Subgroups — C₃₁×#33109 #21489868

Order 7936.

964 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#484	C₂	1	2	yes	maximal
2	C₃₁×#2857	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×C₄⋊C₄×C₃₁	C₂	1	1	yes	maximal, characteristic
4	C₃₁×#1981	C₂	1	2	yes	maximal, complemented
5	C₃₁×#1947	C₂	1	2	yes	maximal, complemented
6	C₃₁×#1928	C₂	1	4	yes	maximal, complemented
7	C₃₁×#1872	C₂	1	2	yes	maximal
8	C₃₁×#1797	C₂	1	1	yes	maximal, characteristic
9	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
10	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	—
11	C₂²×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
12	C₂²×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
13	C₂²×C₄²×C₃₁	—	2	1	no	—
14	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
15	C₃₁×#484	—	2	8	no	—
16	C₂×C₃₁×#107	C₂²	1	4	yes	—
17	C₂×C₃₁×C₄⋊C₈	C₂²	1	2	yes	—
18	C₂×C₃₁×#103	C₂²	1	4	yes	—
19	C₂×C₃₁×#103	C₂²	1	4	yes	—
20	C₂×C₃₁×C₂²⋊C₈	C₂²	1	2	yes	—
21	C₃₁×#391	C₂²	1	2	yes	—
22	C₃₁×#389	—	2	1	no	—
23	C₃₁×#389	—	2	1	no	—
24	C₃₁×#384	C₂²	1	1	yes	characteristic
25	C₃₁×#380	—	2	1	no	—
26	C₃₁×#380	—	2	1	no	—
27	C₄×C₄⋊C₄×C₃₁	—	2	1	no	—
28	C₄×C₄⋊C₄×C₃₁	—	2	1	no	—
29	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
30	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
31	C₂×C₃₁×#95	—	2	1	no	—
32	C₃₁×#340	C₂²	1	4	yes	—
33	C₃₁×#336	C₂²	1	2	yes	—
34	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
35	C₂³×C₄×C₃₁	—	2	1	no	—
36	C₂³×C₄×C₃₁	—	2	1	no	—
37	C₂³×C₄×C₃₁	D₄	1	1	yes	characteristic
38	C₂³×C₄×C₃₁	D₄	1	1	yes	characteristic
39	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
40	C₂²×C₈×C₃₁	C₂³	1	4	yes	—
41	C₃₁×C₄⋊Q₈	—	2	4	no	—
42	C₃₁×C₂²⋊Q₈	—	2	4	no	—
43	C₃₁×C₂²⋊Q₈	—	2	4	no	—
44	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
45	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
46	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
47	C₂×C₄⋊C₄×C₃₁	—	2	4	no	—
48	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
49	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
50	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
51	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
52	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
53	C₂×C₄⋊C₄×C₃₁	D₄	1	4	yes	—
54	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
55	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
56	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
57	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
58	C₂×C₄²×C₃₁	—	2	4	no	—
59	C₂×C₄²×C₃₁	—	2	2	no	—
60	C₂×C₄²×C₃₁	—	2	2	no	—
61	C₂×C₄²×C₃₁	—	4	4	no	—
62	C₂×C₄²×C₃₁	D₄	1	1	yes	characteristic
63	C₂×C₄²×C₃₁	D₄	1	1	yes	characteristic
64	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
65	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
66	C₃₁×#107	—	2	8	no	—
67	C₃₁×C₄⋊C₈	—	2	4	no	—
68	C₃₁×#103	—	2	8	no	—
69	C₃₁×#103	—	2	8	no	—
70	C₃₁×C₂²⋊C₈	—	2	4	no	—
71	C₃₁×#95	—	2	2	no	—
72	C₃₁×#95	—	2	2	no	—
73	C₃₁×#95	—	2	2	no	—
74	C₃₁×#95	—	2	2	no	—
75	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
76	C₂×Q₈×C₃₁	—	2	2	no	—
77	C₂×Q₈×C₃₁	—	2	4	no	—
78	C₂×Q₈×C₃₁	—	2	2	no	—
79	C₂×Q₈×C₃₁	—	2	4	no	—
80	C₂²×C₄×C₃₁	—	2	2	no	—
81	C₂²×C₄×C₃₁	—	2	2	no	—
82	C₂²×C₄×C₃₁	—	2	2	no	—
83	C₂²×C₄×C₃₁	—	2	2	no	—
84	C₂²×C₄×C₃₁	—	2	4	no	—
85	C₂²×C₄×C₃₁	—	2	4	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	2	no	—
90	C₂²×C₄×C₃₁	—	2	2	no	—
91	C₂²×C₄×C₃₁	—	2	2	no	—
92	C₂²×C₄×C₃₁	—	4	1	no	—
93	C₂²×C₄×C₃₁	—	4	2	no	—
94	C₂²×C₄×C₃₁	—	4	2	no	—
95	C₂²×C₄×C₃₁	—	4	2	no	—
96	C₂²×C₄×C₃₁	—	4	2	no	—
97	C₂²×C₄×C₃₁	Q₁₆	1	4	yes	—
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	2	yes	—
101	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₃₁	#41	1	2	yes	—
105	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
106	C₂×C₈×C₃₁	—	2	4	no	—
107	C₂×C₈×C₃₁	—	2	4	no	—
108	C₂×C₈×C₃₁	—	2	4	no	—
109	C₄⋊C₄×C₃₁	—	2	4	no	—
110	C₄⋊C₄×C₃₁	—	2	4	no	—
111	C₄⋊C₄×C₃₁	—	2	2	no	—
112	C₄⋊C₄×C₃₁	—	2	2	no	—
113	C₄⋊C₄×C₃₁	—	2	2	no	—
114	C₄⋊C₄×C₃₁	—	2	2	no	—
115	C₄⋊C₄×C₃₁	—	4	2	no	—
116	C₄⋊C₄×C₃₁	—	4	4	no	—
117	C₄⋊C₄×C₃₁	—	4	2	no	—
118	C₄⋊C₄×C₃₁	—	4	2	no	—
119	C₄⋊C₄×C₃₁	—	4	2	no	—
120	C₄⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
121	C₄⋊C₄×C₃₁	#41	1	4	yes	—
122	C₂²⋊C₄×C₃₁	—	4	4	no	—
123	C₄²×C₃₁	—	2	2	no	—
124	C₄²×C₃₁	—	2	2	no	—
125	C₄²×C₃₁	—	2	2	no	—
126	C₄²×C₃₁	—	4	4	no	—
127	C₄²×C₃₁	—	4	4	no	—
128	C₄²×C₃₁	#41	1	4	yes	—
129	#33109	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
130	C₂³×C₃₁	—	2	1	no	—
131	C₂³×C₃₁	—	2	1	no	—
132	C₂³×C₃₁	—	2	1	no	—
133	C₂³×C₃₁	—	2	1	no	—
134	C₂³×C₃₁	#121	1	2	yes	—
135	C₂³×C₃₁	C₂×Q₁₆	1	2	yes	—
136	C₂³×C₃₁	#137	1	2	yes	—
137	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
138	Q₈×C₃₁	—	4	4	no	—
139	Q₈×C₃₁	—	4	4	no	—
140	C₂×C₄×C₃₁	—	2	1	no	—
141	C₂×C₄×C₃₁	—	2	1	no	—
142	C₂×C₄×C₃₁	—	2	1	no	—
143	C₂×C₄×C₃₁	—	2	1	no	—
144	C₂×C₄×C₃₁	—	2	1	no	—
145	C₂×C₄×C₃₁	—	2	1	no	—
146	C₂×C₄×C₃₁	—	2	4	no	—
147	C₂×C₄×C₃₁	—	2	4	no	—
148	C₂×C₄×C₃₁	—	2	8	no	—
149	C₂×C₄×C₃₁	—	2	4	no	—
150	C₂×C₄×C₃₁	—	2	1	no	—
151	C₂×C₄×C₃₁	—	2	4	no	—
152	C₂×C₄×C₃₁	—	2	1	no	—
153	C₂×C₄×C₃₁	—	2	1	no	—
154	C₂×C₄×C₃₁	—	4	4	no	—
155	C₂×C₄×C₃₁	—	4	8	no	—
156	C₂×C₄×C₃₁	—	4	8	no	—
157	C₂×C₄×C₃₁	—	4	2	no	—
158	C₂×C₄×C₃₁	—	4	2	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	—	4	2	no	—
166	C₂×C₄×C₃₁	—	4	2	no	—
167	C₂×C₄×C₃₁	#121	1	2	yes	—
168	C₂×C₄×C₃₁	#123	1	2	yes	—
169	C₂×C₄×C₃₁	#123	1	2	yes	—
170	C₂×C₄×C₃₁	C₂×Q₁₆	1	2	yes	—
171	C₂×C₄×C₃₁	C₂×Q₁₆	1	2	yes	—
172	C₂×C₄×C₃₁	AGL(1,ℤ/8)	1	2	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	2	yes	—
176	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
177	C₈×C₃₁	—	4	4	no	—
178	C₂×#484	C₂×C₃₁	1	2	yes	—
179	#2857	C₂×C₃₁	1	1	yes	characteristic
180	C₂×C₄×C₄⋊C₄	C₂×C₃₁	1	1	yes	characteristic
181	#1981	C₂×C₃₁	1	2	yes	complemented
182	#1947	C₂×C₃₁	1	2	yes	complemented
183	#1928	C₂×C₃₁	1	4	yes	complemented
184	#1872	C₂×C₃₁	1	2	yes	—
185	#1797	C₂×C₃₁	1	1	yes	characteristic
186	C₂²×C₃₁	—	2	2	no	—
187	C₂²×C₃₁	—	2	2	no	—
188	C₂²×C₃₁	—	2	2	no	—
189	C₂²×C₃₁	—	2	2	no	—
190	C₂²×C₃₁	—	2	2	no	—
191	C₂²×C₃₁	—	2	2	no	—
192	C₂²×C₃₁	#462	1	4	yes	—
193	C₂²×C₃₁	C₂×#121	1	1	yes	characteristic
194	C₂²×C₃₁	C₂×#123	1	1	yes	characteristic
195	C₂²×C₃₁	#525	1	1	yes	characteristic
196	C₂²×C₃₁	C₂²×Q₁₆	1	1	yes	characteristic
197	C₂²×C₃₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
198	C₂²×C₃₁	C₂×#137	1	1	yes	characteristic
199	C₂²×C₃₁	#575	1	1	yes	characteristic
200	C₄×C₃₁	—	2	2	no	—
201	C₄×C₃₁	—	2	2	no	—
202	C₄×C₃₁	—	2	2	no	—
203	C₄×C₃₁	—	4	1	no	—
204	C₄×C₃₁	—	4	4	no	—
205	C₄×C₃₁	—	4	4	no	—
206	C₄×C₃₁	—	8	2	no	—
207	C₄×C₃₁	—	8	2	no	—
208	C₄×C₃₁	#484	1	4	yes	complemented
209	C₄×C₃₁	#529	1	2	yes	—
210	C₄×C₃₁	#532	1	2	yes	—
211	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
212	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	—
213	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
214	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
215	C₂²×C₄²	—	2	1	no	—
216	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
217	#484	—	2	8	no	—
218	C₂×#107	C₂²×C₃₁	1	4	yes	—
219	C₂×C₄⋊C₈	C₂²×C₃₁	1	2	yes	—
220	C₂×#103	C₂²×C₃₁	1	4	yes	—
221	C₂×#103	C₂²×C₃₁	1	4	yes	—
222	C₂×C₂²⋊C₈	C₂²×C₃₁	1	2	yes	—
223	#391	C₂²×C₃₁	1	2	yes	—
224	#389	—	2	1	no	—
225	#389	—	2	1	no	—
226	#384	C₂²×C₃₁	1	1	yes	characteristic
227	#380	—	2	1	no	—
228	#380	—	2	1	no	—
229	C₄×C₄⋊C₄	—	2	1	no	—
230	C₄×C₄⋊C₄	—	2	1	no	—
231	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
232	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
233	C₂×#95	—	2	1	no	—
234	#340	C₂²×C₃₁	1	4	yes	—
235	#336	C₂²×C₃₁	1	2	yes	—
236	C₂×C₃₁	—	2	4	no	—
237	C₂×C₃₁	#2854	1	1	yes	characteristic
238	C₂×C₃₁	C₂×#462	1	1	yes	characteristic
239	C₂×C₃₁	#3036	1	1	yes	characteristic
240	C₂×C₃₁	C₂×#484	1	1	yes	characteristic
241	C₂×C₃₁	#3095	1	1	yes	characteristic
242	C₂×C₃₁	#3104	1	1	yes	characteristic
243	C₂×C₃₁	#3110	1	1	yes	characteristic
244	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
245	C₂³×C₄	—	2	1	no	—
246	C₂³×C₄	—	2	1	no	—
247	C₂³×C₄	D₄×C₃₁	1	1	yes	characteristic
248	C₂³×C₄	D₄×C₃₁	1	1	yes	characteristic
249	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
250	C₂²×C₈	C₂³×C₃₁	1	4	yes	—
251	C₄⋊Q₈	—	2	4	no	—
252	C₂²⋊Q₈	—	2	4	no	—
253	C₂²⋊Q₈	—	2	4	no	—
254	C₂×C₄⋊C₄	—	2	1	no	—
255	C₂×C₄⋊C₄	—	2	1	no	—
256	C₂×C₄⋊C₄	—	2	2	no	—
257	C₂×C₄⋊C₄	—	2	4	no	—
258	C₂×C₄⋊C₄	—	2	2	no	—
259	C₂×C₄⋊C₄	—	2	1	no	—
260	C₂×C₄⋊C₄	—	2	1	no	—
261	C₂×C₄⋊C₄	—	2	1	no	—
262	C₂×C₄⋊C₄	—	2	1	no	—
263	C₂×C₄⋊C₄	D₄×C₃₁	1	4	yes	—
264	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
265	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
266	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
267	C₂×C₂²⋊C₄	—	2	2	no	—
268	C₂×C₄²	—	2	4	no	—
269	C₂×C₄²	—	2	2	no	—
270	C₂×C₄²	—	2	2	no	—
271	C₂×C₄²	—	4	4	no	—
272	C₂×C₄²	D₄×C₃₁	1	1	yes	characteristic
273	C₂×C₄²	D₄×C₃₁	1	1	yes	characteristic
274	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
275	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
276	#107	—	2	8	no	—
277	C₄⋊C₈	—	2	4	no	—
278	#103	—	2	8	no	—
279	#103	—	2	8	no	—
280	C₂²⋊C₈	—	2	4	no	—
281	#95	—	2	2	no	—
282	#95	—	2	2	no	—
283	#95	—	2	2	no	—
284	#95	—	2	2	no	—
285	C₃₁	#33109	1	1	yes	characteristic, direct product factor, Sylow
286	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
287	C₂×Q₈	—	2	2	no	—
288	C₂×Q₈	—	2	4	no	—
289	C₂×Q₈	—	2	2	no	—
290	C₂×Q₈	—	2	4	no	—
291	C₂²×C₄	—	2	2	no	—
292	C₂²×C₄	—	2	2	no	—
293	C₂²×C₄	—	2	2	no	—
294	C₂²×C₄	—	2	2	no	—
295	C₂²×C₄	—	2	4	no	—
296	C₂²×C₄	—	2	4	no	—
297	C₂²×C₄	—	2	2	no	—
298	C₂²×C₄	—	2	2	no	—
299	C₂²×C₄	—	2	2	no	—
300	C₂²×C₄	—	2	2	no	—
301	C₂²×C₄	—	2	2	no	—
302	C₂²×C₄	—	2	2	no	—
303	C₂²×C₄	—	4	1	no	—
304	C₂²×C₄	—	4	2	no	—
305	C₂²×C₄	—	4	2	no	—
306	C₂²×C₄	—	4	2	no	—
307	C₂²×C₄	—	4	2	no	—
308	C₂²×C₄	Q₁₆×C₃₁	1	4	yes	—
309	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
310	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
311	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
312	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
313	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
314	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
315	C₂²×C₄	#41×C₃₁	1	2	yes	—
316	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
317	C₂×C₈	—	2	4	no	—
318	C₂×C₈	—	2	4	no	—
319	C₂×C₈	—	2	4	no	—
320	C₄⋊C₄	—	2	4	no	—
321	C₄⋊C₄	—	2	4	no	—
322	C₄⋊C₄	—	2	2	no	—
323	C₄⋊C₄	—	2	2	no	—
324	C₄⋊C₄	—	2	2	no	—
325	C₄⋊C₄	—	2	2	no	—
326	C₄⋊C₄	—	4	2	no	—
327	C₄⋊C₄	—	4	4	no	—
328	C₄⋊C₄	—	4	2	no	—
329	C₄⋊C₄	—	4	2	no	—
330	C₄⋊C₄	—	4	2	no	—
331	C₄⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
332	C₄⋊C₄	#41×C₃₁	1	4	yes	—
333	C₂²⋊C₄	—	4	4	no	—
334	C₄²	—	2	2	no	—
335	C₄²	—	2	2	no	—
336	C₄²	—	2	2	no	—
337	C₄²	—	4	4	no	—
338	C₄²	—	4	4	no	—
339	C₄²	#41×C₃₁	1	4	yes	—
340	C₂³	—	2	1	no	—
341	C₂³	—	2	1	no	—
342	C₂³	—	2	1	no	—
343	C₂³	—	2	1	no	—
344	C₂³	C₃₁×#121	1	2	yes	—
345	C₂³	C₂×Q₁₆×C₃₁	1	2	yes	—
346	C₂³	C₃₁×#137	1	2	yes	—
347	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
348	Q₈	—	4	4	no	—
349	Q₈	—	4	4	no	—
350	C₂×C₄	—	2	1	no	—
351	C₂×C₄	—	2	1	no	—
352	C₂×C₄	—	2	1	no	—
353	C₂×C₄	—	2	1	no	—
354	C₂×C₄	—	2	1	no	—
355	C₂×C₄	—	2	1	no	—
356	C₂×C₄	—	2	8	no	—
357	C₂×C₄	—	2	4	no	—
358	C₂×C₄	—	2	4	no	—
359	C₂×C₄	—	2	4	no	—
360	C₂×C₄	—	2	1	no	—
361	C₂×C₄	—	2	4	no	—
362	C₂×C₄	—	2	1	no	—
363	C₂×C₄	—	2	1	no	—
364	C₂×C₄	—	4	4	no	—
365	C₂×C₄	—	4	8	no	—
366	C₂×C₄	—	4	8	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	—	4	2	no	—
377	C₂×C₄	C₃₁×#121	1	2	yes	—
378	C₂×C₄	C₃₁×#123	1	2	yes	—
379	C₂×C₄	C₃₁×#123	1	2	yes	—
380	C₂×C₄	C₂×Q₁₆×C₃₁	1	2	yes	—
381	C₂×C₄	C₂×Q₁₆×C₃₁	1	2	yes	—
382	C₂×C₄	C₃₁×AGL(1,ℤ/8)	1	2	yes	—
383	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
384	C₂×C₄	C₂×#41×C₃₁	1	1	yes	characteristic
385	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
386	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
387	C₈	—	4	4	no	—
388	C₂²	—	2	2	no	—
389	C₂²	—	2	2	no	—
390	C₂²	—	2	2	no	—
391	C₂²	—	2	2	no	—
392	C₂²	—	2	2	no	—
393	C₂²	—	2	2	no	—
394	C₂²	C₃₁×#462	1	4	yes	—
395	C₂²	C₂×C₃₁×#121	1	1	yes	characteristic
396	C₂²	C₂×C₃₁×#123	1	1	yes	characteristic
397	C₂²	C₃₁×#525	1	1	yes	characteristic
398	C₂²	C₂²×Q₁₆×C₃₁	1	1	yes	characteristic
399	C₂²	C₂×C₃₁×AGL(1,ℤ/8)	1	1	yes	characteristic
400	C₂²	C₂×C₃₁×#137	1	1	yes	characteristic
401	C₂²	C₃₁×#575	1	1	yes	characteristic
402	C₄	—	2	2	no	—
403	C₄	—	2	2	no	—
404	C₄	—	2	2	no	—
405	C₄	—	4	1	no	—
406	C₄	—	4	4	no	—
407	C₄	—	4	4	no	—
408	C₄	—	8	2	no	—
409	C₄	—	8	2	no	—
410	C₄	C₃₁×#484	1	4	yes	complemented
411	C₄	C₃₁×#529	1	2	yes	—
412	C₄	C₃₁×#532	1	2	yes	—
413	C₂	—	2	4	no	—
414	C₂	C₃₁×#2854	1	1	yes	characteristic
415	C₂	C₂×C₃₁×#462	1	1	yes	characteristic
416	C₂	C₃₁×#3036	1	1	yes	characteristic
417	C₂	C₂×C₃₁×#484	1	1	yes	characteristic
418	C₂	C₃₁×#3095	1	1	yes	characteristic
419	C₂	C₃₁×#3104	1	1	yes	characteristic
420	C₂	C₃₁×#3110	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
4. C₃₁×#1981	C₂	semidirect
5. C₃₁×#1947	C₂	semidirect
6. C₃₁×#1928	C₂	semidirect
129. #33109	C₃₁	direct (N × H)
181. #1981	C₂×C₃₁	semidirect
182. #1947	C₂×C₃₁	semidirect
183. #1928	C₂×C₃₁	semidirect
208. C₄×C₃₁	#484	semidirect
285. C₃₁	#33109	direct (N × H)
410. C₄	C₃₁×#484	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃₁×#484	2
C₃₁×#2857	2
C₂×C₄×C₄⋊C₄×C₃₁	2
C₃₁×#1981	2
C₃₁×#1947	2
C₃₁×#1928	2
C₃₁×#1872	2
C₃₁×#1797	2
#33109	31

Subgroups — C31×#33109 #21489868

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#33109 #21489868