Subgroups — C₃₁×#25647 #21482406

Order 7936.

1022 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#557	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃₁×#487	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃₁×#475	C₂	1	1	yes	maximal, characteristic
4	C₃₁×#2546	C₂	1	1	yes	maximal, characteristic
5	C₃₁×#2043	C₂	1	4	yes	maximal
6	C₃₁×#1984	C₂	1	1	yes	maximal, characteristic
7	C₃₁×#1981	C₂	1	1	yes	maximal, characteristic
8	C₃₁×#1865	C₂	1	4	yes	maximal
9	C₄×C₃₁×#103	C₂	1	1	yes	maximal, characteristic
10	C₃₁×#557	—	2	4	no	—
11	C₃₁×#557	—	2	4	no	—
12	C₂×C₃₁×C₄⋊Q₈	—	2	1	no	—
13	C₂×C₃₁×C₄⋊Q₈	C₂²	1	2	yes	—
14	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
15	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
16	C₂×C₃₁×#125	—	2	2	no	—
17	C₂×C₃₁×#125	—	2	1	no	—
18	C₂×C₄×Q₈×C₃₁	—	2	1	no	—
19	C₂×C₄×Q₈×C₃₁	C₂²	1	2	yes	—
20	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
21	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
22	C₃₁×#487	—	2	4	no	—
23	C₃₁×#475	—	2	4	no	—
24	C₂×C₃₁×#106	C₂²	1	2	yes	—
25	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×C₃₁×#103	C₂²	1	4	yes	—
27	C₂×C₃₁×#103	C₂²	1	4	yes	—
28	C₂×C₃₁×#103	C₂²	1	2	yes	—
29	C₂×C₃₁×#103	C₂²	1	2	yes	—
30	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
31	C₃₁×#398	—	2	2	no	—
32	C₃₁×#391	—	2	1	no	—
33	C₃₁×#389	C₂²	1	4	yes	—
34	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
35	C₃₁×#340	C₂²	1	2	yes	—
36	C₃₁×#336	C₂²	1	4	yes	—
37	C₂²×Q₈×C₃₁	—	2	1	no	—
38	C₂²×Q₈×C₃₁	D₄	1	1	yes	characteristic
39	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
40	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
41	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
42	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
43	C₃₁×C₄⋊Q₈	—	2	4	no	—
44	C₃₁×C₄⋊Q₈	—	2	4	no	—
45	C₃₁×C₄⋊Q₈	—	2	2	no	—
46	C₃₁×C₄⋊Q₈	—	2	2	no	—
47	C₃₁×C₄⋊Q₈	—	2	2	no	—
48	C₃₁×C₄⋊Q₈	—	4	4	no	—
49	C₃₁×C₄⋊Q₈	D₄	1	4	yes	—
50	C₃₁×#125	—	2	16	no	—
51	C₃₁×#125	—	2	8	no	—
52	C₄×Q₈×C₃₁	—	2	8	no	—
53	C₄×Q₈×C₃₁	—	2	4	no	—
54	C₄×Q₈×C₃₁	—	2	4	no	—
55	C₄×Q₈×C₃₁	—	2	2	no	—
56	C₄×Q₈×C₃₁	—	2	2	no	—
57	C₄×Q₈×C₃₁	—	2	2	no	—
58	C₄×Q₈×C₃₁	D₄	1	4	yes	—
59	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
60	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
61	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
62	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
63	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
64	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
65	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
66	C₂×C₄⋊C₄×C₃₁	—	2	4	no	—
67	C₂×C₄⋊C₄×C₃₁	D₄	1	2	yes	—
68	C₂×C₄⋊C₄×C₃₁	D₄	1	1	yes	characteristic
69	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
70	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
71	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
72	C₂×C₄²×C₃₁	—	2	2	no	—
73	C₂×C₄²×C₃₁	—	2	1	no	—
74	C₂×C₄²×C₃₁	—	2	1	no	—
75	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
76	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
77	C₃₁×#106	—	2	4	no	—
78	C₃₁×C₄⋊C₈	—	2	2	no	—
79	C₃₁×#103	—	2	4	no	—
80	C₃₁×#103	—	2	8	no	—
81	C₃₁×#103	—	2	8	no	—
82	C₃₁×#103	—	2	4	no	—
83	C₄×C₈×C₃₁	—	2	2	no	—
84	C₃₁×#95	—	2	1	no	—
85	C₃₁×#95	—	2	4	no	—
86	C₂×Q₈×C₃₁	—	2	2	no	—
87	C₂×Q₈×C₃₁	—	2	2	no	—
88	C₂×Q₈×C₃₁	—	2	2	no	—
89	C₂×Q₈×C₃₁	—	2	1	no	—
90	C₂×Q₈×C₃₁	—	2	2	no	—
91	C₂×Q₈×C₃₁	—	2	4	no	—
92	C₂×Q₈×C₃₁	—	2	2	no	—
93	C₂×Q₈×C₃₁	—	2	4	no	—
94	C₂×Q₈×C₃₁	—	4	2	no	—
95	C₂×Q₈×C₃₁	—	4	2	no	—
96	C₂×Q₈×C₃₁	—	4	2	no	—
97	C₂×Q₈×C₃₁	SD₁₆	1	4	yes	—
98	C₂×Q₈×C₃₁	C₂×D₄	1	4	yes	—
99	C₂×Q₈×C₃₁	C₂×D₄	1	2	yes	—
100	C₂²×C₄×C₃₁	—	2	2	no	—
101	C₂²×C₄×C₃₁	—	2	1	no	—
102	C₂²×C₄×C₃₁	—	2	2	no	—
103	C₂²×C₄×C₃₁	—	2	1	no	—
104	C₂²×C₄×C₃₁	—	2	2	no	—
105	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
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	1	yes	characteristic
109	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
110	C₂×C₈×C₃₁	—	2	2	no	—
111	C₂×C₈×C₃₁	—	2	2	no	—
112	C₂×C₈×C₃₁	—	2	4	no	—
113	C₂×C₈×C₃₁	—	2	2	no	—
114	C₂×C₈×C₃₁	—	2	2	no	—
115	C₄⋊C₄×C₃₁	—	2	8	no	—
116	C₄⋊C₄×C₃₁	—	2	8	no	—
117	C₄⋊C₄×C₃₁	—	2	8	no	—
118	C₄⋊C₄×C₃₁	—	2	4	no	—
119	C₄⋊C₄×C₃₁	—	2	4	no	—
120	C₄⋊C₄×C₃₁	—	2	4	no	—
121	C₄⋊C₄×C₃₁	—	2	4	no	—
122	C₄⋊C₄×C₃₁	—	2	2	no	—
123	C₄⋊C₄×C₃₁	—	2	1	no	—
124	C₄⋊C₄×C₃₁	—	2	2	no	—
125	C₄⋊C₄×C₃₁	—	2	2	no	—
126	C₄⋊C₄×C₃₁	—	2	2	no	—
127	C₄⋊C₄×C₃₁	—	4	2	no	—
128	C₄⋊C₄×C₃₁	—	4	8	no	—
129	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
130	C₄⋊C₄×C₃₁	#41	1	4	yes	—
131	C₄²×C₃₁	—	2	8	no	—
132	C₄²×C₃₁	—	2	4	no	—
133	C₄²×C₃₁	—	2	2	no	—
134	C₄²×C₃₁	—	2	2	no	—
135	C₄²×C₃₁	—	4	2	no	—
136	C₄²×C₃₁	C₂×D₄	1	2	yes	—
137	C₄²×C₃₁	C₂×D₄	1	2	yes	—
138	#25647	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
139	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
140	Q₈×C₃₁	—	2	8	no	—
141	Q₈×C₃₁	—	2	2	no	—
142	Q₈×C₃₁	—	2	2	no	—
143	Q₈×C₃₁	—	2	8	no	—
144	Q₈×C₃₁	—	4	2	no	—
145	Q₈×C₃₁	—	4	2	no	—
146	Q₈×C₃₁	—	4	2	no	—
147	Q₈×C₃₁	—	8	4	no	—
148	C₂×C₄×C₃₁	—	2	2	no	—
149	C₂×C₄×C₃₁	—	2	2	no	—
150	C₂×C₄×C₃₁	—	2	2	no	—
151	C₂×C₄×C₃₁	—	2	2	no	—
152	C₂×C₄×C₃₁	—	2	2	no	—
153	C₂×C₄×C₃₁	—	2	4	no	—
154	C₂×C₄×C₃₁	—	2	2	no	—
155	C₂×C₄×C₃₁	—	2	4	no	—
156	C₂×C₄×C₃₁	—	2	4	no	—
157	C₂×C₄×C₃₁	—	4	2	no	—
158	C₂×C₄×C₃₁	—	4	4	no	—
159	C₂×C₄×C₃₁	—	4	2	no	—
160	C₂×C₄×C₃₁	—	4	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	#120	1	2	yes	—
166	C₂×C₄×C₃₁	#120	1	2	yes	—
167	C₂×C₄×C₃₁	C₂×SD₁₆	1	4	yes	—
168	C₂×C₄×C₃₁	C₂×SD₁₆	1	2	yes	—
169	C₂×C₄×C₃₁	#137	1	2	yes	—
170	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
171	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
172	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
173	C₂×C₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
174	C₈×C₃₁	—	4	2	no	—
175	C₈×C₃₁	—	4	2	no	—
176	C₂×#557	C₂×C₃₁	1	1	yes	characteristic
177	C₂×#487	C₂×C₃₁	1	1	yes	characteristic
178	C₂×#475	C₂×C₃₁	1	1	yes	characteristic
179	#2546	C₂×C₃₁	1	1	yes	characteristic
180	#2043	C₂×C₃₁	1	4	yes	—
181	#1984	C₂×C₃₁	1	1	yes	characteristic
182	#1981	C₂×C₃₁	1	1	yes	characteristic
183	#1865	C₂×C₃₁	1	4	yes	—
184	C₄×#103	C₂×C₃₁	1	1	yes	characteristic
185	C₂²×C₃₁	C₂×#120	1	1	yes	characteristic
186	C₂²×C₃₁	#548	1	2	yes	—
187	C₂²×C₃₁	C₂²×SD₁₆	1	1	yes	characteristic
188	C₂²×C₃₁	C₂×#137	1	1	yes	characteristic
189	C₂²×C₃₁	#578	1	2	yes	—
190	C₄×C₃₁	—	2	4	no	—
191	C₄×C₃₁	—	2	2	no	—
192	C₄×C₃₁	—	4	4	no	—
193	C₄×C₃₁	—	4	2	no	—
194	C₄×C₃₁	—	4	4	no	—
195	C₄×C₃₁	—	4	2	no	—
196	C₄×C₃₁	—	4	2	no	—
197	C₄×C₃₁	—	8	2	no	—
198	C₄×C₃₁	#448	1	4	yes	—
199	C₄×C₃₁	#532	1	1	yes	characteristic
200	C₄×C₃₁	#536	1	1	yes	characteristic
201	C₄×C₃₁	#547	1	2	yes	—
202	#557	—	2	4	no	—
203	#557	—	2	4	no	—
204	C₂×C₄⋊Q₈	—	2	1	no	—
205	C₂×C₄⋊Q₈	C₂²×C₃₁	1	2	yes	—
206	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
207	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
208	C₂×#125	—	2	1	no	—
209	C₂×#125	—	2	2	no	—
210	C₂×C₄×Q₈	—	2	1	no	—
211	C₂×C₄×Q₈	C₂²×C₃₁	1	2	yes	—
212	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
213	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
214	#487	—	2	4	no	—
215	#475	—	2	4	no	—
216	C₂×#106	C₂²×C₃₁	1	2	yes	—
217	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
218	C₂×#103	C₂²×C₃₁	1	2	yes	—
219	C₂×#103	C₂²×C₃₁	1	4	yes	—
220	C₂×#103	C₂²×C₃₁	1	4	yes	—
221	C₂×#103	C₂²×C₃₁	1	2	yes	—
222	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
223	#398	—	2	2	no	—
224	#391	—	2	1	no	—
225	#389	C₂²×C₃₁	1	4	yes	—
226	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
227	#340	C₂²×C₃₁	1	2	yes	—
228	#336	C₂²×C₃₁	1	4	yes	—
229	C₂×C₃₁	#2432	1	1	yes	characteristic
230	C₂×C₃₁	C₂×#448	1	1	yes	characteristic
231	C₂×C₃₁	#3011	1	1	yes	characteristic
232	C₂×C₃₁	#3359	1	2	yes	—
233	C₂×C₃₁	#3374	1	2	yes	—
234	C₂²×Q₈	—	2	1	no	—
235	C₂²×Q₈	D₄×C₃₁	1	1	yes	characteristic
236	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
237	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
238	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
239	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
240	C₄⋊Q₈	—	2	4	no	—
241	C₄⋊Q₈	—	2	4	no	—
242	C₄⋊Q₈	—	2	2	no	—
243	C₄⋊Q₈	—	2	2	no	—
244	C₄⋊Q₈	—	2	2	no	—
245	C₄⋊Q₈	—	4	4	no	—
246	C₄⋊Q₈	D₄×C₃₁	1	4	yes	—
247	#125	—	2	16	no	—
248	#125	—	2	8	no	—
249	C₄×Q₈	—	2	8	no	—
250	C₄×Q₈	—	2	4	no	—
251	C₄×Q₈	—	2	4	no	—
252	C₄×Q₈	—	2	2	no	—
253	C₄×Q₈	—	2	2	no	—
254	C₄×Q₈	—	2	2	no	—
255	C₄×Q₈	D₄×C₃₁	1	4	yes	—
256	C₂×C₄⋊C₄	—	2	2	no	—
257	C₂×C₄⋊C₄	—	2	1	no	—
258	C₂×C₄⋊C₄	—	2	2	no	—
259	C₂×C₄⋊C₄	—	2	1	no	—
260	C₂×C₄⋊C₄	—	2	2	no	—
261	C₂×C₄⋊C₄	—	2	1	no	—
262	C₂×C₄⋊C₄	—	2	4	no	—
263	C₂×C₄⋊C₄	—	2	1	no	—
264	C₂×C₄⋊C₄	D₄×C₃₁	1	1	yes	characteristic
265	C₂×C₄⋊C₄	D₄×C₃₁	1	2	yes	—
266	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
267	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
268	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
269	C₂×C₄²	—	2	2	no	—
270	C₂×C₄²	—	2	1	no	—
271	C₂×C₄²	—	2	1	no	—
272	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
273	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
274	#106	—	2	4	no	—
275	C₄⋊C₈	—	2	2	no	—
276	#103	—	2	4	no	—
277	#103	—	2	8	no	—
278	#103	—	2	8	no	—
279	#103	—	2	4	no	—
280	C₄×C₈	—	2	2	no	—
281	#95	—	2	1	no	—
282	#95	—	2	4	no	—
283	C₃₁	#25647	1	1	yes	characteristic, direct product factor, Sylow
284	C₂×Q₈	—	2	2	no	—
285	C₂×Q₈	—	2	2	no	—
286	C₂×Q₈	—	2	2	no	—
287	C₂×Q₈	—	2	1	no	—
288	C₂×Q₈	—	2	2	no	—
289	C₂×Q₈	—	2	4	no	—
290	C₂×Q₈	—	2	2	no	—
291	C₂×Q₈	—	2	4	no	—
292	C₂×Q₈	—	4	2	no	—
293	C₂×Q₈	—	4	2	no	—
294	C₂×Q₈	—	4	2	no	—
295	C₂×Q₈	SD₁₆×C₃₁	1	4	yes	—
296	C₂×Q₈	C₂×D₄×C₃₁	1	4	yes	—
297	C₂×Q₈	C₂×D₄×C₃₁	1	2	yes	—
298	C₂²×C₄	—	2	2	no	—
299	C₂²×C₄	—	2	1	no	—
300	C₂²×C₄	—	2	2	no	—
301	C₂²×C₄	—	2	1	no	—
302	C₂²×C₄	—	2	2	no	—
303	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
304	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
305	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
306	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
307	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
308	C₂×C₈	—	2	2	no	—
309	C₂×C₈	—	2	2	no	—
310	C₂×C₈	—	2	4	no	—
311	C₂×C₈	—	2	2	no	—
312	C₂×C₈	—	2	2	no	—
313	C₄⋊C₄	—	2	8	no	—
314	C₄⋊C₄	—	2	8	no	—
315	C₄⋊C₄	—	2	8	no	—
316	C₄⋊C₄	—	2	4	no	—
317	C₄⋊C₄	—	2	4	no	—
318	C₄⋊C₄	—	2	4	no	—
319	C₄⋊C₄	—	2	4	no	—
320	C₄⋊C₄	—	2	2	no	—
321	C₄⋊C₄	—	2	1	no	—
322	C₄⋊C₄	—	2	2	no	—
323	C₄⋊C₄	—	2	2	no	—
324	C₄⋊C₄	—	2	2	no	—
325	C₄⋊C₄	—	4	2	no	—
326	C₄⋊C₄	—	4	8	no	—
327	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
328	C₄⋊C₄	#41×C₃₁	1	4	yes	—
329	C₄²	—	2	8	no	—
330	C₄²	—	2	4	no	—
331	C₄²	—	2	2	no	—
332	C₄²	—	2	2	no	—
333	C₄²	—	4	2	no	—
334	C₄²	C₂×D₄×C₃₁	1	2	yes	—
335	C₄²	C₂×D₄×C₃₁	1	2	yes	—
336	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
337	Q₈	—	2	8	no	—
338	Q₈	—	2	2	no	—
339	Q₈	—	2	2	no	—
340	Q₈	—	2	8	no	—
341	Q₈	—	4	2	no	—
342	Q₈	—	4	2	no	—
343	Q₈	—	4	2	no	—
344	Q₈	—	8	4	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	2	2	no	—
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	2	4	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	4	no	—
353	C₂×C₄	—	2	4	no	—
354	C₂×C₄	—	4	2	no	—
355	C₂×C₄	—	4	4	no	—
356	C₂×C₄	—	4	2	no	—
357	C₂×C₄	—	4	2	no	—
358	C₂×C₄	—	4	2	no	—
359	C₂×C₄	—	4	2	no	—
360	C₂×C₄	—	4	2	no	—
361	C₂×C₄	—	4	2	no	—
362	C₂×C₄	C₃₁×#120	1	2	yes	—
363	C₂×C₄	C₃₁×#120	1	2	yes	—
364	C₂×C₄	C₂×SD₁₆×C₃₁	1	4	yes	—
365	C₂×C₄	C₂×SD₁₆×C₃₁	1	2	yes	—
366	C₂×C₄	C₃₁×#137	1	2	yes	—
367	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
368	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
369	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
370	C₂×C₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
371	C₈	—	4	2	no	—
372	C₈	—	4	2	no	—
373	C₂²	C₂×C₃₁×#120	1	1	yes	characteristic
374	C₂²	C₃₁×#548	1	2	yes	—
375	C₂²	C₂²×SD₁₆×C₃₁	1	1	yes	characteristic
376	C₂²	C₂×C₃₁×#137	1	1	yes	characteristic
377	C₂²	C₃₁×#578	1	2	yes	—
378	C₄	—	2	4	no	—
379	C₄	—	2	2	no	—
380	C₄	—	4	4	no	—
381	C₄	—	4	2	no	—
382	C₄	—	4	4	no	—
383	C₄	—	4	2	no	—
384	C₄	—	4	2	no	—
385	C₄	—	8	2	no	—
386	C₄	C₃₁×#448	1	4	yes	—
387	C₄	C₃₁×#532	1	1	yes	characteristic
388	C₄	C₃₁×#536	1	1	yes	characteristic
389	C₄	C₃₁×#547	1	2	yes	—
390	C₂	C₃₁×#2432	1	1	yes	characteristic
391	C₂	C₂×C₃₁×#448	1	1	yes	characteristic
392	C₂	C₃₁×#3011	1	1	yes	characteristic
393	C₂	C₃₁×#3359	1	2	yes	—
394	C₂	C₃₁×#3374	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 ◁ C₂×C₄×Q₈×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
138. #25647	C₃₁	direct (N × H)
283. C₃₁	#25647	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×#557	2
C₂×C₃₁×#487	2
C₂×C₃₁×#475	2
C₃₁×#2546	2
C₃₁×#2043	2
C₃₁×#1984	2
C₃₁×#1981	2
C₃₁×#1865	2
C₄×C₃₁×#103	2
#25647	31

Subgroups — C31×#25647 #21482406

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#25647 #21482406