Subgroups — C₃₁×#25902 #21482661

Order 7936.

1306 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	C₂²×C₃₁×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃₁×#487	C₂	1	2	yes	maximal, complemented
3	C₃₁×#2857	C₂	1	1	yes	maximal, characteristic
4	C₃₁×#2024	C₂	1	4	yes	maximal, complemented
5	C₃₁×#1990	C₂	1	2	yes	maximal, complemented
6	C₃₁×#1872	C₂	1	4	yes	maximal
7	C₄×C₃₁×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic
8	C₂³×Q₈×C₃₁	—	2	1	no	—
9	C₂×C₃₁×C₄⋊Q₈	—	2	8	no	—
10	C₂×C₃₁×C₄⋊Q₈	—	2	1	no	—
11	C₂×C₃₁×C₄⋊Q₈	—	2	1	no	—
12	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
13	C₂×C₃₁×C₄⋊Q₈	C₂²	1	2	yes	—
14	C₂×C₃₁×C₄⋊Q₈	C₂²	1	2	yes	—
15	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	—
16	C₂²×C₄⋊C₄×C₃₁	—	2	1	no	—
17	C₂²×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
18	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
19	C₃₁×#487	—	2	8	no	—
20	C₂×C₃₁×#103	C₂²	1	8	yes	—
21	C₂×C₃₁×C₂²⋊C₈	C₂²	1	2	yes	—
22	C₂×C₄×C₈×C₃₁	C₂²	1	2	yes	—
23	C₃₁×#391	C₂²	1	2	yes	—
24	C₃₁×#389	—	2	1	no	—
25	C₃₁×#389	—	2	1	no	—
26	C₃₁×#384	C₂²	1	1	yes	characteristic
27	C₃₁×#380	—	2	1	no	—
28	C₃₁×#380	—	2	1	no	—
29	C₃₁×#340	C₂²	1	8	yes	—
30	C₃₁×#336	C₂²	1	2	yes	—
31	C₂²×Q₈×C₃₁	—	2	8	no	—
32	C₂²×Q₈×C₃₁	—	2	2	no	—
33	C₂²×Q₈×C₃₁	—	2	2	no	—
34	C₂²×Q₈×C₃₁	—	4	4	no	—
35	C₂²×Q₈×C₃₁	—	4	4	no	—
36	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
37	C₂³×C₄×C₃₁	—	2	2	no	—
38	C₂³×C₄×C₃₁	D₄	1	1	yes	characteristic
39	C₂³×C₄×C₃₁	D₄	1	1	yes	characteristic
40	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
41	C₂²×C₈×C₃₁	C₂³	1	4	yes	—
42	C₃₁×C₄⋊Q₈	—	2	8	no	—
43	C₃₁×C₄⋊Q₈	—	2	8	no	—
44	C₃₁×C₄⋊Q₈	—	2	8	no	—
45	C₃₁×C₄⋊Q₈	—	2	4	no	—
46	C₃₁×C₄⋊Q₈	—	2	4	no	—
47	C₃₁×C₄⋊Q₈	D₄	1	8	yes	—
48	C₃₁×C₂²⋊Q₈	—	2	8	no	—
49	C₂×C₄⋊C₄×C₃₁	—	2	8	no	—
50	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
51	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
52	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
53	C₂×C₄⋊C₄×C₃₁	—	2	8	no	—
54	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
55	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
56	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
57	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
58	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
59	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
60	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
61	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
62	C₂×C₄²×C₃₁	—	2	4	no	—
63	C₂×C₄²×C₃₁	D₄	1	1	yes	characteristic
64	C₂×C₄²×C₃₁	D₄	1	1	yes	characteristic
65	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
66	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
67	C₃₁×#103	—	2	16	no	—
68	C₃₁×C₂²⋊C₈	—	2	4	no	—
69	C₄×C₈×C₃₁	—	2	4	no	—
70	C₃₁×#95	—	2	2	no	—
71	C₃₁×#95	—	2	2	no	—
72	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
73	C₂×Q₈×C₃₁	—	2	8	no	—
74	C₂×Q₈×C₃₁	—	2	8	no	—
75	C₂×Q₈×C₃₁	—	2	4	no	—
76	C₂×Q₈×C₃₁	—	2	4	no	—
77	C₂×Q₈×C₃₁	—	2	4	no	—
78	C₂×Q₈×C₃₁	—	4	4	no	—
79	C₂×Q₈×C₃₁	—	4	32	no	—
80	C₂×Q₈×C₃₁	—	4	4	no	—
81	C₂×Q₈×C₃₁	—	4	4	no	—
82	C₂×Q₈×C₃₁	—	4	4	no	—
83	C₂²×C₄×C₃₁	—	2	2	no	—
84	C₂²×C₄×C₃₁	—	2	2	no	—
85	C₂²×C₄×C₃₁	—	2	2	no	—
86	C₂²×C₄×C₃₁	—	2	2	no	—
87	C₂²×C₄×C₃₁	—	2	2	no	—
88	C₂²×C₄×C₃₁	—	2	2	no	—
89	C₂²×C₄×C₃₁	—	2	8	no	—
90	C₂²×C₄×C₃₁	—	2	4	no	—
91	C₂²×C₄×C₃₁	—	2	2	no	—
92	C₂²×C₄×C₃₁	—	2	2	no	—
93	C₂²×C₄×C₃₁	—	4	4	no	—
94	C₂²×C₄×C₃₁	—	4	4	no	—
95	C₂²×C₄×C₃₁	SD₁₆	1	4	yes	—
96	C₂²×C₄×C₃₁	Q₁₆	1	4	yes	—
97	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₃₁	#41	1	4	yes	—
103	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
104	C₂×C₈×C₃₁	—	2	4	no	—
105	C₂×C₈×C₃₁	—	2	4	no	—
106	C₂×C₈×C₃₁	—	2	4	no	—
107	C₄⋊C₄×C₃₁	—	2	8	no	—
108	C₄⋊C₄×C₃₁	—	2	8	no	—
109	C₄⋊C₄×C₃₁	—	2	8	no	—
110	C₄⋊C₄×C₃₁	—	2	4	no	—
111	C₄⋊C₄×C₃₁	—	2	4	no	—
112	C₄⋊C₄×C₃₁	—	4	2	no	—
113	C₄⋊C₄×C₃₁	—	4	2	no	—
114	C₄⋊C₄×C₃₁	—	4	4	no	—
115	C₄⋊C₄×C₃₁	—	4	2	no	—
116	C₄⋊C₄×C₃₁	—	4	2	no	—
117	C₄⋊C₄×C₃₁	C₂×D₄	1	8	yes	—
118	C₂²⋊C₄×C₃₁	—	4	4	no	—
119	C₄²×C₃₁	—	2	2	no	—
120	C₄²×C₃₁	—	2	2	no	—
121	C₄²×C₃₁	—	2	2	no	—
122	C₄²×C₃₁	C₂×D₄	1	4	yes	—
123	#25902	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
124	C₂³×C₃₁	—	2	1	no	—
125	C₂³×C₃₁	—	2	1	no	—
126	C₂³×C₃₁	—	2	1	no	—
127	C₂³×C₃₁	—	2	1	no	—
128	C₂³×C₃₁	#124	1	2	yes	—
129	C₂³×C₃₁	C₂×SD₁₆	1	2	yes	—
130	C₂³×C₃₁	C₂×Q₁₆	1	2	yes	—
131	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
132	Q₈×C₃₁	—	4	16	no	—
133	Q₈×C₃₁	—	4	16	no	—
134	Q₈×C₃₁	—	4	8	no	—
135	C₂×C₄×C₃₁	—	2	1	no	—
136	C₂×C₄×C₃₁	—	2	1	no	—
137	C₂×C₄×C₃₁	—	2	1	no	—
138	C₂×C₄×C₃₁	—	2	1	no	—
139	C₂×C₄×C₃₁	—	2	1	no	—
140	C₂×C₄×C₃₁	—	2	1	no	—
141	C₂×C₄×C₃₁	—	2	8	no	—
142	C₂×C₄×C₃₁	—	2	8	no	—
143	C₂×C₄×C₃₁	—	2	8	no	—
144	C₂×C₄×C₃₁	—	2	8	no	—
145	C₂×C₄×C₃₁	—	4	16	no	—
146	C₂×C₄×C₃₁	—	4	4	no	—
147	C₂×C₄×C₃₁	—	4	4	no	—
148	C₂×C₄×C₃₁	—	4	2	no	—
149	C₂×C₄×C₃₁	—	4	2	no	—
150	C₂×C₄×C₃₁	—	4	2	no	—
151	C₂×C₄×C₃₁	—	4	2	no	—
152	C₂×C₄×C₃₁	—	4	2	no	—
153	C₂×C₄×C₃₁	—	4	2	no	—
154	C₂×C₄×C₃₁	#120	1	2	yes	—
155	C₂×C₄×C₃₁	#120	1	2	yes	—
156	C₂×C₄×C₃₁	#124	1	2	yes	—
157	C₂×C₄×C₃₁	C₂×SD₁₆	1	2	yes	—
158	C₂×C₄×C₃₁	C₂×SD₁₆	1	2	yes	—
159	C₂×C₄×C₃₁	C₂×Q₁₆	1	2	yes	—
160	C₂×C₄×C₃₁	C₂×Q₁₆	1	2	yes	—
161	C₂×C₄×C₃₁	AGL(1,ℤ/8)	1	2	yes	—
162	C₂×C₄×C₃₁	#137	1	2	yes	—
163	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
164	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
165	C₂×C₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
166	C₈×C₃₁	—	4	4	no	—
167	C₂²×C₄⋊Q₈	C₂×C₃₁	1	1	yes	characteristic
168	C₂×#487	C₂×C₃₁	1	2	yes	complemented
169	#2857	C₂×C₃₁	1	1	yes	characteristic
170	#2024	C₂×C₃₁	1	4	yes	complemented
171	#1990	C₂×C₃₁	1	2	yes	complemented
172	#1872	C₂×C₃₁	1	4	yes	—
173	C₄×C₂²⋊C₈	C₂×C₃₁	1	1	yes	characteristic
174	C₂²×C₃₁	—	2	2	no	—
175	C₂²×C₃₁	—	2	2	no	—
176	C₂²×C₃₁	—	2	2	no	—
177	C₂²×C₃₁	—	2	2	no	—
178	C₂²×C₃₁	—	2	2	no	—
179	C₂²×C₃₁	—	2	2	no	—
180	C₂²×C₃₁	#487	1	4	yes	complemented
181	C₂²×C₃₁	C₂×#120	1	1	yes	characteristic
182	C₂²×C₃₁	C₂×#124	1	1	yes	characteristic
183	C₂²×C₃₁	#536	1	1	yes	characteristic
184	C₂²×C₃₁	C₂²×SD₁₆	1	1	yes	characteristic
185	C₂²×C₃₁	C₂²×Q₁₆	1	1	yes	characteristic
186	C₂²×C₃₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
187	C₂²×C₃₁	C₂×#137	1	1	yes	characteristic
188	C₄×C₃₁	—	2	2	no	—
189	C₄×C₃₁	—	2	2	no	—
190	C₄×C₃₁	—	2	2	no	—
191	C₄×C₃₁	—	4	8	no	—
192	C₄×C₃₁	—	8	2	no	—
193	C₄×C₃₁	—	8	2	no	—
194	C₄×C₃₁	#450	1	4	yes	—
195	C₄×C₃₁	#451	1	4	yes	—
196	C₄×C₃₁	#548	1	4	yes	—
197	C₂³×Q₈	—	2	1	no	—
198	C₂×C₄⋊Q₈	—	2	8	no	—
199	C₂×C₄⋊Q₈	—	2	1	no	—
200	C₂×C₄⋊Q₈	—	2	1	no	—
201	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
202	C₂×C₄⋊Q₈	C₂²×C₃₁	1	2	yes	—
203	C₂×C₄⋊Q₈	C₂²×C₃₁	1	2	yes	—
204	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	—
205	C₂²×C₄⋊C₄	—	2	1	no	—
206	C₂²×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
207	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
208	#487	—	2	8	no	—
209	C₂×#103	C₂²×C₃₁	1	8	yes	—
210	C₂×C₂²⋊C₈	C₂²×C₃₁	1	2	yes	—
211	C₂×C₄×C₈	C₂²×C₃₁	1	2	yes	—
212	#391	C₂²×C₃₁	1	2	yes	—
213	#389	—	2	1	no	—
214	#389	—	2	1	no	—
215	#384	C₂²×C₃₁	1	1	yes	characteristic
216	#380	—	2	1	no	—
217	#380	—	2	1	no	—
218	#340	C₂²×C₃₁	1	8	yes	—
219	#336	C₂²×C₃₁	1	2	yes	—
220	C₂×C₃₁	—	2	4	no	—
221	C₂×C₃₁	#2436	1	1	yes	characteristic
222	C₂×C₃₁	C₂×#450	1	1	yes	characteristic
223	C₂×C₃₁	C₂×#451	1	1	yes	characteristic
224	C₂×C₃₁	C₂×#487	1	1	yes	characteristic
225	C₂×C₃₁	#3141	1	1	yes	characteristic
226	C₂×C₃₁	#3229	1	1	yes	characteristic
227	C₂×C₃₁	#3230	1	1	yes	characteristic
228	C₂²×Q₈	—	2	8	no	—
229	C₂²×Q₈	—	2	2	no	—
230	C₂²×Q₈	—	2	2	no	—
231	C₂²×Q₈	—	4	4	no	—
232	C₂²×Q₈	—	4	4	no	—
233	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
234	C₂³×C₄	—	2	2	no	—
235	C₂³×C₄	D₄×C₃₁	1	1	yes	characteristic
236	C₂³×C₄	D₄×C₃₁	1	1	yes	characteristic
237	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
238	C₂²×C₈	C₂³×C₃₁	1	4	yes	—
239	C₄⋊Q₈	—	2	8	no	—
240	C₄⋊Q₈	—	2	8	no	—
241	C₄⋊Q₈	—	2	8	no	—
242	C₄⋊Q₈	—	2	4	no	—
243	C₄⋊Q₈	—	2	4	no	—
244	C₄⋊Q₈	D₄×C₃₁	1	8	yes	—
245	C₂²⋊Q₈	—	2	8	no	—
246	C₂×C₄⋊C₄	—	2	8	no	—
247	C₂×C₄⋊C₄	—	2	2	no	—
248	C₂×C₄⋊C₄	—	2	2	no	—
249	C₂×C₄⋊C₄	—	2	2	no	—
250	C₂×C₄⋊C₄	—	2	8	no	—
251	C₂×C₄⋊C₄	—	2	2	no	—
252	C₂×C₄⋊C₄	—	2	1	no	—
253	C₂×C₄⋊C₄	—	2	1	no	—
254	C₂×C₄⋊C₄	—	2	1	no	—
255	C₂×C₄⋊C₄	—	2	1	no	—
256	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
257	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
258	C₂×C₂²⋊C₄	—	2	2	no	—
259	C₂×C₄²	—	2	4	no	—
260	C₂×C₄²	D₄×C₃₁	1	1	yes	characteristic
261	C₂×C₄²	D₄×C₃₁	1	1	yes	characteristic
262	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
263	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
264	#103	—	2	16	no	—
265	C₂²⋊C₈	—	2	4	no	—
266	C₄×C₈	—	2	4	no	—
267	#95	—	2	2	no	—
268	#95	—	2	2	no	—
269	C₃₁	#25902	1	1	yes	characteristic, direct product factor, Sylow
270	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
271	C₂×Q₈	—	2	8	no	—
272	C₂×Q₈	—	2	8	no	—
273	C₂×Q₈	—	2	4	no	—
274	C₂×Q₈	—	2	4	no	—
275	C₂×Q₈	—	2	4	no	—
276	C₂×Q₈	—	4	4	no	—
277	C₂×Q₈	—	4	32	no	—
278	C₂×Q₈	—	4	4	no	—
279	C₂×Q₈	—	4	4	no	—
280	C₂×Q₈	—	4	4	no	—
281	C₂²×C₄	—	2	2	no	—
282	C₂²×C₄	—	2	2	no	—
283	C₂²×C₄	—	2	2	no	—
284	C₂²×C₄	—	2	2	no	—
285	C₂²×C₄	—	2	2	no	—
286	C₂²×C₄	—	2	2	no	—
287	C₂²×C₄	—	2	8	no	—
288	C₂²×C₄	—	2	4	no	—
289	C₂²×C₄	—	2	2	no	—
290	C₂²×C₄	—	2	2	no	—
291	C₂²×C₄	—	4	4	no	—
292	C₂²×C₄	—	4	4	no	—
293	C₂²×C₄	SD₁₆×C₃₁	1	4	yes	—
294	C₂²×C₄	Q₁₆×C₃₁	1	4	yes	—
295	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
296	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
297	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
298	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
299	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
300	C₂²×C₄	#41×C₃₁	1	4	yes	—
301	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
302	C₂×C₈	—	2	4	no	—
303	C₂×C₈	—	2	4	no	—
304	C₂×C₈	—	2	4	no	—
305	C₄⋊C₄	—	2	8	no	—
306	C₄⋊C₄	—	2	8	no	—
307	C₄⋊C₄	—	2	8	no	—
308	C₄⋊C₄	—	2	4	no	—
309	C₄⋊C₄	—	2	4	no	—
310	C₄⋊C₄	—	4	2	no	—
311	C₄⋊C₄	—	4	2	no	—
312	C₄⋊C₄	—	4	4	no	—
313	C₄⋊C₄	—	4	2	no	—
314	C₄⋊C₄	—	4	2	no	—
315	C₄⋊C₄	C₂×D₄×C₃₁	1	8	yes	—
316	C₂²⋊C₄	—	4	4	no	—
317	C₄²	—	2	2	no	—
318	C₄²	—	2	2	no	—
319	C₄²	—	2	2	no	—
320	C₄²	C₂×D₄×C₃₁	1	4	yes	—
321	C₂³	—	2	1	no	—
322	C₂³	—	2	1	no	—
323	C₂³	—	2	1	no	—
324	C₂³	—	2	1	no	—
325	C₂³	C₃₁×#124	1	2	yes	—
326	C₂³	C₂×SD₁₆×C₃₁	1	2	yes	—
327	C₂³	C₂×Q₁₆×C₃₁	1	2	yes	—
328	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
329	Q₈	—	4	16	no	—
330	Q₈	—	4	16	no	—
331	Q₈	—	4	8	no	—
332	C₂×C₄	—	2	1	no	—
333	C₂×C₄	—	2	1	no	—
334	C₂×C₄	—	2	1	no	—
335	C₂×C₄	—	2	1	no	—
336	C₂×C₄	—	2	1	no	—
337	C₂×C₄	—	2	1	no	—
338	C₂×C₄	—	2	8	no	—
339	C₂×C₄	—	2	8	no	—
340	C₂×C₄	—	2	8	no	—
341	C₂×C₄	—	2	8	no	—
342	C₂×C₄	—	4	16	no	—
343	C₂×C₄	—	4	4	no	—
344	C₂×C₄	—	4	4	no	—
345	C₂×C₄	—	4	2	no	—
346	C₂×C₄	—	4	2	no	—
347	C₂×C₄	—	4	2	no	—
348	C₂×C₄	—	4	2	no	—
349	C₂×C₄	—	4	2	no	—
350	C₂×C₄	—	4	2	no	—
351	C₂×C₄	C₃₁×#120	1	2	yes	—
352	C₂×C₄	C₃₁×#120	1	2	yes	—
353	C₂×C₄	C₃₁×#124	1	2	yes	—
354	C₂×C₄	C₂×SD₁₆×C₃₁	1	2	yes	—
355	C₂×C₄	C₂×SD₁₆×C₃₁	1	2	yes	—
356	C₂×C₄	C₂×Q₁₆×C₃₁	1	2	yes	—
357	C₂×C₄	C₂×Q₁₆×C₃₁	1	2	yes	—
358	C₂×C₄	C₃₁×AGL(1,ℤ/8)	1	2	yes	—
359	C₂×C₄	C₃₁×#137	1	2	yes	—
360	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
361	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
362	C₂×C₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
363	C₈	—	4	4	no	—
364	C₂²	—	2	2	no	—
365	C₂²	—	2	2	no	—
366	C₂²	—	2	2	no	—
367	C₂²	—	2	2	no	—
368	C₂²	—	2	2	no	—
369	C₂²	—	2	2	no	—
370	C₂²	C₃₁×#487	1	4	yes	complemented
371	C₂²	C₂×C₃₁×#120	1	1	yes	characteristic
372	C₂²	C₂×C₃₁×#124	1	1	yes	characteristic
373	C₂²	C₃₁×#536	1	1	yes	characteristic
374	C₂²	C₂²×SD₁₆×C₃₁	1	1	yes	characteristic
375	C₂²	C₂²×Q₁₆×C₃₁	1	1	yes	characteristic
376	C₂²	C₂×C₃₁×AGL(1,ℤ/8)	1	1	yes	characteristic
377	C₂²	C₂×C₃₁×#137	1	1	yes	characteristic
378	C₄	—	2	2	no	—
379	C₄	—	2	2	no	—
380	C₄	—	2	2	no	—
381	C₄	—	4	8	no	—
382	C₄	—	8	2	no	—
383	C₄	—	8	2	no	—
384	C₄	C₃₁×#450	1	4	yes	—
385	C₄	C₃₁×#451	1	4	yes	—
386	C₄	C₃₁×#548	1	4	yes	—
387	C₂	—	2	4	no	—
388	C₂	C₃₁×#2436	1	1	yes	characteristic
389	C₂	C₂×C₃₁×#450	1	1	yes	characteristic
390	C₂	C₂×C₃₁×#451	1	1	yes	characteristic
391	C₂	C₂×C₃₁×#487	1	1	yes	characteristic
392	C₂	C₃₁×#3141	1	1	yes	characteristic
393	C₂	C₃₁×#3229	1	1	yes	characteristic
394	C₂	C₃₁×#3230	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₃₁
prime radical	C₂⁴×C₃₁	C₂×D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₃₁ ◁ C₂²×C₄²×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₃₁×#487	C₂	semidirect
4. C₃₁×#2024	C₂	semidirect
5. C₃₁×#1990	C₂	semidirect
123. #25902	C₃₁	direct (N × H)
168. C₂×#487	C₂×C₃₁	semidirect
170. #2024	C₂×C₃₁	semidirect
171. #1990	C₂×C₃₁	semidirect
180. C₂²×C₃₁	#487	semidirect
269. C₃₁	#25902	direct (N × H)
370. C₂²	C₃₁×#487	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₃₁×C₄⋊Q₈	2
C₂×C₃₁×#487	2
C₃₁×#2857	2
C₃₁×#2024	2
C₃₁×#1990	2
C₃₁×#1872	2
C₄×C₃₁×C₂²⋊C₈	2
#25902	31

Subgroups — C31×#25902 #21482661

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#25902 #21482661