Subgroups — C₃₁×#17979 #21474738

Order 7936.

658 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3167	C₂	1	1	yes	maximal, characteristic
2	C₃₁×#2960	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#2931	C₂	1	1	yes	maximal, characteristic
4	C₃₁×#1588	C₂	1	4	yes	maximal, complemented
5	C₃₁×#1585	C₂	1	4	yes	maximal, complemented
6	C₃₁×#1567	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#1493	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#1492	C₂	1	1	yes	maximal, characteristic
9	C₂×C₃₁×#322	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₃₁×#131	—	2	1	no	—
11	C₃₁×#533	C₂²	1	1	yes	characteristic
12	C₃₁×#532	C₂²	1	1	yes	characteristic
13	C₃₁×#498	C₄	1	1	yes	characteristic
14	C₃₁×#492	C₄	1	1	yes	characteristic
15	C₃₁×#487	C₄	1	1	yes	characteristic
16	C₃₁×#486	C₄	1	1	yes	characteristic
17	C₃₁×#465	C₄	1	4	yes	—
18	C₃₁×#446	—	2	1	no	—
19	C₃₁×#446	C₂²	1	2	yes	—
20	C₈×Q₈×C₃₁	—	2	1	no	—
21	C₈×Q₈×C₃₁	C₂²	1	2	yes	—
22	C₄×SD₁₆×C₃₁	C₂²	1	4	yes	—
23	C₃₁×#436	—	2	1	no	—
24	C₃₁×#436	C₂²	1	2	yes	—
25	C₈×D₄×C₃₁	—	2	1	no	—
26	C₈×D₄×C₃₁	C₂²	1	2	yes	—
27	C₃₁×#424	—	2	1	no	—
28	C₃₁×#423	C₂²	1	1	yes	characteristic
29	C₃₁×#423	C₂²	1	1	yes	characteristic
30	C₃₁×#408	—	2	1	no	—
31	C₃₁×#405	—	2	1	no	—
32	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
33	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
34	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
35	C₃₁×#335	C₂²	1	4	yes	—
36	C₃₁×Q₈⋊C₈	C₂²	1	4	yes	—
37	C₃₁×D₄⋊C₈	C₂²	1	4	yes	—
38	C₃₁×#322	C₂²	1	2	yes	—
39	C₃₁×#322	C₂²	1	2	yes	—
40	C₂×#41×C₃₁	—	2	1	no	—
41	C₂×SD₁₆×C₃₁	C₂×C₄	1	4	yes	—
42	C₃₁×#131	—	4	4	no	—
43	C₂×M₁₆×C₃₁	—	2	1	no	—
44	C₂×M₁₆×C₃₁	—	2	1	no	—
45	C₂×M₁₆×C₃₁	—	2	2	no	—
46	C₂²×C₈×C₃₁	—	2	1	no	—
47	C₂²×C₈×C₃₁	—	2	2	no	—
48	C₂²×C₈×C₃₁	C₂×C₄	1	2	yes	—
49	C₂²×C₈×C₃₁	D₄	1	1	yes	characteristic
50	C₂²×C₈×C₃₁	D₄	1	1	yes	characteristic
51	C₃₁×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
52	C₃₁×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
53	C₃₁×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
54	C₃₁×#127	C₂×C₄	1	1	yes	characteristic
55	C₃₁×#125	—	2	1	no	—
56	C₃₁×#124	—	2	1	no	—
57	C₃₁×C₂²⋊Q₈	—	2	1	no	—
58	C₃₁×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
59	C₃₁×#121	—	2	1	no	—
60	C₃₁×#121	C₂×C₄	1	2	yes	—
61	C₄×Q₈×C₃₁	—	2	1	no	—
62	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
63	C₄×D₄×C₃₁	—	2	1	no	—
64	C₄×D₄×C₃₁	C₂³	1	2	yes	—
65	C₃₁×#117	—	2	1	no	—
66	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
67	C₃₁×#106	C₂×C₄	1	4	yes	—
68	C₃₁×C₄⋊C₈	—	2	2	no	—
69	C₃₁×C₄⋊C₈	—	2	2	no	—
70	C₃₁×C₄⋊C₈	—	2	1	no	—
71	C₃₁×C₄⋊C₈	—	2	1	no	—
72	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
73	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
74	C₃₁×#103	C₂×C₄	1	4	yes	—
75	C₃₁×#102	C₂×C₄	1	4	yes	—
76	C₃₁×C₂²⋊C₈	—	2	2	no	—
77	C₃₁×C₂²⋊C₈	—	2	2	no	—
78	C₃₁×#97	—	2	2	no	—
79	C₄×C₈×C₃₁	—	2	2	no	—
80	C₄×C₈×C₃₁	—	2	1	no	—
81	C₄×C₈×C₃₁	C₂×C₄	1	1	yes	characteristic
82	C₄×C₈×C₃₁	C₂×C₄	1	1	yes	characteristic
83	C₄×C₈×C₃₁	D₄	1	1	yes	characteristic
84	C₄×C₈×C₃₁	D₄	1	1	yes	characteristic
85	C₄×C₈×C₃₁	C₂³	1	2	yes	—
86	C₄×C₈×C₃₁	C₂³	1	2	yes	—
87	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
88	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
89	#41×C₃₁	—	4	2	no	—
90	#41×C₃₁	—	4	2	no	—
91	C₂×Q₈×C₃₁	—	2	1	no	—
92	C₂×Q₈×C₃₁	—	2	1	no	—
93	C₂×Q₈×C₃₁	C₂²×C₄	1	2	yes	—
94	C₂×D₄×C₃₁	—	2	2	no	—
95	C₂×D₄×C₃₁	—	2	1	no	—
96	C₂×D₄×C₃₁	—	2	1	no	—
97	C₂×D₄×C₃₁	C₂²×C₄	1	2	yes	—
98	C₂²×C₄×C₃₁	—	2	2	no	—
99	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
100	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₃₁	#41	1	1	yes	characteristic
102	SD₁₆×C₃₁	—	4	4	no	—
103	M₁₆×C₃₁	—	4	4	no	—
104	M₁₆×C₃₁	—	4	2	no	—
105	M₁₆×C₃₁	—	4	2	no	—
106	C₂×C₈×C₃₁	—	2	4	no	—
107	C₂×C₈×C₃₁	—	2	2	no	—
108	C₂×C₈×C₃₁	—	2	2	no	—
109	C₂×C₈×C₃₁	—	2	2	no	—
110	C₂×C₈×C₃₁	—	2	2	no	—
111	C₂×C₈×C₃₁	—	2	2	no	—
112	C₂×C₈×C₃₁	—	4	2	no	—
113	C₂×C₈×C₃₁	—	4	4	no	—
114	C₂×C₈×C₃₁	C₂²×C₄	1	2	yes	—
115	C₂×C₈×C₃₁	C₂²×C₄	1	2	yes	—
116	C₂×C₈×C₃₁	C₂×D₄	1	1	yes	characteristic
117	C₂×C₈×C₃₁	C₂×D₄	1	1	yes	characteristic
118	C₂×C₈×C₃₁	C₂×D₄	1	1	yes	characteristic
119	C₂×C₈×C₃₁	C₂×D₄	1	1	yes	characteristic
120	C₄⋊C₄×C₃₁	—	2	1	no	—
121	C₄⋊C₄×C₃₁	—	2	1	no	—
122	C₄⋊C₄×C₃₁	—	2	1	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	C₂²×C₄	1	2	yes	—
127	C₄⋊C₄×C₃₁	C₂²×C₄	1	2	yes	—
128	C₂²⋊C₄×C₃₁	—	2	2	no	—
129	C₂²⋊C₄×C₃₁	—	2	2	no	—
130	C₂²⋊C₄×C₃₁	—	2	2	no	—
131	C₄²×C₃₁	—	2	2	no	—
132	C₄²×C₃₁	C₂²×C₄	1	1	yes	characteristic
133	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
134	C₄²×C₃₁	#41	1	1	yes	characteristic
135	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
136	#17979	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
137	C₂³×C₃₁	—	2	2	no	—
138	C₂³×C₃₁	C₄×D₄	1	1	yes	characteristic
139	Q₈×C₃₁	—	2	4	no	—
140	Q₈×C₃₁	—	4	2	no	—
141	Q₈×C₃₁	—	4	2	no	—
142	D₄×C₃₁	—	2	4	no	—
143	D₄×C₃₁	—	4	4	no	—
144	D₄×C₃₁	—	4	2	no	—
145	D₄×C₃₁	—	4	2	no	—
146	C₂×C₄×C₃₁	—	2	2	no	—
147	C₂×C₄×C₃₁	—	2	2	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	—	4	2	no	—
152	C₂×C₄×C₃₁	—	4	2	no	—
153	C₂×C₄×C₃₁	C₄×D₄	1	1	yes	characteristic
154	C₂×C₄×C₃₁	C₄×D₄	1	1	yes	characteristic
155	C₂×C₄×C₃₁	C₄×D₄	1	1	yes	characteristic
156	C₂×C₄×C₃₁	AGL(1,ℤ/8)	1	2	yes	—
157	C₂×C₄×C₃₁	#137	1	2	yes	—
158	C₂×C₄×C₃₁	C₂³×C₄	1	1	yes	characteristic
159	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
160	C₂×C₄×C₃₁	C₂×#41	1	1	yes	characteristic
161	C₈×C₃₁	—	2	4	no	—
162	C₈×C₃₁	—	2	2	no	—
163	C₈×C₃₁	—	2	2	no	—
164	C₈×C₃₁	—	2	1	no	—
165	C₈×C₃₁	—	2	1	no	—
166	C₈×C₃₁	—	2	1	no	—
167	C₈×C₃₁	—	2	1	no	—
168	C₈×C₃₁	—	4	2	no	—
169	C₈×C₃₁	—	4	2	no	—
170	#3167	C₂×C₃₁	1	1	yes	characteristic
171	#2960	C₂×C₃₁	1	1	yes	characteristic, complemented
172	#2931	C₂×C₃₁	1	1	yes	characteristic
173	#1588	C₂×C₃₁	1	4	yes	complemented
174	#1585	C₂×C₃₁	1	4	yes	complemented
175	#1567	C₂×C₃₁	1	1	yes	characteristic, complemented
176	#1493	C₂×C₃₁	1	1	yes	characteristic, complemented
177	#1492	C₂×C₃₁	1	1	yes	characteristic
178	C₂×#322	C₂×C₃₁	1	1	yes	characteristic, complemented
179	C₂²×C₃₁	—	2	1	no	—
180	C₂²×C₃₁	—	2	1	no	—
181	C₂²×C₃₁	—	4	2	no	—
182	C₂²×C₃₁	—	4	2	no	—
183	C₂²×C₃₁	—	4	2	no	—
184	C₂²×C₃₁	#440	1	2	yes	—
185	C₂²×C₃₁	C₂×C₄×D₄	1	1	yes	characteristic
186	C₄×C₃₁	—	2	1	no	—
187	C₄×C₃₁	—	2	1	no	—
188	C₄×C₃₁	—	4	2	no	—
189	C₄×C₃₁	—	4	2	no	—
190	C₄×C₃₁	—	4	2	no	—
191	C₄×C₃₁	#440	1	2	yes	—
192	C₄×C₃₁	#443	1	2	yes	—
193	C₄×C₃₁	#568	1	2	yes	—
194	C₄×C₃₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
195	C₄×C₃₁	C₂×#137	1	1	yes	characteristic
196	C₂×#131	—	2	1	no	—
197	#533	C₂²×C₃₁	1	1	yes	characteristic
198	#532	C₂²×C₃₁	1	1	yes	characteristic
199	#498	C₄×C₃₁	1	1	yes	characteristic
200	#492	C₄×C₃₁	1	1	yes	characteristic
201	#487	C₄×C₃₁	1	1	yes	characteristic
202	#486	C₄×C₃₁	1	1	yes	characteristic
203	#465	C₄×C₃₁	1	4	yes	—
204	#446	—	2	1	no	—
205	#446	C₂²×C₃₁	1	2	yes	—
206	C₈×Q₈	—	2	1	no	—
207	C₈×Q₈	C₂²×C₃₁	1	2	yes	—
208	C₄×SD₁₆	C₂²×C₃₁	1	4	yes	—
209	#436	—	2	1	no	—
210	#436	C₂²×C₃₁	1	2	yes	—
211	C₈×D₄	—	2	1	no	—
212	C₈×D₄	C₂²×C₃₁	1	2	yes	—
213	#424	—	2	1	no	—
214	#423	C₂²×C₃₁	1	1	yes	characteristic
215	#423	C₂²×C₃₁	1	1	yes	characteristic
216	#408	—	2	1	no	—
217	#405	—	2	1	no	—
218	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
219	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
220	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
221	#335	C₂²×C₃₁	1	4	yes	—
222	Q₈⋊C₈	C₂²×C₃₁	1	4	yes	—
223	D₄⋊C₈	C₂²×C₃₁	1	4	yes	—
224	#322	C₂²×C₃₁	1	2	yes	—
225	#322	C₂²×C₃₁	1	2	yes	—
226	C₂×C₃₁	—	2	2	no	—
227	C₂×C₃₁	—	8	2	no	—
228	C₂×C₃₁	#2932	1	1	yes	characteristic
229	C₂×C₃₁	C₂×#440	1	1	yes	characteristic
230	C₂×C₃₁	C₂×#443	1	1	yes	characteristic
231	C₂×#41	—	2	1	no	—
232	C₂×SD₁₆	C₂×C₄×C₃₁	1	4	yes	—
233	#131	—	4	4	no	—
234	C₂×M₁₆	—	2	1	no	—
235	C₂×M₁₆	—	2	1	no	—
236	C₂×M₁₆	—	2	2	no	—
237	C₂²×C₈	—	2	1	no	—
238	C₂²×C₈	—	2	2	no	—
239	C₂²×C₈	C₂×C₄×C₃₁	1	2	yes	—
240	C₂²×C₈	D₄×C₃₁	1	1	yes	characteristic
241	C₂²×C₈	D₄×C₃₁	1	1	yes	characteristic
242	C₄⋊Q₈	C₂×C₄×C₃₁	1	1	yes	characteristic
243	C₄⋊Q₈	C₂×C₄×C₃₁	1	1	yes	characteristic
244	C₄⋊Q₈	C₂×C₄×C₃₁	1	1	yes	characteristic
245	#127	C₂×C₄×C₃₁	1	1	yes	characteristic
246	#125	—	2	1	no	—
247	#124	—	2	1	no	—
248	C₂²⋊Q₈	—	2	1	no	—
249	C₂²⋊Q₈	C₂×C₄×C₃₁	1	2	yes	—
250	#121	—	2	1	no	—
251	#121	C₂×C₄×C₃₁	1	2	yes	—
252	C₄×Q₈	—	2	1	no	—
253	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
254	C₄×D₄	—	2	1	no	—
255	C₄×D₄	C₂³×C₃₁	1	2	yes	—
256	#117	—	2	1	no	—
257	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
258	#106	C₂×C₄×C₃₁	1	4	yes	—
259	C₄⋊C₈	—	2	2	no	—
260	C₄⋊C₈	—	2	2	no	—
261	C₄⋊C₈	—	2	1	no	—
262	C₄⋊C₈	—	2	1	no	—
263	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
264	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
265	#103	C₂×C₄×C₃₁	1	4	yes	—
266	#102	C₂×C₄×C₃₁	1	4	yes	—
267	C₂²⋊C₈	—	2	2	no	—
268	C₂²⋊C₈	—	2	2	no	—
269	#97	—	2	2	no	—
270	C₄×C₈	—	2	2	no	—
271	C₄×C₈	—	2	1	no	—
272	C₄×C₈	C₂×C₄×C₃₁	1	1	yes	characteristic
273	C₄×C₈	C₂×C₄×C₃₁	1	1	yes	characteristic
274	C₄×C₈	D₄×C₃₁	1	1	yes	characteristic
275	C₄×C₈	D₄×C₃₁	1	1	yes	characteristic
276	C₄×C₈	C₂³×C₃₁	1	2	yes	—
277	C₄×C₈	C₂³×C₃₁	1	2	yes	—
278	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
279	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
280	C₃₁	#17979	1	1	yes	characteristic, direct product factor, Sylow
281	#41	—	4	2	no	—
282	#41	—	4	2	no	—
283	C₂×Q₈	—	2	1	no	—
284	C₂×Q₈	—	2	1	no	—
285	C₂×Q₈	C₂²×C₄×C₃₁	1	2	yes	—
286	C₂×D₄	—	2	2	no	—
287	C₂×D₄	—	2	1	no	—
288	C₂×D₄	—	2	1	no	—
289	C₂×D₄	C₂²×C₄×C₃₁	1	2	yes	—
290	C₂²×C₄	—	2	2	no	—
291	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
292	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
293	C₂²×C₄	#41×C₃₁	1	1	yes	characteristic
294	SD₁₆	—	4	4	no	—
295	M₁₆	—	4	4	no	—
296	M₁₆	—	4	2	no	—
297	M₁₆	—	4	2	no	—
298	C₂×C₈	—	2	4	no	—
299	C₂×C₈	—	2	2	no	—
300	C₂×C₈	—	2	2	no	—
301	C₂×C₈	—	2	2	no	—
302	C₂×C₈	—	2	2	no	—
303	C₂×C₈	—	2	2	no	—
304	C₂×C₈	—	4	2	no	—
305	C₂×C₈	—	4	4	no	—
306	C₂×C₈	C₂²×C₄×C₃₁	1	2	yes	—
307	C₂×C₈	C₂²×C₄×C₃₁	1	2	yes	—
308	C₂×C₈	C₂×D₄×C₃₁	1	1	yes	characteristic
309	C₂×C₈	C₂×D₄×C₃₁	1	1	yes	characteristic
310	C₂×C₈	C₂×D₄×C₃₁	1	1	yes	characteristic
311	C₂×C₈	C₂×D₄×C₃₁	1	1	yes	characteristic
312	C₄⋊C₄	—	2	1	no	—
313	C₄⋊C₄	—	2	1	no	—
314	C₄⋊C₄	—	2	1	no	—
315	C₄⋊C₄	—	2	1	no	—
316	C₄⋊C₄	—	2	2	no	—
317	C₄⋊C₄	—	2	2	no	—
318	C₄⋊C₄	C₂²×C₄×C₃₁	1	2	yes	—
319	C₄⋊C₄	C₂²×C₄×C₃₁	1	2	yes	—
320	C₂²⋊C₄	—	2	2	no	—
321	C₂²⋊C₄	—	2	2	no	—
322	C₂²⋊C₄	—	2	2	no	—
323	C₄²	—	2	2	no	—
324	C₄²	C₂²×C₄×C₃₁	1	1	yes	characteristic
325	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
326	C₄²	#41×C₃₁	1	1	yes	characteristic
327	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
328	C₂³	—	2	2	no	—
329	C₂³	C₄×D₄×C₃₁	1	1	yes	characteristic
330	Q₈	—	2	4	no	—
331	Q₈	—	4	2	no	—
332	Q₈	—	4	2	no	—
333	D₄	—	2	4	no	—
334	D₄	—	4	4	no	—
335	D₄	—	4	2	no	—
336	D₄	—	4	2	no	—
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	2	2	no	—
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	2	2	no	—
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	4	2	no	—
343	C₂×C₄	—	4	2	no	—
344	C₂×C₄	C₄×D₄×C₃₁	1	1	yes	characteristic
345	C₂×C₄	C₄×D₄×C₃₁	1	1	yes	characteristic
346	C₂×C₄	C₄×D₄×C₃₁	1	1	yes	characteristic
347	C₂×C₄	C₃₁×AGL(1,ℤ/8)	1	2	yes	—
348	C₂×C₄	C₃₁×#137	1	2	yes	—
349	C₂×C₄	C₂³×C₄×C₃₁	1	1	yes	characteristic
350	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
351	C₂×C₄	C₂×#41×C₃₁	1	1	yes	characteristic
352	C₈	—	2	4	no	—
353	C₈	—	2	2	no	—
354	C₈	—	2	2	no	—
355	C₈	—	2	1	no	—
356	C₈	—	2	1	no	—
357	C₈	—	2	1	no	—
358	C₈	—	2	1	no	—
359	C₈	—	4	2	no	—
360	C₈	—	4	2	no	—
361	C₂²	—	2	1	no	—
362	C₂²	—	2	1	no	—
363	C₂²	—	4	2	no	—
364	C₂²	—	4	2	no	—
365	C₂²	—	4	2	no	—
366	C₂²	C₃₁×#440	1	2	yes	—
367	C₂²	C₂×C₄×D₄×C₃₁	1	1	yes	characteristic
368	C₄	—	2	1	no	—
369	C₄	—	2	1	no	—
370	C₄	—	4	2	no	—
371	C₄	—	4	2	no	—
372	C₄	—	4	2	no	—
373	C₄	C₃₁×#440	1	2	yes	—
374	C₄	C₃₁×#443	1	2	yes	—
375	C₄	C₃₁×#568	1	2	yes	—
376	C₄	C₂×C₃₁×AGL(1,ℤ/8)	1	1	yes	characteristic
377	C₄	C₂×C₃₁×#137	1	1	yes	characteristic
378	C₂	—	2	2	no	—
379	C₂	—	8	2	no	—
380	C₂	C₃₁×#2932	1	1	yes	characteristic
381	C₂	C₂×C₃₁×#440	1	1	yes	characteristic
382	C₂	C₂×C₃₁×#443	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₃₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₃₁
Frattini, cosocle	C₄²	C₂⁴×C₃₁
socle	C₂²×C₃₁	C₂×C₄×D₄
prime radical	C₃₁×#532	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₃₁ ◁ C₂×C₄×C₈×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃₁×#2960	C₂	semidirect
4. C₃₁×#1588	C₂	semidirect
5. C₃₁×#1585	C₂	semidirect
6. C₃₁×#1567	C₂	semidirect
7. C₃₁×#1493	C₂	semidirect
9. C₂×C₃₁×#322	C₂	semidirect
136. #17979	C₃₁	direct (N × H)
171. #2960	C₂×C₃₁	semidirect
173. #1588	C₂×C₃₁	semidirect
174. #1585	C₂×C₃₁	semidirect
175. #1567	C₂×C₃₁	semidirect
176. #1493	C₂×C₃₁	semidirect
178. C₂×#322	C₂×C₃₁	semidirect
280. C₃₁	#17979	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃₁×#3167	2
C₃₁×#2960	2
C₃₁×#2931	2
C₃₁×#1588	2
C₃₁×#1585	2
C₃₁×#1567	2
C₃₁×#1493	2
C₃₁×#1492	2
C₂×C₃₁×#322	2
#17979	31

Subgroups — C31×#17979 #21474738

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#17979 #21474738