Subgroups — C₃₁×#36704 #21493463

Order 7936.

3018 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#535	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃₁×#121	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#2849	C₂	1	2	yes	maximal, complemented
4	C₃₁×#2688	C₂	1	4	yes	maximal, complemented
5	C₃₁×#2686	C₂	1	4	yes	maximal, complemented
6	C₃₁×#2673	C₂	1	4	yes	maximal, complemented
7	C₃₁×#2671	C₂	1	4	yes	maximal, complemented
8	C₃₁×#2613	C₂	1	2	yes	maximal, complemented
9	C₃₁×#2484	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#2482	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#2412	C₂	1	2	yes	maximal, complemented
12	C₃₁×#2410	C₂	1	2	yes	maximal, complemented
13	C₃₁×#2406	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#2404	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#2308	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#41×C₃₁	C₂²	1	1	yes	characteristic
17	C₂³×D₄×C₃₁	C₂²	1	1	yes	characteristic
18	C₂³×D₄×C₃₁	C₂²	1	1	yes	characteristic
19	C₂³×D₄×C₃₁	C₂²	1	1	yes	characteristic
20	C₂⁴×C₄×C₃₁	C₂²	1	1	yes	characteristic
21	C₃₁×#535	—	2	8	no	—
22	C₂×C₃₁×#127	C₂²	1	2	yes	complemented
23	C₂×C₃₁×#124	C₂²	1	2	yes	complemented
24	C₂×C₃₁×#123	C₂²	1	2	yes	—
25	C₂×C₃₁×#123	C₂²	1	4	yes	complemented
26	C₂×C₃₁×#121	—	2	8	no	—
27	C₂×C₃₁×#121	C₂²	1	4	yes	—
28	C₂×C₃₁×#121	C₂²	1	4	yes	—
29	C₂×C₃₁×#121	C₂²	1	2	yes	complemented
30	C₂×C₃₁×#121	C₂²	1	2	yes	complemented
31	C₂×C₃₁×#121	C₂²	1	4	yes	complemented
32	C₂×C₃₁×#120	C₂²	1	2	yes	—
33	C₂×C₃₁×#120	C₂²	1	2	yes	—
34	C₂×C₃₁×#120	C₂²	1	2	yes	—
35	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
36	C₂²×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
37	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
38	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
39	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
40	C₃₁×#400	C₂²	1	2	yes	complemented
41	C₃₁×#399	C₂²	1	2	yes	complemented
42	C₃₁×#398	C₂²	1	2	yes	complemented
43	C₃₁×#397	C₂²	1	4	yes	complemented
44	C₃₁×#397	C₂²	1	2	yes	complemented
45	C₃₁×#395	C₂²	1	2	yes	complemented
46	C₃₁×#394	C₂²	1	4	yes	complemented
47	C₃₁×#394	C₂²	1	4	yes	complemented
48	C₃₁×#394	C₂²	1	2	yes	complemented
49	C₃₁×#394	C₂²	1	4	yes	complemented
50	C₃₁×#394	C₂²	1	4	yes	complemented
51	C₃₁×#393	C₂²	1	2	yes	complemented
52	C₃₁×#392	C₂²	1	4	yes	complemented
53	C₃₁×#392	C₂²	1	4	yes	complemented
54	C₃₁×#392	C₂²	1	2	yes	complemented
55	C₃₁×#392	C₂²	1	4	yes	complemented
56	C₃₁×#388	C₂²	1	4	yes	complemented
57	C₃₁×#387	C₂²	1	4	yes	complemented
58	C₃₁×#386	C₂²	1	2	yes	—
59	C₃₁×#386	C₂²	1	2	yes	—
60	C₃₁×#386	C₂²	1	4	yes	complemented
61	C₃₁×#386	C₂²	1	4	yes	complemented
62	C₃₁×#386	C₂²	1	4	yes	complemented
63	C₃₁×#386	C₂²	1	4	yes	complemented
64	C₃₁×#386	C₂²	1	4	yes	complemented
65	C₃₁×#386	C₂²	1	4	yes	complemented
66	C₃₁×#385	C₂²	1	2	yes	—
67	C₃₁×#385	C₂²	1	2	yes	—
68	C₃₁×#385	C₂²	1	4	yes	complemented
69	C₃₁×#385	C₂²	1	4	yes	complemented
70	C₃₁×#381	C₂²	1	1	yes	characteristic
71	C₃₁×#381	C₂²	1	1	yes	characteristic
72	C₃₁×#381	C₂²	1	2	yes	—
73	C₃₁×#381	C₂²	1	4	yes	complemented
74	C₃₁×#380	C₂²	1	4	yes	complemented
75	C₃₁×#379	C₂²	1	2	yes	—
76	C₃₁×#379	C₂²	1	2	yes	—
77	C₂⁵×C₃₁	C₂³	1	1	yes	characteristic
78	C₂⁵×C₃₁	C₂³	1	1	yes	characteristic
79	C₂⁵×C₃₁	C₂³	1	1	yes	characteristic
80	C₂×#41×C₃₁	—	2	4	no	—
81	C₂×#41×C₃₁	—	4	4	no	—
82	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
83	C₂²×D₄×C₃₁	—	2	4	no	—
84	C₂²×D₄×C₃₁	—	2	4	no	—
85	C₂²×D₄×C₃₁	—	4	4	no	—
86	C₂²×D₄×C₃₁	—	4	4	no	—
87	C₂²×D₄×C₃₁	—	4	4	no	—
88	C₂²×D₄×C₃₁	D₄	1	8	yes	complemented
89	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
90	C₂²×D₄×C₃₁	C₂³	1	4	yes	—
91	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
92	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
93	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
94	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
95	C₂²×D₄×C₃₁	C₂³	1	4	yes	—
96	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
97	C₂²×D₄×C₃₁	C₂³	1	4	yes	—
98	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
99	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
100	C₂³×C₄×C₃₁	—	2	4	no	—
101	C₂³×C₄×C₃₁	—	4	4	no	—
102	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
103	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
104	C₂³×C₄×C₃₁	C₂³	1	4	yes	—
105	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
106	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
107	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
108	C₂³×C₄×C₃₁	C₂³	1	4	yes	—
109	C₃₁×#127	—	2	8	no	—
110	C₃₁×#124	—	2	8	no	—
111	C₃₁×#123	—	4	8	no	—
112	C₃₁×#123	—	4	4	no	—
113	C₃₁×#121	—	2	16	no	—
114	C₃₁×#121	—	2	16	no	—
115	C₃₁×#121	—	2	8	no	—
116	C₃₁×#121	—	2	8	no	—
117	C₃₁×#121	—	4	8	no	—
118	C₃₁×#120	—	2	8	no	—
119	C₃₁×#120	—	2	8	no	—
120	C₃₁×#120	—	4	4	no	—
121	C₃₁×#117	—	2	4	no	—
122	C₂×C₄⋊C₄×C₃₁	—	2	4	no	—
123	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
124	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
125	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
126	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
127	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
128	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
129	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
130	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
131	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
132	C₂×C₂²⋊C₄×C₃₁	—	4	4	no	—
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	2	yes	—
139	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	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	4	yes	—
144	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
145	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
146	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
147	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
148	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
149	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
150	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
151	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
152	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
153	C₃₁×#95	C₂³	1	2	yes	—
154	C₃₁×#95	C₂³	1	4	yes	—
155	C₃₁×#95	C₂³	1	4	yes	—
156	C₃₁×#95	C₂³	1	2	yes	—
157	C₃₁×#95	C₂³	1	4	yes	—
158	C₃₁×#95	C₂³	1	4	yes	—
159	C₃₁×#95	C₂³	1	2	yes	—
160	C₃₁×#95	C₂³	1	4	yes	—
161	C₃₁×#95	C₂³	1	4	yes	—
162	C₃₁×#95	C₂³	1	2	yes	—
163	C₂⁴×C₃₁	—	2	4	no	—
164	C₂⁴×C₃₁	—	2	4	no	—
165	C₂⁴×C₃₁	—	2	2	no	—
166	C₂⁴×C₃₁	—	2	4	no	—
167	C₂⁴×C₃₁	—	4	2	no	—
168	C₂⁴×C₃₁	—	4	2	no	—
169	C₂⁴×C₃₁	—	4	2	no	—
170	C₂⁴×C₃₁	—	4	2	no	—
171	C₂⁴×C₃₁	—	4	2	no	—
172	C₂⁴×C₃₁	—	4	2	no	—
173	C₂⁴×C₃₁	C₂×D₄	1	4	yes	—
174	C₂⁴×C₃₁	C₂×D₄	1	4	yes	—
175	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
176	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
177	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
178	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
179	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
180	#41×C₃₁	—	4	16	no	—
181	C₂×Q₈×C₃₁	—	2	2	no	—
182	C₂×Q₈×C₃₁	—	4	2	no	—
183	C₂×D₄×C₃₁	—	2	4	no	—
184	C₂×D₄×C₃₁	—	2	8	no	—
185	C₂×D₄×C₃₁	—	2	8	no	—
186	C₂×D₄×C₃₁	—	2	4	no	—
187	C₂×D₄×C₃₁	—	2	4	no	—
188	C₂×D₄×C₃₁	—	2	4	no	—
189	C₂×D₄×C₃₁	—	2	4	no	—
190	C₂×D₄×C₃₁	—	2	4	no	—
191	C₂×D₄×C₃₁	—	2	4	no	—
192	C₂×D₄×C₃₁	—	2	2	no	—
193	C₂×D₄×C₃₁	—	2	8	no	—
194	C₂×D₄×C₃₁	—	4	16	no	—
195	C₂×D₄×C₃₁	—	4	2	no	—
196	C₂×D₄×C₃₁	—	4	2	no	—
197	C₂×D₄×C₃₁	—	4	4	no	—
198	C₂×D₄×C₃₁	—	4	2	no	—
199	C₂×D₄×C₃₁	—	4	2	no	—
200	C₂×D₄×C₃₁	—	4	4	no	—
201	C₂×D₄×C₃₁	—	4	4	no	—
202	C₂×D₄×C₃₁	—	4	2	no	—
203	C₂×D₄×C₃₁	—	4	16	no	—
204	C₂×D₄×C₃₁	—	4	4	no	—
205	C₂×D₄×C₃₁	—	4	4	no	—
206	C₂×D₄×C₃₁	—	4	4	no	—
207	C₂×D₄×C₃₁	—	4	4	no	—
208	C₂×D₄×C₃₁	—	4	4	no	—
209	C₂×D₄×C₃₁	—	4	4	no	—
210	C₂×D₄×C₃₁	—	4	4	no	—
211	C₂×D₄×C₃₁	—	4	16	no	—
212	C₂×D₄×C₃₁	C₂×D₄	1	8	yes	—
213	C₂×D₄×C₃₁	C₂×D₄	1	8	yes	—
214	C₂²×C₄×C₃₁	—	2	2	no	—
215	C₂²×C₄×C₃₁	—	2	4	no	—
216	C₂²×C₄×C₃₁	—	2	4	no	—
217	C₂²×C₄×C₃₁	—	2	2	no	—
218	C₂²×C₄×C₃₁	—	2	2	no	—
219	C₂²×C₄×C₃₁	—	2	8	no	—
220	C₂²×C₄×C₃₁	—	2	4	no	—
221	C₂²×C₄×C₃₁	—	2	4	no	—
222	C₂²×C₄×C₃₁	—	2	8	no	—
223	C₂²×C₄×C₃₁	—	4	4	no	—
224	C₂²×C₄×C₃₁	—	4	2	no	—
225	C₂²×C₄×C₃₁	—	4	2	no	—
226	C₂²×C₄×C₃₁	—	4	2	no	—
227	C₂²×C₄×C₃₁	—	4	4	no	—
228	C₂²×C₄×C₃₁	—	4	4	no	—
229	C₂²×C₄×C₃₁	—	4	4	no	—
230	C₂²×C₄×C₃₁	—	4	16	no	—
231	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
232	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
233	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
234	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
235	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
236	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
237	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
238	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
239	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
240	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
241	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
242	C₄⋊C₄×C₃₁	—	2	4	no	—
243	C₄⋊C₄×C₃₁	—	2	4	no	—
244	C₄⋊C₄×C₃₁	—	2	2	no	—
245	C₄⋊C₄×C₃₁	—	2	2	no	—
246	C₄⋊C₄×C₃₁	—	2	8	no	—
247	C₄⋊C₄×C₃₁	—	4	4	no	—
248	C₄⋊C₄×C₃₁	—	4	4	no	—
249	C₂²⋊C₄×C₃₁	—	2	8	no	—
250	C₂²⋊C₄×C₃₁	—	2	4	no	—
251	C₂²⋊C₄×C₃₁	—	2	4	no	—
252	C₂²⋊C₄×C₃₁	—	2	4	no	—
253	C₂²⋊C₄×C₃₁	—	2	4	no	—
254	C₂²⋊C₄×C₃₁	—	2	4	no	—
255	C₂²⋊C₄×C₃₁	—	2	4	no	—
256	C₂²⋊C₄×C₃₁	—	2	4	no	—
257	C₂²⋊C₄×C₃₁	—	2	4	no	—
258	C₂²⋊C₄×C₃₁	—	2	4	no	—
259	C₂²⋊C₄×C₃₁	—	2	8	no	—
260	C₂²⋊C₄×C₃₁	—	4	4	no	—
261	C₂²⋊C₄×C₃₁	—	4	4	no	—
262	C₂²⋊C₄×C₃₁	—	4	4	no	—
263	C₂²⋊C₄×C₃₁	—	4	4	no	—
264	C₂²⋊C₄×C₃₁	—	4	4	no	—
265	C₂²⋊C₄×C₃₁	—	4	4	no	—
266	C₂²⋊C₄×C₃₁	—	4	4	no	—
267	C₂²⋊C₄×C₃₁	—	4	4	no	—
268	C₄²×C₃₁	—	2	4	no	—
269	#36704	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
270	C₂³×C₃₁	—	2	2	no	—
271	C₂³×C₃₁	—	2	2	no	—
272	C₂³×C₃₁	—	2	8	no	—
273	C₂³×C₃₁	—	2	2	no	—
274	C₂³×C₃₁	—	2	4	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	4	no	—
280	C₂³×C₃₁	—	2	4	no	—
281	C₂³×C₃₁	—	2	8	no	—
282	C₂³×C₃₁	—	2	2	no	—
283	C₂³×C₃₁	—	2	2	no	—
284	C₂³×C₃₁	—	2	4	no	—
285	C₂³×C₃₁	—	2	2	no	—
286	C₂³×C₃₁	—	2	4	no	—
287	C₂³×C₃₁	—	2	4	no	—
288	C₂³×C₃₁	—	2	2	no	—
289	C₂³×C₃₁	—	2	2	no	—
290	C₂³×C₃₁	—	2	4	no	—
291	C₂³×C₃₁	—	2	2	no	—
292	C₂³×C₃₁	—	4	4	no	—
293	C₂³×C₃₁	—	4	4	no	—
294	C₂³×C₃₁	—	4	4	no	—
295	C₂³×C₃₁	—	4	4	no	—
296	C₂³×C₃₁	—	4	16	no	—
297	C₂³×C₃₁	—	4	4	no	—
298	C₂³×C₃₁	—	4	4	no	—
299	C₂³×C₃₁	—	4	4	no	—
300	C₂³×C₃₁	—	8	8	no	—
301	C₂³×C₃₁	—	8	8	no	—
302	C₂³×C₃₁	C₂²×D₄	1	4	yes	—
303	C₂³×C₃₁	C₂²×D₄	1	4	yes	—
304	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
305	C₂³×C₃₁	H(5,𝔽₂)	1	4	yes	—
306	C₂³×C₃₁	C₂⁵	1	1	yes	characteristic
307	Q₈×C₃₁	—	4	4	no	—
308	D₄×C₃₁	—	4	8	no	—
309	D₄×C₃₁	—	4	8	no	—
310	D₄×C₃₁	—	4	16	no	—
311	D₄×C₃₁	—	4	4	no	—
312	D₄×C₃₁	—	4	16	no	—
313	D₄×C₃₁	—	4	8	no	—
314	D₄×C₃₁	—	8	4	no	—
315	D₄×C₃₁	—	8	4	no	—
316	D₄×C₃₁	—	8	4	no	—
317	D₄×C₃₁	—	8	4	no	—
318	D₄×C₃₁	—	8	8	no	—
319	C₂×C₄×C₃₁	—	2	8	no	—
320	C₂×C₄×C₃₁	—	2	8	no	—
321	C₂×C₄×C₃₁	—	2	2	no	—
322	C₂×C₄×C₃₁	—	2	2	no	—
323	C₂×C₄×C₃₁	—	2	2	no	—
324	C₂×C₄×C₃₁	—	2	2	no	—
325	C₂×C₄×C₃₁	—	2	2	no	—
326	C₂×C₄×C₃₁	—	2	2	no	—
327	C₂×C₄×C₃₁	—	2	2	no	—
328	C₂×C₄×C₃₁	—	2	2	no	—
329	C₂×C₄×C₃₁	—	2	2	no	—
330	C₂×C₄×C₃₁	—	2	4	no	—
331	C₂×C₄×C₃₁	—	2	4	no	—
332	C₂×C₄×C₃₁	—	2	4	no	—
333	C₂×C₄×C₃₁	—	2	4	no	—
334	C₂×C₄×C₃₁	—	2	2	no	—
335	C₂×C₄×C₃₁	—	2	4	no	—
336	C₂×C₄×C₃₁	—	2	4	no	—
337	C₂×C₄×C₃₁	—	2	4	no	—
338	C₂×C₄×C₃₁	—	2	2	no	—
339	C₂×C₄×C₃₁	—	2	4	no	—
340	C₂×C₄×C₃₁	—	2	4	no	—
341	C₂×C₄×C₃₁	—	2	4	no	—
342	C₂×C₄×C₃₁	—	4	16	no	—
343	C₂×C₄×C₃₁	—	4	8	no	—
344	C₂×C₄×C₃₁	—	4	4	no	—
345	C₂×C₄×C₃₁	—	4	4	no	—
346	C₂×C₄×C₃₁	—	8	8	no	—
347	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
348	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
349	C₂×C₄×C₃₁	H(5,𝔽₂)	1	4	yes	—
350	C₂×#535	C₂×C₃₁	1	1	yes	characteristic, complemented
351	C₂²×#121	C₂×C₃₁	1	1	yes	characteristic, complemented
352	#2849	C₂×C₃₁	1	2	yes	complemented
353	#2688	C₂×C₃₁	1	4	yes	complemented
354	#2686	C₂×C₃₁	1	4	yes	complemented
355	#2673	C₂×C₃₁	1	4	yes	complemented
356	#2671	C₂×C₃₁	1	4	yes	complemented
357	#2613	C₂×C₃₁	1	2	yes	complemented
358	#2484	C₂×C₃₁	1	1	yes	characteristic, complemented
359	#2482	C₂×C₃₁	1	1	yes	characteristic, complemented
360	#2412	C₂×C₃₁	1	2	yes	complemented
361	#2410	C₂×C₃₁	1	2	yes	complemented
362	#2406	C₂×C₃₁	1	1	yes	characteristic, complemented
363	#2404	C₂×C₃₁	1	1	yes	characteristic, complemented
364	#2308	C₂×C₃₁	1	1	yes	characteristic, complemented
365	C₂²×C₃₁	—	2	2	no	—
366	C₂²×C₃₁	—	2	2	no	—
367	C₂²×C₃₁	—	2	8	no	—
368	C₂²×C₃₁	—	2	4	no	—
369	C₂²×C₃₁	—	2	4	no	—
370	C₂²×C₃₁	—	2	4	no	—
371	C₂²×C₃₁	—	2	4	no	—
372	C₂²×C₃₁	—	2	4	no	—
373	C₂²×C₃₁	—	2	4	no	—
374	C₂²×C₃₁	—	4	16	no	—
375	C₂²×C₃₁	—	4	4	no	—
376	C₂²×C₃₁	—	4	4	no	—
377	C₂²×C₃₁	—	4	4	no	—
378	C₂²×C₃₁	—	4	4	no	—
379	C₂²×C₃₁	—	4	2	no	—
380	C₂²×C₃₁	—	4	2	no	—
381	C₂²×C₃₁	—	4	2	no	—
382	C₂²×C₃₁	—	4	2	no	—
383	C₂²×C₃₁	—	4	2	no	—
384	C₂²×C₃₁	—	4	2	no	—
385	C₂²×C₃₁	—	4	4	no	—
386	C₂²×C₃₁	—	4	4	no	—
387	C₂²×C₃₁	—	4	4	no	—
388	C₂²×C₃₁	—	4	4	no	—
389	C₂²×C₃₁	—	8	8	no	—
390	C₂²×C₃₁	—	8	8	no	—
391	C₂²×C₃₁	#534	1	4	yes	—
392	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
393	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	2	yes	—
394	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	2	yes	—
395	C₂²×C₃₁	#585	1	2	yes	—
396	C₄×C₃₁	—	2	2	no	—
397	C₄×C₃₁	—	2	2	no	—
398	C₄×C₃₁	—	2	4	no	—
399	C₄×C₃₁	—	4	2	no	—
400	C₄×C₃₁	—	4	2	no	—
401	C₄×C₃₁	—	4	2	no	—
402	C₄×C₃₁	—	4	2	no	—
403	C₄×C₃₁	—	4	2	no	—
404	C₄×C₃₁	—	4	4	no	—
405	C₄×C₃₁	—	4	4	no	—
406	C₂²×#41	C₂²×C₃₁	1	1	yes	characteristic
407	C₂³×D₄	C₂²×C₃₁	1	1	yes	characteristic
408	C₂³×D₄	C₂²×C₃₁	1	1	yes	characteristic
409	C₂³×D₄	C₂²×C₃₁	1	1	yes	characteristic
410	C₂⁴×C₄	C₂²×C₃₁	1	1	yes	characteristic
411	#535	—	2	8	no	—
412	C₂×#127	C₂²×C₃₁	1	2	yes	complemented
413	C₂×#124	C₂²×C₃₁	1	2	yes	complemented
414	C₂×#123	C₂²×C₃₁	1	2	yes	—
415	C₂×#123	C₂²×C₃₁	1	4	yes	complemented
416	C₂×#121	—	2	8	no	—
417	C₂×#121	C₂²×C₃₁	1	4	yes	—
418	C₂×#121	C₂²×C₃₁	1	4	yes	—
419	C₂×#121	C₂²×C₃₁	1	2	yes	complemented
420	C₂×#121	C₂²×C₃₁	1	2	yes	complemented
421	C₂×#121	C₂²×C₃₁	1	4	yes	complemented
422	C₂×#120	C₂²×C₃₁	1	2	yes	—
423	C₂×#120	C₂²×C₃₁	1	2	yes	—
424	C₂×#120	C₂²×C₃₁	1	2	yes	—
425	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
426	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
427	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
428	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
429	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
430	#400	C₂²×C₃₁	1	2	yes	complemented
431	#399	C₂²×C₃₁	1	2	yes	complemented
432	#398	C₂²×C₃₁	1	2	yes	complemented
433	#397	C₂²×C₃₁	1	4	yes	complemented
434	#397	C₂²×C₃₁	1	2	yes	complemented
435	#395	C₂²×C₃₁	1	2	yes	complemented
436	#394	C₂²×C₃₁	1	4	yes	complemented
437	#394	C₂²×C₃₁	1	4	yes	complemented
438	#394	C₂²×C₃₁	1	2	yes	complemented
439	#394	C₂²×C₃₁	1	4	yes	complemented
440	#394	C₂²×C₃₁	1	4	yes	complemented
441	#393	C₂²×C₃₁	1	2	yes	complemented
442	#392	C₂²×C₃₁	1	4	yes	complemented
443	#392	C₂²×C₃₁	1	4	yes	complemented
444	#392	C₂²×C₃₁	1	2	yes	complemented
445	#392	C₂²×C₃₁	1	4	yes	complemented
446	#388	C₂²×C₃₁	1	4	yes	complemented
447	#387	C₂²×C₃₁	1	4	yes	complemented
448	#386	C₂²×C₃₁	1	2	yes	—
449	#386	C₂²×C₃₁	1	2	yes	—
450	#386	C₂²×C₃₁	1	4	yes	complemented
451	#386	C₂²×C₃₁	1	4	yes	complemented
452	#386	C₂²×C₃₁	1	4	yes	complemented
453	#386	C₂²×C₃₁	1	4	yes	complemented
454	#386	C₂²×C₃₁	1	4	yes	complemented
455	#386	C₂²×C₃₁	1	4	yes	complemented
456	#385	C₂²×C₃₁	1	2	yes	—
457	#385	C₂²×C₃₁	1	2	yes	—
458	#385	C₂²×C₃₁	1	4	yes	complemented
459	#385	C₂²×C₃₁	1	4	yes	complemented
460	#381	C₂²×C₃₁	1	1	yes	characteristic
461	#381	C₂²×C₃₁	1	1	yes	characteristic
462	#381	C₂²×C₃₁	1	2	yes	—
463	#381	C₂²×C₃₁	1	4	yes	complemented
464	#380	C₂²×C₃₁	1	4	yes	complemented
465	#379	C₂²×C₃₁	1	2	yes	—
466	#379	C₂²×C₃₁	1	2	yes	—
467	C₂×C₃₁	—	2	4	no	—
468	C₂×C₃₁	—	4	4	no	—
469	C₂×C₃₁	—	4	4	no	—
470	C₂×C₃₁	—	8	2	no	—
471	C₂×C₃₁	—	8	2	no	—
472	C₂×C₃₁	C₂×#534	1	1	yes	characteristic
473	C₂×C₃₁	#3484	1	1	yes	characteristic
474	C₂×C₃₁	#3485	1	1	yes	characteristic
475	C₂×C₃₁	#3542	1	4	yes	—
476	C₂⁵	C₂³×C₃₁	1	1	yes	characteristic
477	C₂⁵	C₂³×C₃₁	1	1	yes	characteristic
478	C₂⁵	C₂³×C₃₁	1	1	yes	characteristic
479	C₂×#41	—	2	4	no	—
480	C₂×#41	—	4	4	no	—
481	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
482	C₂²×D₄	—	2	4	no	—
483	C₂²×D₄	—	2	4	no	—
484	C₂²×D₄	—	4	4	no	—
485	C₂²×D₄	—	4	4	no	—
486	C₂²×D₄	—	4	4	no	—
487	C₂²×D₄	D₄×C₃₁	1	8	yes	complemented
488	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
489	C₂²×D₄	C₂³×C₃₁	1	4	yes	—
490	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
491	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
492	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
493	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
494	C₂²×D₄	C₂³×C₃₁	1	4	yes	—
495	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
496	C₂²×D₄	C₂³×C₃₁	1	4	yes	—
497	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
498	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
499	C₂³×C₄	—	2	4	no	—
500	C₂³×C₄	—	4	4	no	—
501	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
502	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
503	C₂³×C₄	C₂³×C₃₁	1	4	yes	—
504	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
505	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
506	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
507	C₂³×C₄	C₂³×C₃₁	1	4	yes	—
508	#127	—	2	8	no	—
509	#124	—	2	8	no	—
510	#123	—	4	8	no	—
511	#123	—	4	4	no	—
512	#121	—	2	16	no	—
513	#121	—	2	16	no	—
514	#121	—	2	8	no	—
515	#121	—	2	8	no	—
516	#121	—	4	8	no	—
517	#120	—	2	8	no	—
518	#120	—	2	8	no	—
519	#120	—	4	4	no	—
520	#117	—	2	4	no	—
521	C₂×C₄⋊C₄	—	2	4	no	—
522	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
523	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
524	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
525	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
526	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
527	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
528	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
529	C₂×C₂²⋊C₄	—	2	4	no	—
530	C₂×C₂²⋊C₄	—	2	4	no	—
531	C₂×C₂²⋊C₄	—	4	4	no	—
532	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
533	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
534	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
535	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
536	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
537	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
538	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
539	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
540	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
541	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
542	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
543	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
544	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
545	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
546	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
547	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
548	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
549	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
550	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
551	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
552	#95	C₂³×C₃₁	1	4	yes	—
553	#95	C₂³×C₃₁	1	4	yes	—
554	#95	C₂³×C₃₁	1	2	yes	—
555	#95	C₂³×C₃₁	1	2	yes	—
556	#95	C₂³×C₃₁	1	2	yes	—
557	#95	C₂³×C₃₁	1	2	yes	—
558	#95	C₂³×C₃₁	1	4	yes	—
559	#95	C₂³×C₃₁	1	4	yes	—
560	#95	C₂³×C₃₁	1	4	yes	—
561	#95	C₂³×C₃₁	1	4	yes	—
562	C₃₁	#36704	1	1	yes	characteristic, direct product factor, Sylow
563	C₂⁴	—	2	4	no	—
564	C₂⁴	—	2	4	no	—
565	C₂⁴	—	2	2	no	—
566	C₂⁴	—	2	4	no	—
567	C₂⁴	—	4	2	no	—
568	C₂⁴	—	4	2	no	—
569	C₂⁴	—	4	2	no	—
570	C₂⁴	—	4	2	no	—
571	C₂⁴	—	4	2	no	—
572	C₂⁴	—	4	2	no	—
573	C₂⁴	C₂×D₄×C₃₁	1	4	yes	—
574	C₂⁴	C₂×D₄×C₃₁	1	4	yes	—
575	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
576	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
577	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
578	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
579	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
580	#41	—	4	16	no	—
581	C₂×Q₈	—	2	2	no	—
582	C₂×Q₈	—	4	2	no	—
583	C₂×D₄	—	2	4	no	—
584	C₂×D₄	—	2	8	no	—
585	C₂×D₄	—	2	8	no	—
586	C₂×D₄	—	2	4	no	—
587	C₂×D₄	—	2	4	no	—
588	C₂×D₄	—	2	4	no	—
589	C₂×D₄	—	2	4	no	—
590	C₂×D₄	—	2	4	no	—
591	C₂×D₄	—	2	4	no	—
592	C₂×D₄	—	2	2	no	—
593	C₂×D₄	—	2	8	no	—
594	C₂×D₄	—	4	16	no	—
595	C₂×D₄	—	4	2	no	—
596	C₂×D₄	—	4	2	no	—
597	C₂×D₄	—	4	4	no	—
598	C₂×D₄	—	4	2	no	—
599	C₂×D₄	—	4	2	no	—
600	C₂×D₄	—	4	4	no	—
601	C₂×D₄	—	4	4	no	—
602	C₂×D₄	—	4	2	no	—
603	C₂×D₄	—	4	16	no	—
604	C₂×D₄	—	4	4	no	—
605	C₂×D₄	—	4	4	no	—
606	C₂×D₄	—	4	4	no	—
607	C₂×D₄	—	4	4	no	—
608	C₂×D₄	—	4	4	no	—
609	C₂×D₄	—	4	4	no	—
610	C₂×D₄	—	4	4	no	—
611	C₂×D₄	—	4	16	no	—
612	C₂×D₄	C₂×D₄×C₃₁	1	8	yes	—
613	C₂×D₄	C₂×D₄×C₃₁	1	8	yes	—
614	C₂²×C₄	—	2	2	no	—
615	C₂²×C₄	—	2	4	no	—
616	C₂²×C₄	—	2	4	no	—
617	C₂²×C₄	—	2	2	no	—
618	C₂²×C₄	—	2	2	no	—
619	C₂²×C₄	—	2	8	no	—
620	C₂²×C₄	—	2	4	no	—
621	C₂²×C₄	—	2	4	no	—
622	C₂²×C₄	—	2	8	no	—
623	C₂²×C₄	—	4	4	no	—
624	C₂²×C₄	—	4	2	no	—
625	C₂²×C₄	—	4	2	no	—
626	C₂²×C₄	—	4	2	no	—
627	C₂²×C₄	—	4	4	no	—
628	C₂²×C₄	—	4	4	no	—
629	C₂²×C₄	—	4	4	no	—
630	C₂²×C₄	—	4	16	no	—
631	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
632	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
633	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
634	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
635	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
636	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
637	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
638	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
639	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
640	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
641	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
642	C₄⋊C₄	—	2	4	no	—
643	C₄⋊C₄	—	2	4	no	—
644	C₄⋊C₄	—	2	2	no	—
645	C₄⋊C₄	—	2	2	no	—
646	C₄⋊C₄	—	2	8	no	—
647	C₄⋊C₄	—	4	4	no	—
648	C₄⋊C₄	—	4	4	no	—
649	C₂²⋊C₄	—	2	8	no	—
650	C₂²⋊C₄	—	2	4	no	—
651	C₂²⋊C₄	—	2	4	no	—
652	C₂²⋊C₄	—	2	4	no	—
653	C₂²⋊C₄	—	2	4	no	—
654	C₂²⋊C₄	—	2	4	no	—
655	C₂²⋊C₄	—	2	4	no	—
656	C₂²⋊C₄	—	2	4	no	—
657	C₂²⋊C₄	—	2	4	no	—
658	C₂²⋊C₄	—	2	4	no	—
659	C₂²⋊C₄	—	2	8	no	—
660	C₂²⋊C₄	—	4	4	no	—
661	C₂²⋊C₄	—	4	4	no	—
662	C₂²⋊C₄	—	4	4	no	—
663	C₂²⋊C₄	—	4	4	no	—
664	C₂²⋊C₄	—	4	4	no	—
665	C₂²⋊C₄	—	4	4	no	—
666	C₂²⋊C₄	—	4	4	no	—
667	C₂²⋊C₄	—	4	4	no	—
668	C₄²	—	2	4	no	—
669	C₂³	—	2	2	no	—
670	C₂³	—	2	2	no	—
671	C₂³	—	2	8	no	—
672	C₂³	—	2	2	no	—
673	C₂³	—	2	4	no	—
674	C₂³	—	2	2	no	—
675	C₂³	—	2	4	no	—
676	C₂³	—	2	2	no	—
677	C₂³	—	2	2	no	—
678	C₂³	—	2	4	no	—
679	C₂³	—	2	4	no	—
680	C₂³	—	2	8	no	—
681	C₂³	—	2	2	no	—
682	C₂³	—	2	2	no	—
683	C₂³	—	2	4	no	—
684	C₂³	—	2	2	no	—
685	C₂³	—	2	4	no	—
686	C₂³	—	2	4	no	—
687	C₂³	—	2	2	no	—
688	C₂³	—	2	2	no	—
689	C₂³	—	2	4	no	—
690	C₂³	—	2	2	no	—
691	C₂³	—	4	4	no	—
692	C₂³	—	4	4	no	—
693	C₂³	—	4	4	no	—
694	C₂³	—	4	4	no	—
695	C₂³	—	4	16	no	—
696	C₂³	—	4	4	no	—
697	C₂³	—	4	4	no	—
698	C₂³	—	4	4	no	—
699	C₂³	—	8	8	no	—
700	C₂³	—	8	8	no	—
701	C₂³	C₂²×D₄×C₃₁	1	4	yes	—
702	C₂³	C₂²×D₄×C₃₁	1	4	yes	—
703	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
704	C₂³	C₃₁×H(5,𝔽₂)	1	4	yes	—
705	C₂³	C₂⁵×C₃₁	1	1	yes	characteristic
706	Q₈	—	4	4	no	—
707	D₄	—	4	8	no	—
708	D₄	—	4	8	no	—
709	D₄	—	4	16	no	—
710	D₄	—	4	4	no	—
711	D₄	—	4	16	no	—
712	D₄	—	4	8	no	—
713	D₄	—	8	4	no	—
714	D₄	—	8	4	no	—
715	D₄	—	8	4	no	—
716	D₄	—	8	4	no	—
717	D₄	—	8	8	no	—
718	C₂×C₄	—	2	8	no	—
719	C₂×C₄	—	2	8	no	—
720	C₂×C₄	—	2	2	no	—
721	C₂×C₄	—	2	2	no	—
722	C₂×C₄	—	2	2	no	—
723	C₂×C₄	—	2	2	no	—
724	C₂×C₄	—	2	2	no	—
725	C₂×C₄	—	2	2	no	—
726	C₂×C₄	—	2	2	no	—
727	C₂×C₄	—	2	2	no	—
728	C₂×C₄	—	2	2	no	—
729	C₂×C₄	—	2	4	no	—
730	C₂×C₄	—	2	4	no	—
731	C₂×C₄	—	2	4	no	—
732	C₂×C₄	—	2	4	no	—
733	C₂×C₄	—	2	2	no	—
734	C₂×C₄	—	2	4	no	—
735	C₂×C₄	—	2	4	no	—
736	C₂×C₄	—	2	4	no	—
737	C₂×C₄	—	2	2	no	—
738	C₂×C₄	—	2	4	no	—
739	C₂×C₄	—	2	4	no	—
740	C₂×C₄	—	2	4	no	—
741	C₂×C₄	—	4	16	no	—
742	C₂×C₄	—	4	8	no	—
743	C₂×C₄	—	4	4	no	—
744	C₂×C₄	—	4	4	no	—
745	C₂×C₄	—	8	8	no	—
746	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
747	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
748	C₂×C₄	C₃₁×H(5,𝔽₂)	1	4	yes	—
749	C₂²	—	2	2	no	—
750	C₂²	—	2	2	no	—
751	C₂²	—	2	8	no	—
752	C₂²	—	2	4	no	—
753	C₂²	—	2	4	no	—
754	C₂²	—	2	4	no	—
755	C₂²	—	2	4	no	—
756	C₂²	—	2	4	no	—
757	C₂²	—	2	4	no	—
758	C₂²	—	4	16	no	—
759	C₂²	—	4	4	no	—
760	C₂²	—	4	4	no	—
761	C₂²	—	4	4	no	—
762	C₂²	—	4	4	no	—
763	C₂²	—	4	2	no	—
764	C₂²	—	4	2	no	—
765	C₂²	—	4	2	no	—
766	C₂²	—	4	2	no	—
767	C₂²	—	4	2	no	—
768	C₂²	—	4	2	no	—
769	C₂²	—	4	4	no	—
770	C₂²	—	4	4	no	—
771	C₂²	—	4	4	no	—
772	C₂²	—	4	4	no	—
773	C₂²	—	8	8	no	—
774	C₂²	—	8	8	no	—
775	C₂²	C₃₁×#534	1	4	yes	—
776	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
777	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	2	yes	—
778	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	2	yes	—
779	C₂²	C₃₁×#585	1	2	yes	—
780	C₄	—	2	2	no	—
781	C₄	—	2	2	no	—
782	C₄	—	2	4	no	—
783	C₄	—	4	2	no	—
784	C₄	—	4	2	no	—
785	C₄	—	4	2	no	—
786	C₄	—	4	2	no	—
787	C₄	—	4	2	no	—
788	C₄	—	4	4	no	—
789	C₄	—	4	4	no	—
790	C₂	—	2	4	no	—
791	C₂	—	4	4	no	—
792	C₂	—	4	4	no	—
793	C₂	—	8	2	no	—
794	C₂	—	8	2	no	—
795	C₂	C₂×C₃₁×#534	1	1	yes	characteristic
796	C₂	C₃₁×#3484	1	1	yes	characteristic
797	C₂	C₃₁×#3485	1	1	yes	characteristic
798	C₂	C₃₁×#3542	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₃₁	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₃₁
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. C₂×C₃₁×#535	C₂	semidirect
2. C₂²×C₃₁×#121	C₂	semidirect
3. C₃₁×#2849	C₂	semidirect
4. C₃₁×#2688	C₂	semidirect
5. C₃₁×#2686	C₂	semidirect
6. C₃₁×#2673	C₂	semidirect
7. C₃₁×#2671	C₂	semidirect
8. C₃₁×#2613	C₂	semidirect
9. C₃₁×#2484	C₂	semidirect
10. C₃₁×#2482	C₂	semidirect
11. C₃₁×#2412	C₂	semidirect
12. C₃₁×#2410	C₂	semidirect
13. C₃₁×#2406	C₂	semidirect
14. C₃₁×#2404	C₂	semidirect
15. C₃₁×#2308	C₂	semidirect
22. C₂×C₃₁×#127	C₂²	semidirect
23. C₂×C₃₁×#124	C₂²	semidirect
25. C₂×C₃₁×#123	C₂²	semidirect
29. C₂×C₃₁×#121	C₂²	semidirect
30. C₂×C₃₁×#121	C₂²	semidirect
31. C₂×C₃₁×#121	C₂²	semidirect
40. C₃₁×#400	C₂²	semidirect
41. C₃₁×#399	C₂²	semidirect
42. C₃₁×#398	C₂²	semidirect
43. C₃₁×#397	C₂²	semidirect
44. C₃₁×#397	C₂²	semidirect
45. C₃₁×#395	C₂²	semidirect
46. C₃₁×#394	C₂²	semidirect
47. C₃₁×#394	C₂²	semidirect
48. C₃₁×#394	C₂²	semidirect
49. C₃₁×#394	C₂²	semidirect
50. C₃₁×#394	C₂²	semidirect
51. C₃₁×#393	C₂²	semidirect
52. C₃₁×#392	C₂²	semidirect
53. C₃₁×#392	C₂²	semidirect
54. C₃₁×#392	C₂²	semidirect
55. C₃₁×#392	C₂²	semidirect
56. C₃₁×#388	C₂²	semidirect
57. C₃₁×#387	C₂²	semidirect
60. C₃₁×#386	C₂²	semidirect
61. C₃₁×#386	C₂²	semidirect
62. C₃₁×#386	C₂²	semidirect
63. C₃₁×#386	C₂²	semidirect
64. C₃₁×#386	C₂²	semidirect
65. C₃₁×#386	C₂²	semidirect
68. C₃₁×#385	C₂²	semidirect
69. C₃₁×#385	C₂²	semidirect
73. C₃₁×#381	C₂²	semidirect
74. C₃₁×#380	C₂²	semidirect
88. C₂²×D₄×C₃₁	D₄	semidirect
269. #36704	C₃₁	direct (N × H)
350. C₂×#535	C₂×C₃₁	semidirect
351. C₂²×#121	C₂×C₃₁	semidirect
352. #2849	C₂×C₃₁	semidirect
353. #2688	C₂×C₃₁	semidirect
354. #2686	C₂×C₃₁	semidirect
355. #2673	C₂×C₃₁	semidirect
356. #2671	C₂×C₃₁	semidirect
357. #2613	C₂×C₃₁	semidirect
358. #2484	C₂×C₃₁	semidirect
359. #2482	C₂×C₃₁	semidirect
360. #2412	C₂×C₃₁	semidirect
361. #2410	C₂×C₃₁	semidirect
362. #2406	C₂×C₃₁	semidirect
363. #2404	C₂×C₃₁	semidirect
364. #2308	C₂×C₃₁	semidirect
412. C₂×#127	C₂²×C₃₁	semidirect
413. C₂×#124	C₂²×C₃₁	semidirect
415. C₂×#123	C₂²×C₃₁	semidirect
419. C₂×#121	C₂²×C₃₁	semidirect
420. C₂×#121	C₂²×C₃₁	semidirect
421. C₂×#121	C₂²×C₃₁	semidirect
430. #400	C₂²×C₃₁	semidirect
431. #399	C₂²×C₃₁	semidirect
432. #398	C₂²×C₃₁	semidirect
433. #397	C₂²×C₃₁	semidirect
434. #397	C₂²×C₃₁	semidirect
435. #395	C₂²×C₃₁	semidirect
436. #394	C₂²×C₃₁	semidirect
437. #394	C₂²×C₃₁	semidirect
438. #394	C₂²×C₃₁	semidirect
439. #394	C₂²×C₃₁	semidirect
440. #394	C₂²×C₃₁	semidirect
441. #393	C₂²×C₃₁	semidirect
442. #392	C₂²×C₃₁	semidirect
443. #392	C₂²×C₃₁	semidirect
444. #392	C₂²×C₃₁	semidirect
445. #392	C₂²×C₃₁	semidirect
446. #388	C₂²×C₃₁	semidirect
447. #387	C₂²×C₃₁	semidirect
450. #386	C₂²×C₃₁	semidirect
451. #386	C₂²×C₃₁	semidirect
452. #386	C₂²×C₃₁	semidirect
453. #386	C₂²×C₃₁	semidirect
454. #386	C₂²×C₃₁	semidirect
455. #386	C₂²×C₃₁	semidirect
458. #385	C₂²×C₃₁	semidirect
459. #385	C₂²×C₃₁	semidirect
463. #381	C₂²×C₃₁	semidirect
464. #380	C₂²×C₃₁	semidirect
487. C₂²×D₄	D₄×C₃₁	semidirect
562. C₃₁	#36704	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×#535	2
C₂²×C₃₁×#121	2
C₃₁×#2849	2
C₃₁×#2688	2
C₃₁×#2686	2
C₃₁×#2673	2
C₃₁×#2671	2
C₃₁×#2613	2
C₃₁×#2484	2
C₃₁×#2482	2
C₃₁×#2412	2
C₃₁×#2410	2
C₃₁×#2406	2
C₃₁×#2404	2
C₃₁×#2308	2
#36704	31

Subgroups — C31×#36704 #21493463

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#36704 #21493463