₃₁	1	2	yes	—
674	C₂³	C₂×#41×C₃₁	1	4	yes	—
675	C₂³	C₃₁×H(5,𝔽₂)	1	2	yes	—
676	C₂³	C₃₁×2₋¹⁺⁴	1	2	yes	—
677	C₂³	C₂⁵×C₃₁	1	1	yes	characteristic
678	Q₈	—	2	8	no	—
679	D₄	—	2	16	no	—
680	D₄	—	2	16	no	—
681	D₄	—	2	8	no	—
682	D₄	—	4	8	no	—
683	C₂×C₄	—	2	4	no	—
684	C₂×C₄	—	2	2	no	—
685	C₂×C₄	—	2	2	no	—
686	C₂×C₄	—	2	2	no	—
687	C₂×C₄	—	2	2	no	—
688	C₂×C₄	—	2	2	no	—
689	C₂×C₄	—	2	4	no	—
690	C₂×C₄	—	2	2	no	—
691	C₂×C₄	—	2	2	no	—
692	C₂×C₄	—	2	2	no	—
693	C₂×C₄	—	2	2	no	—
694	C₂×C₄	—	2	8	no	—
695	C₂×C₄	—	2	8	no	—
696	C₂×C₄	—	2	8	no	—
697	C₂×C₄	—	2	4	no	—
698	C₂×C₄	—	2	2	no	—
699	C₂×C₄	—	2	2	no	—
700	C₂×C₄	—	2	4	no	—
701	C₂×C₄	—	2	2	no	—
702	C₂×C₄	—	2	2	no	—
703	C₂×C₄	—	2	4	no	—
704	C₂×C₄	—	2	4	no	—
705	C₂×C₄	—	2	4	no	—
706	C₂×C₄	—	2	2	no	—
707	C₂×C₄	—	2	4	no	—
708	C₂×C₄	—	2	2	no	—
709	C₂×C₄	—	4	4	no	—
710	C₂×C₄	—	4	4	no	—
711	C₂×C₄	—	4	4	no	—
712	C₂×C₄	—	4	8	no	—
713	C₂×C₄	—	4	8	no	—
714	C₂×C₄	—	4	8	no	—
715	C₂×C₄	—	8	8	no	—
716	C₂×C₄	—	8	8	no	—
717	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
718	C₂×C₄	C₂³×C₄×C₃₁	1	4	yes	—
719	C₂×C₄	C₂³×C₄×C₃₁	1	4	yes	—
720	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
721	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
722	C₂×C₄	C₂³×C₄×C₃₁	1	4	yes	—
723	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
724	C₂×C₄	C₂×#41×C₃₁	1	4	yes	—
725	C₂×C₄	C₂×#41×C₃₁	1	4	yes	—
726	C₂×C₄	C₃₁×H(5,𝔽₂)	1	4	yes	—
727	C₂²	—	2	2	no	—
728	C₂²	—	2	2	no	—
729	C₂²	—	2	2	no	—
730	C₂²	—	2	2	no	—
731	C₂²	—	2	4	no	—
732	C₂²	—	2	4	no	—
733	C₂²	—	2	4	no	—
734	C₂²	—	2	4	no	—
735	C₂²	—	2	4	no	—
736	C₂²	—	2	2	no	—
737	C₂²	—	2	2	no	—
738	C₂²	—	2	4	no	—
739	C₂²	—	2	4	no	—
740	C₂²	—	2	2	no	—
741	C₂²	—	4	16	no	—
742	C₂²	—	4	4	no	—
743	C₂²	—	4	2	no	—
744	C₂²	—	4	2	no	—
745	C₂²	—	4	4	no	—
746	C₂²	C₄×#41×C₃₁	1	4	yes	—
747	C₂²	C₃₁×#520	1	4	yes	—
748	C₂²	C₂⁴×C₄×C₃₁	1	1	yes	characteristic
749	C₂²	C₂²×#41×C₃₁	1	2	yes	—
750	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	2	yes	—
751	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
752	C₂²	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
753	C₄	—	2	4	no	—
754	C₄	—	2	2	no	—
755	C₄	—	2	2	no	—
756	C₄	—	2	2	no	—
757	C₄	—	2	4	no	—
758	C₄	—	2	4	no	—
759	C₄	—	2	4	no	—
760	C₄	—	2	4	no	—
761	C₄	—	4	2	no	—
762	C₄	—	4	4	no	—
763	C₄	—	4	4	no	—
764	C₄	—	4	2	no	—
765	C₄	C₃₁×#518	1	4	yes	—
766	C₂	—	2	4	no	—
767	C₂	—	2	4	no	—
768	C₂	—	4	2	no	—
769	C₂	—	4	4	no	—
770	C₂	C₂×C₄×#41×C₃₁	1	1	yes	characteristic
771	C₂	C₂×C₃₁×#518	1	1	yes	characteristic
772	C₂	C₂×C₃₁×#520	1	1	yes	characteristic
773	C₂	C₃₁×#3519	1	2	yes	—
774	C₂	C₃₁×#3520	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃₁	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₃₁
Frattini, cosocle	C₂³	C₂⁵×C₃₁
prime radical	C₂×C₃₁×#525	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃₁×#2361	C₂	semidirect
3. C₃₁×#2360	C₂	semidirect
4. C₃₁×#2358	C₂	semidirect
5. C₃₁×#2353	C₂	semidirect
6. C₃₁×#2349	C₂	semidirect
7. C₃₁×#2347	C₂	semidirect
8. C₃₁×#2346	C₂	semidirect
9. C₃₁×#2341	C₂	semidirect
10. C₃₁×#2339	C₂	semidirect
11. C₃₁×#2335	C₂	semidirect
12. C₃₁×#2318	C₂	semidirect
13. C₄×C₃₁×C₂²⋊Q₈	C₂	semidirect
14. C₄×C₃₁×#121	C₂	semidirect
15. C₂×C₃₁×#380	C₂	semidirect
16. C₃₁×#2275	C₂	semidirect
17. C₂×C₄×C₂²⋊C₄×C₃₁	C₂	semidirect
20. C₃₁×#525	C₄	semidirect
27. C₂×C₄×Q₈×C₃₁	C₂²	semidirect
32. C₂×C₄×D₄×C₃₁	C₂²	semidirect
38. C₃₁×#391	C₂²	semidirect
40. C₃₁×#390	C₂²	semidirect
41. C₃₁×#389	C₂²	semidirect
42. C₃₁×#389	C₂²	semidirect
43. C₃₁×#389	C₂²	semidirect
46. C₃₁×#388	C₂²	semidirect
47. C₃₁×#388	C₂²	semidirect
48. C₃₁×#387	C₂²	semidirect
49. C₃₁×#387	C₂²	semidirect
55. C₃₁×#385	C₂²	semidirect
56. C₃₁×#383	C₂²	semidirect
57. C₃₁×#382	C₂²	semidirect
58. C₃₁×#381	C₂²	semidirect
64. C₃₁×#380	C₂²	semidirect
65. C₄×C₄⋊C₄×C₃₁	C₂²	semidirect
66. C₄×C₄⋊C₄×C₃₁	C₂²	semidirect
67. C₄×C₄⋊C₄×C₃₁	C₂²	semidirect
68. C₄×C₄⋊C₄×C₃₁	C₂²	semidirect
77. C₄×C₂²⋊C₄×C₃₁	C₂²	semidirect
78. C₄×C₂²⋊C₄×C₃₁	C₂²	semidirect
79. C₃₁×#376	C₂²	semidirect
83. C₂×C₃₁×#95	C₂²	semidirect
86. C₂×#41×C₃₁	C₂×C₄	semidirect
93. C₂³×C₄×C₃₁	C₂×C₄	semidirect
105. C₃₁×#123	C₂×C₄	semidirect
106. C₃₁×C₂²⋊Q₈	C₂×C₄	semidirect
107. C₃₁×C₂²⋊Q₈	C₂×C₄	semidirect
108. C₃₁×#121	C₂×C₄	semidirect
109. C₃₁×#121	C₂×C₄	semidirect
110. C₃₁×#120	C₂×C₄	semidirect
115. C₄×D₄×C₃₁	C₂×C₄	semidirect
116. C₄×D₄×C₃₁	C₂×C₄	semidirect
117. C₃₁×#117	C₂×C₄	semidirect
255. C₂²⋊C₄×C₃₁	#41	semidirect
264. #34233	C₃₁	direct (N × H)
341. #2361	C₂×C₃₁	semidirect
342. #2360	C₂×C₃₁	semidirect
343. #2358	C₂×C₃₁	semidirect
344. #2353	C₂×C₃₁	semidirect
345. #2349	C₂×C₃₁	semidirect
346. #2347	C₂×C₃₁	semidirect
347. #2346	C₂×C₃₁	semidirect
348. #2341	C₂×C₃₁	semidirect
349. #2339	C₂×C₃₁	semidirect
350. #2335	C₂×C₃₁	semidirect
351. #2318	C₂×C₃₁	semidirect
352. C₄×C₂²⋊Q₈	C₂×C₃₁	semidirect
353. C₄×#121	C₂×C₃₁	semidirect
354. C₂×#380	C₂×C₃₁	semidirect
355. #2275	C₂×C₃₁	semidirect
356. C₂×C₄×C₂²⋊C₄	C₂×C₃₁	semidirect
398. #525	C₄×C₃₁	semidirect
405. C₂×C₄×Q₈	C₂²×C₃₁	semidirect
410. C₂×C₄×D₄	C₂²×C₃₁	semidirect
416. #391	C₂²×C₃₁	semidirect
418. #390	C₂²×C₃₁	semidirect
419. #389	C₂²×C₃₁	semidirect
420. #389	C₂²×C₃₁	semidirect
421. #389	C₂²×C₃₁	semidirect
424. #388	C₂²×C₃₁	semidirect
425. #388	C₂²×C₃₁	semidirect
426. #387	C₂²×C₃₁	semidirect
427. #387	C₂²×C₃₁	semidirect
433. #385	C₂²×C₃₁	semidirect
434. #383	C₂²×C₃₁	semidirect
435. #382	C₂²×C₃₁	semidirect
436. #381	C₂²×C₃₁	semidirect
442. #380	C₂²×C₃₁	semidirect
443. C₄×C₄⋊C₄	C₂²×C₃₁	semidirect
444. C₄×C₄⋊C₄	C₂²×C₃₁	semidirect
445. C₄×C₄⋊C₄	C₂²×C₃₁	semidirect
446. C₄×C₄⋊C₄	C₂²×C₃₁	semidirect
455. C₄×C₂²⋊C₄	C₂²×C₃₁	semidirect
456. C₄×C₂²⋊C₄	C₂²×C₃₁	semidirect
457. #376	C₂²×C₃₁	semidirect
461. C₂×#95	C₂²×C₃₁	semidirect
473. C₂×#41	C₂×C₄×C₃₁	semidirect
480. C₂³×C₄	C₂×C₄×C₃₁	semidirect
492. #123	C₂×C₄×C₃₁	semidirect
493. C₂²⋊Q₈	C₂×C₄×C₃₁	semidirect
494. C₂²⋊Q₈	C₂×C₄×C₃₁	semidirect
495. #121	C₂×C₄×C₃₁	semidirect
496. #121	C₂×C₄×C₃₁	semidirect
497. #120	C₂×C₄×C₃₁	semidirect
502. C₄×D₄	C₂×C₄×C₃₁	semidirect
503. C₄×D₄	C₂×C₄×C₃₁	semidirect
504. #117	C₂×C₄×C₃₁	semidirect
557. C₃₁	#34233	direct (N × H)
643. C₂²⋊C₄	#41×C₃₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃₁×#525	2
C₃₁×#2361	2
C₃₁×#2360	2
C₃₁×#2358	2
C₃₁×#2353	2
C₃₁×#2349	2
C₃₁×#2347	2
C₃₁×#2346	2
C₃₁×#2341	2
C₃₁×#2339	2
C₃₁×#2335	2
C₃₁×#2318	2
C₄×C₃₁×C₂²⋊Q₈	2
C₄×C₃₁×#121	2
C₂×C₃₁×#380	2
C₃₁×#2275	2
C₂×C₄×C₂²⋊C₄×C₃₁	2
#34233	31

Subgroups — C31×#34233 #21490992

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#34233 #21490992