Subgroups — C₃₁×#26265 #21483024

Order 7936.

802 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#494	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃₁×#441	C₂	1	1	yes	maximal, characteristic
3	C₃₁×#2446	C₂	1	2	yes	maximal
4	C₃₁×#2056	C₂	1	2	yes	maximal
5	C₃₁×#2043	C₂	1	2	yes	maximal
6	C₃₁×#1971	C₂	1	1	yes	maximal, characteristic
7	C₃₁×#1971	C₂	1	1	yes	maximal, characteristic
8	C₃₁×#1971	C₂	1	1	yes	maximal, characteristic
9	C₃₁×#1941	C₂	1	1	yes	maximal, characteristic
10	C₃₁×#1878	C₂	1	2	yes	maximal
11	C₃₁×#1771	C₂	1	1	yes	maximal, characteristic
12	C₂²×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
13	C₂²×Q₁₆×C₃₁	C₂²	1	2	yes	—
14	C₂²×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
15	C₂×C₃₁×C₄⋊Q₈	C₂²	1	2	yes	—
16	C₂×C₄×Q₈×C₃₁	C₂²	1	2	yes	—
17	C₃₁×#494	—	2	4	no	—
18	C₃₁×#441	—	2	4	no	—
19	C₂×C₃₁×#106	C₂²	1	1	yes	characteristic
20	C₂×C₃₁×#106	C₂²	1	1	yes	characteristic
21	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×C₃₁×#103	C₂²	1	2	yes	—
23	C₂×C₃₁×#103	C₂²	1	2	yes	—
24	C₂×C₃₁×#103	C₂²	1	2	yes	—
25	C₂×C₃₁×#103	C₂²	1	2	yes	—
26	C₂×C₃₁×#97	C₂²	1	1	yes	characteristic
27	C₂×C₃₁×#97	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
29	C₃₁×#400	—	2	2	no	—
30	C₃₁×#398	—	2	2	no	—
31	C₃₁×#391	C₂²	1	2	yes	—
32	C₃₁×#391	C₂²	1	2	yes	—
33	C₃₁×#391	C₂²	1	2	yes	—
34	C₃₁×#389	C₂²	1	2	yes	—
35	C₃₁×#387	—	2	2	no	—
36	C₃₁×#387	—	2	2	no	—
37	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
38	C₃₁×#340	C₂²	1	2	yes	—
39	C₃₁×#336	C₂²	1	1	yes	characteristic
40	C₃₁×#336	C₂²	1	1	yes	characteristic
41	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
42	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
43	C₂×Q₁₆×C₃₁	—	2	4	no	—
44	C₂×Q₁₆×C₃₁	—	2	2	no	—
45	C₂×Q₁₆×C₃₁	—	2	2	no	—
46	C₂×Q₁₆×C₃₁	—	2	2	no	—
47	C₂×Q₁₆×C₃₁	—	2	4	no	—
48	C₂×Q₁₆×C₃₁	—	2	2	no	—
49	C₂×Q₁₆×C₃₁	—	2	2	no	—
50	C₂×Q₁₆×C₃₁	—	4	2	no	—
51	C₂×Q₁₆×C₃₁	D₄	1	4	yes	—
52	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
53	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
54	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
55	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
56	C₃₁×C₄⋊Q₈	—	2	4	no	—
57	C₃₁×C₄⋊Q₈	—	4	2	no	—
58	C₄×Q₈×C₃₁	—	2	4	no	—
59	C₄×Q₈×C₃₁	—	4	2	no	—
60	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
61	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
62	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
63	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
64	C₂×C₄⋊C₄×C₃₁	D₄	1	2	yes	—
65	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
66	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
67	C₂×C₄²×C₃₁	—	2	2	no	—
68	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
69	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
70	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
71	C₃₁×#106	—	2	2	no	—
72	C₃₁×#106	—	2	2	no	—
73	C₃₁×C₄⋊C₈	—	2	2	no	—
74	C₃₁×#103	—	2	4	no	—
75	C₃₁×#103	—	4	2	no	—
76	C₃₁×#103	—	4	2	no	—
77	C₃₁×#103	—	4	2	no	—
78	C₃₁×#97	—	2	2	no	—
79	C₃₁×#97	—	2	2	no	—
80	C₄×C₈×C₃₁	—	2	2	no	—
81	C₃₁×#95	—	2	2	no	—
82	C₃₁×#95	—	2	2	no	—
83	C₃₁×#95	—	2	2	no	—
84	C₃₁×#95	—	2	2	no	—
85	C₃₁×#95	—	2	2	no	—
86	C₃₁×#95	—	2	2	no	—
87	C₃₁×#95	—	2	2	no	—
88	C₃₁×#95	D₄	1	2	yes	—
89	C₂×Q₈×C₃₁	—	2	2	no	—
90	C₂×Q₈×C₃₁	—	2	2	no	—
91	C₂×Q₈×C₃₁	—	2	2	no	—
92	C₂×Q₈×C₃₁	—	2	2	no	—
93	C₂×Q₈×C₃₁	—	2	2	no	—
94	C₂×Q₈×C₃₁	—	2	2	no	—
95	C₂×Q₈×C₃₁	—	2	2	no	—
96	C₂×Q₈×C₃₁	—	2	2	no	—
97	C₂×Q₈×C₃₁	—	2	2	no	—
98	C₂×Q₈×C₃₁	—	2	2	no	—
99	C₂×Q₈×C₃₁	—	2	2	no	—
100	C₂×Q₈×C₃₁	C₂×D₄	1	4	yes	—
101	C₂²×C₄×C₃₁	—	2	2	no	—
102	C₂²×C₄×C₃₁	—	2	2	no	—
103	C₂²×C₄×C₃₁	—	2	2	no	—
104	C₂²×C₄×C₃₁	—	2	2	no	—
105	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
108	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
109	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
110	Q₁₆×C₃₁	—	2	8	no	—
111	Q₁₆×C₃₁	—	4	8	no	—
112	Q₁₆×C₃₁	—	4	4	no	—
113	C₂×C₈×C₃₁	—	2	1	no	—
114	C₂×C₈×C₃₁	—	2	1	no	—
115	C₂×C₈×C₃₁	—	2	1	no	—
116	C₂×C₈×C₃₁	—	2	1	no	—
117	C₂×C₈×C₃₁	—	2	1	no	—
118	C₂×C₈×C₃₁	—	2	1	no	—
119	C₂×C₈×C₃₁	—	2	1	no	—
120	C₂×C₈×C₃₁	—	2	1	no	—
121	C₂×C₈×C₃₁	C₂×D₄	1	2	yes	—
122	C₂×C₈×C₃₁	#41	1	2	yes	—
123	C₂×C₈×C₃₁	#41	1	2	yes	—
124	C₂×C₈×C₃₁	#41	1	2	yes	—
125	C₄⋊C₄×C₃₁	—	2	4	no	—
126	C₄⋊C₄×C₃₁	—	2	2	no	—
127	C₄⋊C₄×C₃₁	—	2	2	no	—
128	C₄⋊C₄×C₃₁	—	2	2	no	—
129	C₄⋊C₄×C₃₁	—	2	2	no	—
130	C₄⋊C₄×C₃₁	—	4	4	no	—
131	C₄⋊C₄×C₃₁	—	4	4	no	—
132	C₄⋊C₄×C₃₁	—	4	4	no	—
133	C₄⋊C₄×C₃₁	—	4	4	no	—
134	C₄²×C₃₁	—	2	1	no	—
135	C₄²×C₃₁	—	2	1	no	—
136	C₄²×C₃₁	—	2	1	no	—
137	C₄²×C₃₁	—	2	1	no	—
138	C₄²×C₃₁	—	2	1	no	—
139	C₄²×C₃₁	—	2	1	no	—
140	C₄²×C₃₁	—	4	4	no	—
141	#26265	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
142	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
143	Q₈×C₃₁	—	2	4	no	—
144	Q₈×C₃₁	—	2	4	no	—
145	Q₈×C₃₁	—	4	2	no	—
146	Q₈×C₃₁	—	4	2	no	—
147	Q₈×C₃₁	—	4	2	no	—
148	Q₈×C₃₁	—	4	2	no	—
149	Q₈×C₃₁	—	4	2	no	—
150	Q₈×C₃₁	—	4	2	no	—
151	C₂×C₄×C₃₁	—	2	2	no	—
152	C₂×C₄×C₃₁	—	2	2	no	—
153	C₂×C₄×C₃₁	—	2	1	no	—
154	C₂×C₄×C₃₁	—	2	1	no	—
155	C₂×C₄×C₃₁	—	2	2	no	—
156	C₂×C₄×C₃₁	—	2	4	no	—
157	C₂×C₄×C₃₁	—	2	2	no	—
158	C₂×C₄×C₃₁	—	2	2	no	—
159	C₂×C₄×C₃₁	—	2	2	no	—
160	C₂×C₄×C₃₁	—	2	2	no	—
161	C₂×C₄×C₃₁	—	4	2	no	—
162	C₂×C₄×C₃₁	—	4	2	no	—
163	C₂×C₄×C₃₁	—	4	2	no	—
164	C₂×C₄×C₃₁	—	4	2	no	—
165	C₂×C₄×C₃₁	—	4	2	no	—
166	C₂×C₄×C₃₁	—	4	2	no	—
167	C₂×C₄×C₃₁	—	4	2	no	—
168	C₂×C₄×C₃₁	—	4	2	no	—
169	C₂×C₄×C₃₁	—	4	2	no	—
170	C₂×C₄×C₃₁	—	4	2	no	—
171	C₂×C₄×C₃₁	—	4	2	no	—
172	C₂×C₄×C₃₁	#137	1	4	yes	—
173	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
174	C₂×C₄×C₃₁	C₂×#41	1	1	yes	characteristic
175	C₂×C₄×C₃₁	C₂×#41	1	1	yes	characteristic
176	C₂×C₄×C₃₁	C₂×#41	1	1	yes	characteristic
177	C₂×C₄×C₃₁	H(5,𝔽₂)	1	1	yes	characteristic
178	C₂×C₄×C₃₁	H(5,𝔽₂)	1	1	yes	characteristic
179	C₈×C₃₁	—	2	2	no	—
180	C₈×C₃₁	—	4	1	no	—
181	C₈×C₃₁	—	4	1	no	—
182	C₈×C₃₁	#123	1	4	yes	—
183	C₂×#494	C₂×C₃₁	1	1	yes	characteristic
184	C₂×#441	C₂×C₃₁	1	1	yes	characteristic
185	#2446	C₂×C₃₁	1	2	yes	—
186	#2056	C₂×C₃₁	1	2	yes	—
187	#2043	C₂×C₃₁	1	2	yes	—
188	#1971	C₂×C₃₁	1	1	yes	characteristic
189	#1971	C₂×C₃₁	1	1	yes	characteristic
190	#1971	C₂×C₃₁	1	1	yes	characteristic
191	#1941	C₂×C₃₁	1	1	yes	characteristic
192	#1878	C₂×C₃₁	1	2	yes	—
193	#1771	C₂×C₃₁	1	1	yes	characteristic
194	C₂²×C₃₁	#532	1	1	yes	characteristic
195	C₂²×C₃₁	D₄²	1	1	yes	characteristic
196	C₂²×C₃₁	#550	1	1	yes	characteristic
197	C₂²×C₃₁	C₂×#137	1	2	yes	—
198	C₂²×C₃₁	#578	1	2	yes	—
199	C₄×C₃₁	—	2	4	no	—
200	C₄×C₃₁	—	4	1	no	—
201	C₄×C₃₁	—	4	1	no	—
202	C₄×C₃₁	—	4	4	no	—
203	C₄×C₃₁	—	4	2	no	—
204	C₄×C₃₁	—	8	2	no	—
205	C₄×C₃₁	—	8	2	no	—
206	C₄×C₃₁	—	8	2	no	—
207	C₄×C₃₁	C₂×#123	1	1	yes	characteristic
208	C₄×C₃₁	#540	1	1	yes	characteristic
209	C₄×C₃₁	#546	1	1	yes	characteristic
210	C₄×C₃₁	#559	1	1	yes	characteristic
211	C₂²×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
212	C₂²×Q₁₆	C₂²×C₃₁	1	2	yes	—
213	C₂²×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
214	C₂×C₄⋊Q₈	C₂²×C₃₁	1	2	yes	—
215	C₂×C₄×Q₈	C₂²×C₃₁	1	2	yes	—
216	#494	—	2	4	no	—
217	#441	—	2	4	no	—
218	C₂×#106	C₂²×C₃₁	1	1	yes	characteristic
219	C₂×#106	C₂²×C₃₁	1	1	yes	characteristic
220	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
221	C₂×#103	C₂²×C₃₁	1	2	yes	—
222	C₂×#103	C₂²×C₃₁	1	2	yes	—
223	C₂×#103	C₂²×C₃₁	1	2	yes	—
224	C₂×#103	C₂²×C₃₁	1	2	yes	—
225	C₂×#97	C₂²×C₃₁	1	1	yes	characteristic
226	C₂×#97	C₂²×C₃₁	1	1	yes	characteristic
227	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
228	#400	—	2	2	no	—
229	#398	—	2	2	no	—
230	#391	C₂²×C₃₁	1	2	yes	—
231	#391	C₂²×C₃₁	1	2	yes	—
232	#391	C₂²×C₃₁	1	2	yes	—
233	#389	C₂²×C₃₁	1	2	yes	—
234	#387	—	2	2	no	—
235	#387	—	2	2	no	—
236	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
237	#340	C₂²×C₃₁	1	2	yes	—
238	#336	C₂²×C₃₁	1	1	yes	characteristic
239	#336	C₂²×C₃₁	1	1	yes	characteristic
240	C₂×C₃₁	#2445	1	1	yes	characteristic
241	C₂×C₃₁	#3177	1	1	yes	characteristic
242	C₂×C₃₁	#3185	1	1	yes	characteristic
243	C₂×C₃₁	#3270	1	2	yes	—
244	C₂×C₃₁	#3398	1	2	yes	—
245	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
246	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
247	C₂×Q₁₆	—	2	4	no	—
248	C₂×Q₁₆	—	2	2	no	—
249	C₂×Q₁₆	—	2	2	no	—
250	C₂×Q₁₆	—	2	2	no	—
251	C₂×Q₁₆	—	2	4	no	—
252	C₂×Q₁₆	—	2	2	no	—
253	C₂×Q₁₆	—	2	2	no	—
254	C₂×Q₁₆	—	4	2	no	—
255	C₂×Q₁₆	D₄×C₃₁	1	4	yes	—
256	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
257	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
258	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
259	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
260	C₄⋊Q₈	—	2	4	no	—
261	C₄⋊Q₈	—	4	2	no	—
262	C₄×Q₈	—	2	4	no	—
263	C₄×Q₈	—	4	2	no	—
264	C₂×C₄⋊C₄	—	2	2	no	—
265	C₂×C₄⋊C₄	—	2	2	no	—
266	C₂×C₄⋊C₄	—	2	2	no	—
267	C₂×C₄⋊C₄	—	2	2	no	—
268	C₂×C₄⋊C₄	D₄×C₃₁	1	2	yes	—
269	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
270	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
271	C₂×C₄²	—	2	2	no	—
272	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
273	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
274	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
275	#106	—	2	2	no	—
276	#106	—	2	2	no	—
277	C₄⋊C₈	—	2	2	no	—
278	#103	—	2	4	no	—
279	#103	—	4	2	no	—
280	#103	—	4	2	no	—
281	#103	—	4	2	no	—
282	#97	—	2	2	no	—
283	#97	—	2	2	no	—
284	C₄×C₈	—	2	2	no	—
285	#95	—	2	2	no	—
286	#95	—	2	2	no	—
287	#95	—	2	2	no	—
288	#95	—	2	2	no	—
289	#95	—	2	2	no	—
290	#95	—	2	2	no	—
291	#95	—	2	2	no	—
292	#95	D₄×C₃₁	1	2	yes	—
293	C₃₁	#26265	1	1	yes	characteristic, direct product factor, Sylow
294	C₂×Q₈	—	2	2	no	—
295	C₂×Q₈	—	2	2	no	—
296	C₂×Q₈	—	2	2	no	—
297	C₂×Q₈	—	2	2	no	—
298	C₂×Q₈	—	2	2	no	—
299	C₂×Q₈	—	2	2	no	—
300	C₂×Q₈	—	2	2	no	—
301	C₂×Q₈	—	2	2	no	—
302	C₂×Q₈	—	2	2	no	—
303	C₂×Q₈	—	2	2	no	—
304	C₂×Q₈	—	2	2	no	—
305	C₂×Q₈	C₂×D₄×C₃₁	1	4	yes	—
306	C₂²×C₄	—	2	2	no	—
307	C₂²×C₄	—	2	2	no	—
308	C₂²×C₄	—	2	2	no	—
309	C₂²×C₄	—	2	2	no	—
310	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
311	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
312	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
313	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
314	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
315	Q₁₆	—	2	8	no	—
316	Q₁₆	—	4	8	no	—
317	Q₁₆	—	4	4	no	—
318	C₂×C₈	—	2	1	no	—
319	C₂×C₈	—	2	1	no	—
320	C₂×C₈	—	2	1	no	—
321	C₂×C₈	—	2	1	no	—
322	C₂×C₈	—	2	1	no	—
323	C₂×C₈	—	2	1	no	—
324	C₂×C₈	—	2	1	no	—
325	C₂×C₈	—	2	1	no	—
326	C₂×C₈	C₂×D₄×C₃₁	1	2	yes	—
327	C₂×C₈	#41×C₃₁	1	2	yes	—
328	C₂×C₈	#41×C₃₁	1	2	yes	—
329	C₂×C₈	#41×C₃₁	1	2	yes	—
330	C₄⋊C₄	—	2	4	no	—
331	C₄⋊C₄	—	2	2	no	—
332	C₄⋊C₄	—	2	2	no	—
333	C₄⋊C₄	—	2	2	no	—
334	C₄⋊C₄	—	2	2	no	—
335	C₄⋊C₄	—	4	4	no	—
336	C₄⋊C₄	—	4	4	no	—
337	C₄⋊C₄	—	4	4	no	—
338	C₄⋊C₄	—	4	4	no	—
339	C₄²	—	2	1	no	—
340	C₄²	—	2	1	no	—
341	C₄²	—	2	1	no	—
342	C₄²	—	2	1	no	—
343	C₄²	—	2	1	no	—
344	C₄²	—	2	1	no	—
345	C₄²	—	4	4	no	—
346	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
347	Q₈	—	2	4	no	—
348	Q₈	—	2	4	no	—
349	Q₈	—	4	2	no	—
350	Q₈	—	4	2	no	—
351	Q₈	—	4	2	no	—
352	Q₈	—	4	2	no	—
353	Q₈	—	4	2	no	—
354	Q₈	—	4	2	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	1	no	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	2	4	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	4	2	no	—
366	C₂×C₄	—	4	2	no	—
367	C₂×C₄	—	4	2	no	—
368	C₂×C₄	—	4	2	no	—
369	C₂×C₄	—	4	2	no	—
370	C₂×C₄	—	4	2	no	—
371	C₂×C₄	—	4	2	no	—
372	C₂×C₄	—	4	2	no	—
373	C₂×C₄	—	4	2	no	—
374	C₂×C₄	—	4	2	no	—
375	C₂×C₄	—	4	2	no	—
376	C₂×C₄	C₃₁×#137	1	4	yes	—
377	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
378	C₂×C₄	C₂×#41×C₃₁	1	1	yes	characteristic
379	C₂×C₄	C₂×#41×C₃₁	1	1	yes	characteristic
380	C₂×C₄	C₂×#41×C₃₁	1	1	yes	characteristic
381	C₂×C₄	C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
382	C₂×C₄	C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
383	C₈	—	2	2	no	—
384	C₈	—	4	1	no	—
385	C₈	—	4	1	no	—
386	C₈	C₃₁×#123	1	4	yes	—
387	C₂²	C₃₁×#532	1	1	yes	characteristic
388	C₂²	D₄²×C₃₁	1	1	yes	characteristic
389	C₂²	C₃₁×#550	1	1	yes	characteristic
390	C₂²	C₂×C₃₁×#137	1	2	yes	—
391	C₂²	C₃₁×#578	1	2	yes	—
392	C₄	—	2	4	no	—
393	C₄	—	4	1	no	—
394	C₄	—	4	1	no	—
395	C₄	—	4	4	no	—
396	C₄	—	4	2	no	—
397	C₄	—	8	2	no	—
398	C₄	—	8	2	no	—
399	C₄	—	8	2	no	—
400	C₄	C₂×C₃₁×#123	1	1	yes	characteristic
401	C₄	C₃₁×#540	1	1	yes	characteristic
402	C₄	C₃₁×#546	1	1	yes	characteristic
403	C₄	C₃₁×#559	1	1	yes	characteristic
404	C₂	C₃₁×#2445	1	1	yes	characteristic
405	C₂	C₃₁×#3177	1	1	yes	characteristic
406	C₂	C₃₁×#3185	1	1	yes	characteristic
407	C₂	C₃₁×#3270	1	2	yes	—
408	C₂	C₃₁×#3398	1	2	yes	—

	subgroup	G/H
center, socle, prime radical	C₂³×C₃₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₃₁
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₃₁ ◁ C₄×C₄⋊C₄×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
141. #26265	C₃₁	direct (N × H)
293. C₃₁	#26265	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×#494	2
C₂×C₃₁×#441	2
C₃₁×#2446	2
C₃₁×#2056	2
C₃₁×#2043	2
C₃₁×#1971	2
C₃₁×#1941	2
C₃₁×#1878	2
C₃₁×#1771	2
#26265	31

Subgroups — C31×#26265 #21483024

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#26265 #21483024