Subgroups — C₃₁×#25634 #21482393

Order 7936.

1082 conjugacy classes of subgroups.

The subgroup lattice has 404 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×#494	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃₁×#462	C₂	1	1	yes	maximal, characteristic
4	C₃₁×#2568	C₂	1	1	yes	maximal, characteristic
5	C₃₁×#2016	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×#1878	C₂	1	4	yes	maximal
9	C₄×C₃₁×#103	C₂	1	1	yes	maximal, characteristic
10	C₂²×Q₁₆×C₃₁	C₂²	1	4	yes	—
11	C₂²×Q₁₆×C₃₁	C₂²	1	2	yes	—
12	C₃₁×#557	—	2	4	no	—
13	C₃₁×#557	—	2	4	no	—
14	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
15	C₂×C₃₁×C₄⋊Q₈	C₂²	1	2	yes	—
16	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
17	C₂×C₃₁×#125	—	2	2	no	—
18	C₂×C₃₁×#125	—	2	1	no	—
19	C₂×C₄×Q₈×C₃₁	—	2	1	no	—
20	C₂×C₄×Q₈×C₃₁	C₂²	1	2	yes	—
21	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
22	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
23	C₃₁×#494	—	2	4	no	—
24	C₃₁×#462	—	2	4	no	—
25	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×C₃₁×#103	C₂²	1	2	yes	—
27	C₂×C₃₁×#103	C₂²	1	2	yes	—
28	C₂×C₃₁×#103	C₂²	1	4	yes	—
29	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
30	C₃₁×#400	—	2	2	no	—
31	C₃₁×#391	—	2	1	no	—
32	C₃₁×#391	C₂²	1	4	yes	—
33	C₃₁×#382	—	2	1	no	—
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	D₄	1	1	yes	characteristic
38	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
39	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
40	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
41	C₂×Q₁₆×C₃₁	—	2	4	no	—
42	C₂×Q₁₆×C₃₁	—	2	8	no	—
43	C₂×Q₁₆×C₃₁	—	2	8	no	—
44	C₂×Q₁₆×C₃₁	—	4	4	no	—
45	C₂×Q₁₆×C₃₁	—	4	4	no	—
46	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
47	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
48	C₃₁×C₄⋊Q₈	—	2	4	no	—
49	C₃₁×C₄⋊Q₈	—	2	4	no	—
50	C₃₁×C₄⋊Q₈	—	2	2	no	—
51	C₃₁×C₄⋊Q₈	—	2	2	no	—
52	C₃₁×C₄⋊Q₈	—	2	2	no	—
53	C₃₁×C₄⋊Q₈	D₄	1	4	yes	—
54	C₃₁×#125	—	2	16	no	—
55	C₃₁×#125	—	2	8	no	—
56	C₄×Q₈×C₃₁	—	2	8	no	—
57	C₄×Q₈×C₃₁	—	2	4	no	—
58	C₄×Q₈×C₃₁	—	2	4	no	—
59	C₄×Q₈×C₃₁	—	2	2	no	—
60	C₄×Q₈×C₃₁	—	2	2	no	—
61	C₄×Q₈×C₃₁	—	2	2	no	—
62	C₄×Q₈×C₃₁	D₄	1	4	yes	—
63	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
64	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
65	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
66	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
67	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
68	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
69	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
70	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
71	C₂×C₄⋊C₄×C₃₁	D₄	1	2	yes	—
72	C₂×C₄⋊C₄×C₃₁	D₄	1	1	yes	characteristic
73	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
74	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
75	C₂×C₄²×C₃₁	—	2	2	no	—
76	C₂×C₄²×C₃₁	—	2	1	no	—
77	C₂×C₄²×C₃₁	—	2	1	no	—
78	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
79	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
80	C₃₁×C₄⋊C₈	—	2	2	no	—
81	C₃₁×#103	—	2	4	no	—
82	C₃₁×#103	—	2	4	no	—
83	C₃₁×#103	—	4	4	no	—
84	C₄×C₈×C₃₁	—	2	2	no	—
85	C₃₁×#95	—	2	1	no	—
86	C₃₁×#95	—	2	4	no	—
87	C₃₁×#95	—	2	4	no	—
88	C₂×Q₈×C₃₁	—	2	2	no	—
89	C₂×Q₈×C₃₁	—	2	2	no	—
90	C₂×Q₈×C₃₁	—	2	2	no	—
91	C₂×Q₈×C₃₁	—	2	1	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	4	no	—
96	C₂×Q₈×C₃₁	—	2	4	no	—
97	C₂×Q₈×C₃₁	—	2	4	no	—
98	C₂×Q₈×C₃₁	—	2	2	no	—
99	C₂×Q₈×C₃₁	—	2	4	no	—
100	C₂×Q₈×C₃₁	Q₁₆	1	4	yes	complemented
101	C₂×Q₈×C₃₁	C₂×D₄	1	4	yes	—
102	C₂×Q₈×C₃₁	C₂×D₄	1	2	yes	—
103	C₂²×C₄×C₃₁	—	2	1	no	—
104	C₂²×C₄×C₃₁	—	2	2	no	—
105	C₂²×C₄×C₃₁	—	2	1	no	—
106	C₂²×C₄×C₃₁	—	2	2	no	—
107	C₂²×C₄×C₃₁	—	2	2	no	—
108	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
109	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
111	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
113	Q₁₆×C₃₁	—	4	16	no	—
114	Q₁₆×C₃₁	—	4	8	no	—
115	C₂×C₈×C₃₁	—	2	2	no	—
116	C₂×C₈×C₃₁	—	2	2	no	—
117	C₂×C₈×C₃₁	—	2	2	no	—
118	C₂×C₈×C₃₁	—	2	4	no	—
119	C₂×C₈×C₃₁	#41	1	4	yes	—
120	C₄⋊C₄×C₃₁	—	2	8	no	—
121	C₄⋊C₄×C₃₁	—	2	8	no	—
122	C₄⋊C₄×C₃₁	—	2	8	no	—
123	C₄⋊C₄×C₃₁	—	2	4	no	—
124	C₄⋊C₄×C₃₁	—	2	4	no	—
125	C₄⋊C₄×C₃₁	—	2	4	no	—
126	C₄⋊C₄×C₃₁	—	2	4	no	—
127	C₄⋊C₄×C₃₁	—	2	2	no	—
128	C₄⋊C₄×C₃₁	—	2	1	no	—
129	C₄⋊C₄×C₃₁	—	2	2	no	—
130	C₄⋊C₄×C₃₁	—	2	2	no	—
131	C₄⋊C₄×C₃₁	—	4	2	no	—
132	C₄⋊C₄×C₃₁	—	4	2	no	—
133	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
134	C₄²×C₃₁	—	2	8	no	—
135	C₄²×C₃₁	—	2	4	no	—
136	C₄²×C₃₁	—	2	2	no	—
137	C₄²×C₃₁	—	2	2	no	—
138	C₄²×C₃₁	—	4	2	no	—
139	C₄²×C₃₁	C₂×D₄	1	2	yes	—
140	C₄²×C₃₁	C₂×D₄	1	2	yes	—
141	#25634	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
142	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
143	Q₈×C₃₁	—	2	8	no	—
144	Q₈×C₃₁	—	2	2	no	—
145	Q₈×C₃₁	—	2	2	no	—
146	Q₈×C₃₁	—	2	8	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	Q₈×C₃₁	—	4	2	no	—
152	Q₈×C₃₁	—	4	4	no	—
153	C₂×C₄×C₃₁	—	2	2	no	—
154	C₂×C₄×C₃₁	—	2	2	no	—
155	C₂×C₄×C₃₁	—	2	2	no	—
156	C₂×C₄×C₃₁	—	2	2	no	—
157	C₂×C₄×C₃₁	—	2	2	no	—
158	C₂×C₄×C₃₁	—	2	4	no	—
159	C₂×C₄×C₃₁	—	2	2	no	—
160	C₂×C₄×C₃₁	—	2	4	no	—
161	C₂×C₄×C₃₁	—	4	2	no	—
162	C₂×C₄×C₃₁	—	4	4	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	4	no	—
167	C₂×C₄×C₃₁	—	4	2	no	—
168	C₂×C₄×C₃₁	—	4	2	no	—
169	C₂×C₄×C₃₁	#120	1	2	yes	—
170	C₂×C₄×C₃₁	#120	1	2	yes	—
171	C₂×C₄×C₃₁	C₂×Q₁₆	1	4	yes	—
172	C₂×C₄×C₃₁	C₂×Q₁₆	1	2	yes	—
173	C₂×C₄×C₃₁	#137	1	2	yes	—
174	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
175	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
176	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
177	C₂×C₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
178	C₈×C₃₁	—	2	4	no	—
179	C₈×C₃₁	—	4	2	no	—
180	C₂×#557	C₂×C₃₁	1	1	yes	characteristic
181	C₂×#494	C₂×C₃₁	1	1	yes	characteristic
182	C₂×#462	C₂×C₃₁	1	1	yes	characteristic
183	#2568	C₂×C₃₁	1	1	yes	characteristic
184	#2016	C₂×C₃₁	1	4	yes	—
185	#1984	C₂×C₃₁	1	1	yes	characteristic
186	#1981	C₂×C₃₁	1	1	yes	characteristic
187	#1878	C₂×C₃₁	1	4	yes	—
188	C₄×#103	C₂×C₃₁	1	1	yes	characteristic
189	C₂²×C₃₁	C₂×#120	1	1	yes	characteristic
190	C₂²×C₃₁	#550	1	2	yes	—
191	C₂²×C₃₁	C₂²×Q₁₆	1	1	yes	characteristic
192	C₂²×C₃₁	C₂×#137	1	1	yes	characteristic
193	C₂²×C₃₁	#578	1	2	yes	—
194	C₄×C₃₁	—	2	4	no	—
195	C₄×C₃₁	—	2	2	no	—
196	C₄×C₃₁	—	4	2	no	—
197	C₄×C₃₁	—	4	4	no	—
198	C₄×C₃₁	—	4	2	no	—
199	C₄×C₃₁	—	4	2	no	—
200	C₄×C₃₁	—	8	2	no	—
201	C₄×C₃₁	—	8	2	no	—
202	C₄×C₃₁	#451	1	4	yes	—
203	C₄×C₃₁	#532	1	1	yes	characteristic
204	C₄×C₃₁	#535	1	1	yes	characteristic
205	C₄×C₃₁	#546	1	2	yes	—
206	C₂²×Q₁₆	C₂²×C₃₁	1	4	yes	—
207	C₂²×Q₁₆	C₂²×C₃₁	1	2	yes	—
208	#557	—	2	4	no	—
209	#557	—	2	4	no	—
210	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
211	C₂×C₄⋊Q₈	C₂²×C₃₁	1	2	yes	—
212	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
213	C₂×#125	—	2	1	no	—
214	C₂×#125	—	2	2	no	—
215	C₂×C₄×Q₈	—	2	1	no	—
216	C₂×C₄×Q₈	C₂²×C₃₁	1	2	yes	—
217	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
218	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
219	#494	—	2	4	no	—
220	#462	—	2	4	no	—
221	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
222	C₂×#103	C₂²×C₃₁	1	2	yes	—
223	C₂×#103	C₂²×C₃₁	1	2	yes	—
224	C₂×#103	C₂²×C₃₁	1	4	yes	—
225	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
226	#400	—	2	2	no	—
227	#391	—	2	1	no	—
228	#391	C₂²×C₃₁	1	4	yes	—
229	#382	—	2	1	no	—
230	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
231	#340	C₂²×C₃₁	1	2	yes	—
232	#336	C₂²×C₃₁	1	4	yes	—
233	C₂×C₃₁	#2431	1	1	yes	characteristic
234	C₂×C₃₁	C₂×#451	1	1	yes	characteristic
235	C₂×C₃₁	#3011	1	1	yes	characteristic
236	C₂×C₃₁	#3395	1	2	yes	—
237	C₂×C₃₁	#3398	1	2	yes	—
238	C₂²×Q₈	D₄×C₃₁	1	1	yes	characteristic
239	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
240	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
241	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
242	C₂×Q₁₆	—	2	4	no	—
243	C₂×Q₁₆	—	2	8	no	—
244	C₂×Q₁₆	—	2	8	no	—
245	C₂×Q₁₆	—	4	4	no	—
246	C₂×Q₁₆	—	4	4	no	—
247	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
248	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
249	C₄⋊Q₈	—	2	4	no	—
250	C₄⋊Q₈	—	2	4	no	—
251	C₄⋊Q₈	—	2	2	no	—
252	C₄⋊Q₈	—	2	2	no	—
253	C₄⋊Q₈	—	2	2	no	—
254	C₄⋊Q₈	D₄×C₃₁	1	4	yes	—
255	#125	—	2	16	no	—
256	#125	—	2	8	no	—
257	C₄×Q₈	—	2	8	no	—
258	C₄×Q₈	—	2	4	no	—
259	C₄×Q₈	—	2	4	no	—
260	C₄×Q₈	—	2	2	no	—
261	C₄×Q₈	—	2	2	no	—
262	C₄×Q₈	—	2	2	no	—
263	C₄×Q₈	D₄×C₃₁	1	4	yes	—
264	C₂×C₄⋊C₄	—	2	2	no	—
265	C₂×C₄⋊C₄	—	2	1	no	—
266	C₂×C₄⋊C₄	—	2	2	no	—
267	C₂×C₄⋊C₄	—	2	1	no	—
268	C₂×C₄⋊C₄	—	2	2	no	—
269	C₂×C₄⋊C₄	—	2	1	no	—
270	C₂×C₄⋊C₄	—	2	1	no	—
271	C₂×C₄⋊C₄	—	2	1	no	—
272	C₂×C₄⋊C₄	D₄×C₃₁	1	1	yes	characteristic
273	C₂×C₄⋊C₄	D₄×C₃₁	1	2	yes	—
274	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
275	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
276	C₂×C₄²	—	2	2	no	—
277	C₂×C₄²	—	2	1	no	—
278	C₂×C₄²	—	2	1	no	—
279	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
280	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
281	C₄⋊C₈	—	2	2	no	—
282	#103	—	2	4	no	—
283	#103	—	2	4	no	—
284	#103	—	4	4	no	—
285	C₄×C₈	—	2	2	no	—
286	#95	—	2	1	no	—
287	#95	—	2	4	no	—
288	#95	—	2	4	no	—
289	C₃₁	#25634	1	1	yes	characteristic, direct product factor, Sylow
290	C₂×Q₈	—	2	2	no	—
291	C₂×Q₈	—	2	2	no	—
292	C₂×Q₈	—	2	2	no	—
293	C₂×Q₈	—	2	1	no	—
294	C₂×Q₈	—	2	2	no	—
295	C₂×Q₈	—	2	2	no	—
296	C₂×Q₈	—	2	2	no	—
297	C₂×Q₈	—	2	4	no	—
298	C₂×Q₈	—	2	4	no	—
299	C₂×Q₈	—	2	4	no	—
300	C₂×Q₈	—	2	2	no	—
301	C₂×Q₈	—	2	4	no	—
302	C₂×Q₈	Q₁₆×C₃₁	1	4	yes	complemented
303	C₂×Q₈	C₂×D₄×C₃₁	1	4	yes	—
304	C₂×Q₈	C₂×D₄×C₃₁	1	2	yes	—
305	C₂²×C₄	—	2	1	no	—
306	C₂²×C₄	—	2	2	no	—
307	C₂²×C₄	—	2	1	no	—
308	C₂²×C₄	—	2	2	no	—
309	C₂²×C₄	—	2	2	no	—
310	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
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	1	yes	characteristic
314	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
315	Q₁₆	—	4	16	no	—
316	Q₁₆	—	4	8	no	—
317	C₂×C₈	—	2	2	no	—
318	C₂×C₈	—	2	2	no	—
319	C₂×C₈	—	2	2	no	—
320	C₂×C₈	—	2	4	no	—
321	C₂×C₈	#41×C₃₁	1	4	yes	—
322	C₄⋊C₄	—	2	8	no	—
323	C₄⋊C₄	—	2	8	no	—
324	C₄⋊C₄	—	2	8	no	—
325	C₄⋊C₄	—	2	4	no	—
326	C₄⋊C₄	—	2	4	no	—
327	C₄⋊C₄	—	2	4	no	—
328	C₄⋊C₄	—	2	4	no	—
329	C₄⋊C₄	—	2	2	no	—
330	C₄⋊C₄	—	2	1	no	—
331	C₄⋊C₄	—	2	2	no	—
332	C₄⋊C₄	—	2	2	no	—
333	C₄⋊C₄	—	4	2	no	—
334	C₄⋊C₄	—	4	2	no	—
335	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
336	C₄²	—	2	8	no	—
337	C₄²	—	2	4	no	—
338	C₄²	—	2	2	no	—
339	C₄²	—	2	2	no	—
340	C₄²	—	4	2	no	—
341	C₄²	C₂×D₄×C₃₁	1	2	yes	—
342	C₄²	C₂×D₄×C₃₁	1	2	yes	—
343	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
344	Q₈	—	2	8	no	—
345	Q₈	—	2	2	no	—
346	Q₈	—	2	2	no	—
347	Q₈	—	2	8	no	—
348	Q₈	—	4	2	no	—
349	Q₈	—	4	2	no	—
350	Q₈	—	4	2	no	—
351	Q₈	—	4	2	no	—
352	Q₈	—	4	2	no	—
353	Q₈	—	4	4	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	2	4	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	4	no	—
362	C₂×C₄	—	4	2	no	—
363	C₂×C₄	—	4	4	no	—
364	C₂×C₄	—	4	2	no	—
365	C₂×C₄	—	4	2	no	—
366	C₂×C₄	—	4	2	no	—
367	C₂×C₄	—	4	4	no	—
368	C₂×C₄	—	4	2	no	—
369	C₂×C₄	—	4	2	no	—
370	C₂×C₄	C₃₁×#120	1	2	yes	—
371	C₂×C₄	C₃₁×#120	1	2	yes	—
372	C₂×C₄	C₂×Q₁₆×C₃₁	1	4	yes	—
373	C₂×C₄	C₂×Q₁₆×C₃₁	1	2	yes	—
374	C₂×C₄	C₃₁×#137	1	2	yes	—
375	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
376	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
377	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
378	C₂×C₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
379	C₈	—	2	4	no	—
380	C₈	—	4	2	no	—
381	C₂²	C₂×C₃₁×#120	1	1	yes	characteristic
382	C₂²	C₃₁×#550	1	2	yes	—
383	C₂²	C₂²×Q₁₆×C₃₁	1	1	yes	characteristic
384	C₂²	C₂×C₃₁×#137	1	1	yes	characteristic
385	C₂²	C₃₁×#578	1	2	yes	—
386	C₄	—	2	4	no	—
387	C₄	—	2	2	no	—
388	C₄	—	4	2	no	—
389	C₄	—	4	4	no	—
390	C₄	—	4	2	no	—
391	C₄	—	4	2	no	—
392	C₄	—	8	2	no	—
393	C₄	—	8	2	no	—
394	C₄	C₃₁×#451	1	4	yes	—
395	C₄	C₃₁×#532	1	1	yes	characteristic
396	C₄	C₃₁×#535	1	1	yes	characteristic
397	C₄	C₃₁×#546	1	2	yes	—
398	C₂	C₃₁×#2431	1	1	yes	characteristic
399	C₂	C₂×C₃₁×#451	1	1	yes	characteristic
400	C₂	C₃₁×#3011	1	1	yes	characteristic
401	C₂	C₃₁×#3395	1	2	yes	—
402	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 ◁ C₂×C₄×Q₈×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
100. C₂×Q₈×C₃₁	Q₁₆	semidirect
141. #25634	C₃₁	direct (N × H)
289. C₃₁	#25634	direct (N × H)
302. C₂×Q₈	Q₁₆×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×#557	2
C₂×C₃₁×#494	2
C₂×C₃₁×#462	2
C₃₁×#2568	2
C₃₁×#2016	2
C₃₁×#1984	2
C₃₁×#1981	2
C₃₁×#1878	2
C₄×C₃₁×#103	2
#25634	31

Subgroups — C31×#25634 #21482393

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#25634 #21482393