Subgroups — C₃₁×#33170 #21489929

Order 7936.

1282 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#492	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃₁×#465	C₂	1	4	yes	maximal, complemented
3	C₂²×C₄×C₈×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#2857	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#2856	C₂	1	1	yes	maximal, characteristic
6	C₃₁×#1968	C₂	1	4	yes	maximal, complemented
7	C₃₁×#1957	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#1956	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#1844	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×SD₁₆×C₃₁	C₂²	1	4	yes	—
11	C₂³×C₈×C₃₁	C₂²	1	2	yes	—
12	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
13	C₂×C₃₁×#127	C₂²	1	1	yes	characteristic
14	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	—
15	C₂×C₃₁×#121	—	2	2	no	—
16	C₂×C₃₁×#121	C₂²	1	2	yes	—
17	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
18	C₃₁×#492	—	2	4	no	—
19	C₃₁×#465	—	2	16	no	—
20	C₂×C₃₁×#106	C₂²	1	4	yes	—
21	C₂×C₃₁×#103	C₂²	1	4	yes	—
22	C₂×C₃₁×#102	C₂²	1	4	yes	—
23	C₂×C₄×C₈×C₃₁	—	2	4	no	—
24	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
25	C₂×C₄×C₈×C₃₁	C₂²	1	2	yes	—
26	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
27	C₃₁×#391	C₂²	1	2	yes	—
28	C₃₁×#390	—	2	2	no	—
29	C₃₁×#390	C₂²	1	2	yes	—
30	C₃₁×#389	—	2	2	no	—
31	C₃₁×#384	C₂²	1	1	yes	characteristic
32	C₃₁×#384	C₂²	1	1	yes	characteristic
33	C₃₁×#380	—	2	2	no	—
34	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
35	C₂²×D₄×C₃₁	—	2	2	no	—
36	C₂²×D₄×C₃₁	—	2	2	no	—
37	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
38	C₂³×C₄×C₃₁	D₄	1	2	yes	—
39	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
40	C₂×SD₁₆×C₃₁	—	2	8	no	—
41	C₂×SD₁₆×C₃₁	—	2	8	no	—
42	C₂×SD₁₆×C₃₁	—	2	8	no	—
43	C₂²×C₈×C₃₁	—	2	4	no	—
44	C₂²×C₈×C₃₁	—	2	4	no	—
45	C₂²×C₈×C₃₁	D₄	1	8	yes	complemented
46	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
47	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
48	C₃₁×C₄⋊Q₈	—	2	2	no	—
49	C₃₁×C₄⋊Q₈	—	2	2	no	—
50	C₃₁×#127	—	2	2	no	—
51	C₃₁×#127	—	2	2	no	—
52	C₃₁×C₂²⋊Q₈	—	2	8	no	—
53	C₃₁×#121	—	2	8	no	—
54	C₃₁×#121	—	4	8	no	—
55	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
56	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
57	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
58	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
59	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
60	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
61	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
62	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
63	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
64	C₂×C₄²×C₃₁	—	2	2	no	—
65	C₂×C₄²×C₃₁	—	2	2	no	—
66	C₂×C₄²×C₃₁	D₄	1	2	yes	—
67	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
68	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
69	C₃₁×#106	—	2	8	no	—
70	C₃₁×#103	—	2	8	no	—
71	C₃₁×#102	—	2	8	no	—
72	C₄×C₈×C₃₁	—	2	4	no	—
73	C₄×C₈×C₃₁	—	2	2	no	—
74	C₄×C₈×C₃₁	D₄	1	4	yes	complemented
75	C₃₁×#95	—	2	4	no	—
76	C₂⁴×C₃₁	—	2	2	no	—
77	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
78	C₂×Q₈×C₃₁	—	2	4	no	—
79	C₂×Q₈×C₃₁	—	2	2	no	—
80	C₂×Q₈×C₃₁	—	2	2	no	—
81	C₂×Q₈×C₃₁	—	2	4	no	—
82	C₂×D₄×C₃₁	—	2	4	no	—
83	C₂×D₄×C₃₁	—	2	2	no	—
84	C₂×D₄×C₃₁	—	2	2	no	—
85	C₂×D₄×C₃₁	—	2	4	no	—
86	C₂×D₄×C₃₁	—	4	4	no	—
87	C₂×D₄×C₃₁	—	4	8	no	—
88	C₂×D₄×C₃₁	—	4	4	no	—
89	C₂×D₄×C₃₁	—	4	4	no	—
90	C₂×D₄×C₃₁	—	4	4	no	—
91	C₂²×C₄×C₃₁	—	2	4	no	—
92	C₂²×C₄×C₃₁	—	2	4	no	—
93	C₂²×C₄×C₃₁	—	2	1	no	—
94	C₂²×C₄×C₃₁	—	2	1	no	—
95	C₂²×C₄×C₃₁	—	2	2	no	—
96	C₂²×C₄×C₃₁	—	2	2	no	—
97	C₂²×C₄×C₃₁	—	2	2	no	—
98	C₂²×C₄×C₃₁	—	2	2	no	—
99	C₂²×C₄×C₃₁	SD₁₆	1	8	yes	complemented
100	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
102	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
103	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
104	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
105	SD₁₆×C₃₁	—	4	16	no	—
106	C₂×C₈×C₃₁	—	2	2	no	—
107	C₂×C₈×C₃₁	—	2	2	no	—
108	C₂×C₈×C₃₁	—	2	16	no	—
109	C₂×C₈×C₃₁	C₂×D₄	1	4	yes	—
110	C₂×C₈×C₃₁	C₂×D₄	1	4	yes	—
111	C₂×C₈×C₃₁	C₂×D₄	1	4	yes	—
112	C₂×C₈×C₃₁	#41	1	4	yes	—
113	C₄⋊C₄×C₃₁	—	2	4	no	—
114	C₄⋊C₄×C₃₁	—	2	4	no	—
115	C₄⋊C₄×C₃₁	—	4	4	no	—
116	C₄⋊C₄×C₃₁	—	4	4	no	—
117	C₄⋊C₄×C₃₁	—	4	4	no	—
118	C₄⋊C₄×C₃₁	—	4	4	no	—
119	C₂²⋊C₄×C₃₁	—	4	4	no	—
120	C₂²⋊C₄×C₃₁	—	4	4	no	—
121	C₂²⋊C₄×C₃₁	—	4	8	no	—
122	C₄²×C₃₁	—	2	4	no	—
123	C₄²×C₃₁	—	2	1	no	—
124	C₄²×C₃₁	—	2	1	no	—
125	C₄²×C₃₁	C₂×D₄	1	2	yes	—
126	C₄²×C₃₁	#41	1	2	yes	—
127	#33170	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
128	C₂³×C₃₁	—	2	1	no	—
129	C₂³×C₃₁	—	2	1	no	—
130	C₂³×C₃₁	—	2	2	no	—
131	C₂³×C₃₁	—	4	2	no	—
132	C₂³×C₃₁	—	4	2	no	—
133	C₂³×C₃₁	—	4	2	no	—
134	C₂³×C₃₁	—	4	4	no	—
135	C₂³×C₃₁	—	4	4	no	—
136	C₂³×C₃₁	#127	1	2	yes	—
137	C₂³×C₃₁	C₂×SD₁₆	1	4	yes	—
138	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
139	Q₈×C₃₁	—	4	4	no	—
140	Q₈×C₃₁	—	4	4	no	—
141	D₄×C₃₁	—	4	4	no	—
142	D₄×C₃₁	—	4	4	no	—
143	D₄×C₃₁	—	8	8	no	—
144	D₄×C₃₁	—	8	8	no	—
145	C₂×C₄×C₃₁	—	2	1	no	—
146	C₂×C₄×C₃₁	—	2	2	no	—
147	C₂×C₄×C₃₁	—	2	1	no	—
148	C₂×C₄×C₃₁	—	2	2	no	—
149	C₂×C₄×C₃₁	—	2	4	no	—
150	C₂×C₄×C₃₁	—	2	4	no	—
151	C₂×C₄×C₃₁	—	2	16	no	—
152	C₂×C₄×C₃₁	—	4	2	no	—
153	C₂×C₄×C₃₁	—	4	2	no	—
154	C₂×C₄×C₃₁	—	4	2	no	—
155	C₂×C₄×C₃₁	—	4	2	no	—
156	C₂×C₄×C₃₁	—	4	2	no	—
157	C₂×C₄×C₃₁	—	4	4	no	—
158	C₂×C₄×C₃₁	—	4	4	no	—
159	C₂×C₄×C₃₁	#121	1	4	yes	—
160	C₂×C₄×C₃₁	#127	1	2	yes	—
161	C₂×C₄×C₃₁	C₂×SD₁₆	1	4	yes	—
162	C₂×C₄×C₃₁	C₂×SD₁₆	1	4	yes	—
163	C₂×C₄×C₃₁	#135	1	4	yes	—
164	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
165	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
166	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
167	C₂×C₄×C₃₁	C₂×#41	1	1	yes	characteristic
168	C₈×C₃₁	—	2	4	no	—
169	C₈×C₃₁	#121	1	8	yes	complemented
170	C₂×#492	C₂×C₃₁	1	1	yes	characteristic, complemented
171	C₂×#465	C₂×C₃₁	1	4	yes	complemented
172	C₂²×C₄×C₈	C₂×C₃₁	1	1	yes	characteristic, complemented
173	#2857	C₂×C₃₁	1	1	yes	characteristic, complemented
174	#2856	C₂×C₃₁	1	1	yes	characteristic
175	#1968	C₂×C₃₁	1	4	yes	complemented
176	#1957	C₂×C₃₁	1	1	yes	characteristic, complemented
177	#1956	C₂×C₃₁	1	1	yes	characteristic, complemented
178	#1844	C₂×C₃₁	1	1	yes	characteristic, complemented
179	C₂²×C₃₁	—	2	2	no	—
180	C₂²×C₃₁	—	2	2	no	—
181	C₂²×C₃₁	—	2	4	no	—
182	C₂²×C₃₁	—	2	4	no	—
183	C₂²×C₃₁	—	8	2	no	—
184	C₂²×C₃₁	—	8	2	no	—
185	C₂²×C₃₁	—	8	2	no	—
186	C₂²×C₃₁	—	8	4	no	—
187	C₂²×C₃₁	—	8	4	no	—
188	C₂²×C₃₁	#492	1	4	yes	complemented
189	C₂²×C₃₁	C₂×#121	1	1	yes	characteristic
190	C₂²×C₃₁	C₂×#127	1	1	yes	characteristic
191	C₂²×C₃₁	#532	1	1	yes	characteristic
192	C₂²×C₃₁	C₂²×SD₁₆	1	2	yes	—
193	C₂²×C₃₁	C₂×#135	1	2	yes	—
194	C₄×C₃₁	—	2	2	no	—
195	C₄×C₃₁	—	2	4	no	—
196	C₄×C₃₁	—	8	2	no	—
197	C₄×C₃₁	—	8	2	no	—
198	C₄×C₃₁	—	8	2	no	—
199	C₄×C₃₁	#465	1	8	yes	complemented
200	C₄×C₃₁	C₂×#121	1	2	yes	—
201	C₄×C₃₁	#532	1	2	yes	—
202	C₂²×SD₁₆	C₂²×C₃₁	1	4	yes	—
203	C₂³×C₈	C₂²×C₃₁	1	2	yes	—
204	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
205	C₂×#127	C₂²×C₃₁	1	1	yes	characteristic
206	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	—
207	C₂×#121	—	2	2	no	—
208	C₂×#121	C₂²×C₃₁	1	2	yes	—
209	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
210	#492	—	2	4	no	—
211	#465	—	2	16	no	—
212	C₂×#106	C₂²×C₃₁	1	4	yes	—
213	C₂×#103	C₂²×C₃₁	1	4	yes	—
214	C₂×#102	C₂²×C₃₁	1	4	yes	—
215	C₂×C₄×C₈	—	2	4	no	—
216	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
217	C₂×C₄×C₈	C₂²×C₃₁	1	2	yes	—
218	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
219	#391	C₂²×C₃₁	1	2	yes	—
220	#390	—	2	2	no	—
221	#390	C₂²×C₃₁	1	2	yes	—
222	#389	—	2	2	no	—
223	#384	C₂²×C₃₁	1	1	yes	characteristic
224	#384	C₂²×C₃₁	1	1	yes	characteristic
225	#380	—	2	2	no	—
226	C₂×C₃₁	—	2	4	no	—
227	C₂×C₃₁	—	16	2	no	—
228	C₂×C₃₁	#2856	1	1	yes	characteristic
229	C₂×C₃₁	C₂×#465	1	2	yes	—
230	C₂×C₃₁	C₂×#492	1	1	yes	characteristic
231	C₂×C₃₁	#3147	1	1	yes	characteristic
232	C₂×C₃₁	#3167	1	2	yes	—
233	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
234	C₂²×D₄	—	2	2	no	—
235	C₂²×D₄	—	2	2	no	—
236	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
237	C₂³×C₄	D₄×C₃₁	1	2	yes	—
238	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
239	C₂×SD₁₆	—	2	8	no	—
240	C₂×SD₁₆	—	2	8	no	—
241	C₂×SD₁₆	—	2	8	no	—
242	C₂²×C₈	—	2	4	no	—
243	C₂²×C₈	—	2	4	no	—
244	C₂²×C₈	D₄×C₃₁	1	8	yes	complemented
245	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
246	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
247	C₄⋊Q₈	—	2	2	no	—
248	C₄⋊Q₈	—	2	2	no	—
249	#127	—	2	2	no	—
250	#127	—	2	2	no	—
251	C₂²⋊Q₈	—	2	8	no	—
252	#121	—	2	8	no	—
253	#121	—	4	8	no	—
254	C₂×C₄⋊C₄	—	2	2	no	—
255	C₂×C₄⋊C₄	—	2	2	no	—
256	C₂×C₄⋊C₄	—	2	2	no	—
257	C₂×C₄⋊C₄	—	2	2	no	—
258	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
259	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
260	C₂×C₂²⋊C₄	—	2	2	no	—
261	C₂×C₂²⋊C₄	—	2	4	no	—
262	C₂×C₂²⋊C₄	—	2	2	no	—
263	C₂×C₄²	—	2	2	no	—
264	C₂×C₄²	—	2	2	no	—
265	C₂×C₄²	D₄×C₃₁	1	2	yes	—
266	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
267	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
268	#106	—	2	8	no	—
269	#103	—	2	8	no	—
270	#102	—	2	8	no	—
271	C₄×C₈	—	2	4	no	—
272	C₄×C₈	—	2	2	no	—
273	C₄×C₈	D₄×C₃₁	1	4	yes	complemented
274	#95	—	2	4	no	—
275	C₃₁	#33170	1	1	yes	characteristic, direct product factor, Sylow
276	C₂⁴	—	2	2	no	—
277	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
278	C₂×Q₈	—	2	4	no	—
279	C₂×Q₈	—	2	2	no	—
280	C₂×Q₈	—	2	2	no	—
281	C₂×Q₈	—	2	4	no	—
282	C₂×D₄	—	2	4	no	—
283	C₂×D₄	—	2	2	no	—
284	C₂×D₄	—	2	2	no	—
285	C₂×D₄	—	2	4	no	—
286	C₂×D₄	—	4	4	no	—
287	C₂×D₄	—	4	8	no	—
288	C₂×D₄	—	4	4	no	—
289	C₂×D₄	—	4	4	no	—
290	C₂×D₄	—	4	4	no	—
291	C₂²×C₄	—	2	4	no	—
292	C₂²×C₄	—	2	4	no	—
293	C₂²×C₄	—	2	1	no	—
294	C₂²×C₄	—	2	1	no	—
295	C₂²×C₄	—	2	2	no	—
296	C₂²×C₄	—	2	2	no	—
297	C₂²×C₄	—	2	2	no	—
298	C₂²×C₄	—	2	2	no	—
299	C₂²×C₄	SD₁₆×C₃₁	1	8	yes	complemented
300	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
301	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
302	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
303	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
304	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
305	SD₁₆	—	4	16	no	—
306	C₂×C₈	—	2	2	no	—
307	C₂×C₈	—	2	2	no	—
308	C₂×C₈	—	2	16	no	—
309	C₂×C₈	C₂×D₄×C₃₁	1	4	yes	—
310	C₂×C₈	C₂×D₄×C₃₁	1	4	yes	—
311	C₂×C₈	C₂×D₄×C₃₁	1	4	yes	—
312	C₂×C₈	#41×C₃₁	1	4	yes	—
313	C₄⋊C₄	—	2	4	no	—
314	C₄⋊C₄	—	2	4	no	—
315	C₄⋊C₄	—	4	4	no	—
316	C₄⋊C₄	—	4	4	no	—
317	C₄⋊C₄	—	4	4	no	—
318	C₄⋊C₄	—	4	4	no	—
319	C₂²⋊C₄	—	4	4	no	—
320	C₂²⋊C₄	—	4	4	no	—
321	C₂²⋊C₄	—	4	8	no	—
322	C₄²	—	2	4	no	—
323	C₄²	—	2	1	no	—
324	C₄²	—	2	1	no	—
325	C₄²	C₂×D₄×C₃₁	1	2	yes	—
326	C₄²	#41×C₃₁	1	2	yes	—
327	C₂³	—	2	1	no	—
328	C₂³	—	2	1	no	—
329	C₂³	—	2	2	no	—
330	C₂³	—	4	2	no	—
331	C₂³	—	4	2	no	—
332	C₂³	—	4	2	no	—
333	C₂³	—	4	4	no	—
334	C₂³	—	4	4	no	—
335	C₂³	C₃₁×#127	1	2	yes	—
336	C₂³	C₂×SD₁₆×C₃₁	1	4	yes	—
337	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
338	Q₈	—	4	4	no	—
339	Q₈	—	4	4	no	—
340	D₄	—	4	4	no	—
341	D₄	—	4	4	no	—
342	D₄	—	8	8	no	—
343	D₄	—	8	8	no	—
344	C₂×C₄	—	2	1	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	1	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	2	16	no	—
349	C₂×C₄	—	2	4	no	—
350	C₂×C₄	—	2	4	no	—
351	C₂×C₄	—	4	2	no	—
352	C₂×C₄	—	4	2	no	—
353	C₂×C₄	—	4	2	no	—
354	C₂×C₄	—	4	2	no	—
355	C₂×C₄	—	4	2	no	—
356	C₂×C₄	—	4	4	no	—
357	C₂×C₄	—	4	4	no	—
358	C₂×C₄	C₃₁×#121	1	4	yes	—
359	C₂×C₄	C₃₁×#127	1	2	yes	—
360	C₂×C₄	C₂×SD₁₆×C₃₁	1	4	yes	—
361	C₂×C₄	C₂×SD₁₆×C₃₁	1	4	yes	—
362	C₂×C₄	C₃₁×#135	1	4	yes	—
363	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
364	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
365	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
366	C₂×C₄	C₂×#41×C₃₁	1	1	yes	characteristic
367	C₈	—	2	4	no	—
368	C₈	C₃₁×#121	1	8	yes	complemented
369	C₂²	—	2	2	no	—
370	C₂²	—	2	2	no	—
371	C₂²	—	2	4	no	—
372	C₂²	—	2	4	no	—
373	C₂²	—	8	2	no	—
374	C₂²	—	8	2	no	—
375	C₂²	—	8	2	no	—
376	C₂²	—	8	4	no	—
377	C₂²	—	8	4	no	—
378	C₂²	C₃₁×#492	1	4	yes	complemented
379	C₂²	C₂×C₃₁×#121	1	1	yes	characteristic
380	C₂²	C₂×C₃₁×#127	1	1	yes	characteristic
381	C₂²	C₃₁×#532	1	1	yes	characteristic
382	C₂²	C₂²×SD₁₆×C₃₁	1	2	yes	—
383	C₂²	C₂×C₃₁×#135	1	2	yes	—
384	C₄	—	2	2	no	—
385	C₄	—	2	4	no	—
386	C₄	—	8	2	no	—
387	C₄	—	8	2	no	—
388	C₄	—	8	2	no	—
389	C₄	C₃₁×#465	1	8	yes	complemented
390	C₄	C₂×C₃₁×#121	1	2	yes	—
391	C₄	C₃₁×#532	1	2	yes	—
392	C₂	—	2	4	no	—
393	C₂	—	16	2	no	—
394	C₂	C₃₁×#2856	1	1	yes	characteristic
395	C₂	C₂×C₃₁×#465	1	2	yes	—
396	C₂	C₂×C₃₁×#492	1	1	yes	characteristic
397	C₂	C₃₁×#3147	1	1	yes	characteristic
398	C₂	C₃₁×#3167	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₃₁
prime radical	C₃₁×#2856	C₂
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
1. C₂×C₃₁×#492	C₂	semidirect
2. C₂×C₃₁×#465	C₂	semidirect
3. C₂²×C₄×C₈×C₃₁	C₂	semidirect
4. C₃₁×#2857	C₂	semidirect
6. C₃₁×#1968	C₂	semidirect
7. C₃₁×#1957	C₂	semidirect
8. C₃₁×#1956	C₂	semidirect
9. C₃₁×#1844	C₂	semidirect
45. C₂²×C₈×C₃₁	D₄	semidirect
74. C₄×C₈×C₃₁	D₄	semidirect
99. C₂²×C₄×C₃₁	SD₁₆	semidirect
127. #33170	C₃₁	direct (N × H)
169. C₈×C₃₁	#121	semidirect
170. C₂×#492	C₂×C₃₁	semidirect
171. C₂×#465	C₂×C₃₁	semidirect
172. C₂²×C₄×C₈	C₂×C₃₁	semidirect
173. #2857	C₂×C₃₁	semidirect
175. #1968	C₂×C₃₁	semidirect
176. #1957	C₂×C₃₁	semidirect
177. #1956	C₂×C₃₁	semidirect
178. #1844	C₂×C₃₁	semidirect
188. C₂²×C₃₁	#492	semidirect
199. C₄×C₃₁	#465	semidirect
244. C₂²×C₈	D₄×C₃₁	semidirect
273. C₄×C₈	D₄×C₃₁	semidirect
275. C₃₁	#33170	direct (N × H)
299. C₂²×C₄	SD₁₆×C₃₁	semidirect
368. C₈	C₃₁×#121	semidirect
378. C₂²	C₃₁×#492	semidirect
389. C₄	C₃₁×#465	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃₁×#492	2
C₂×C₃₁×#465	2
C₂²×C₄×C₈×C₃₁	2
C₃₁×#2857	2
C₃₁×#2856	2
C₃₁×#1968	2
C₃₁×#1957	2
C₃₁×#1956	2
C₃₁×#1844	2
#33170	31

Subgroups — C31×#33170 #21489929

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#33170 #21489929