Subgroups — C₃₁×#10757 #21467516

Order 7936.

1168 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#568	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃₁×#410	C₂	1	1	yes	maximal, characteristic
3	C₃₁×#2879	C₂	1	1	yes	maximal, characteristic
4	C₂×C₃₁×#344	C₂	1	2	yes	maximal, complemented
5	C₃₁×#1742	C₂	1	2	yes	maximal, complemented
6	C₂²×#41×C₃₁	C₂²	1	1	yes	characteristic
7	C₃₁×#568	—	2	2	no	—
8	C₃₁×#568	—	2	4	no	—
9	C₃₁×#568	C₄	1	4	yes	complemented
10	C₂×C₃₁×#131	—	2	4	no	—
11	C₂²×M₁₆×C₃₁	—	2	2	no	—
12	C₂²×M₁₆×C₃₁	C₂²	1	1	yes	characteristic
13	C₂²×M₁₆×C₃₁	C₂²	1	2	yes	—
14	C₂²×M₁₆×C₃₁	C₂²	1	1	yes	characteristic
15	C₂×C₃₁×#117	C₂²	1	2	yes	—
16	C₃₁×#410	—	2	2	no	—
17	C₃₁×#410	—	2	2	no	—
18	C₂×C₃₁×#99	C₄	1	4	yes	—
19	C₃₁×#408	—	2	2	no	—
20	C₃₁×#408	C₄	1	4	yes	complemented
21	C₃₁×#407	—	2	2	no	—
22	C₃₁×#344	—	2	4	no	—
23	C₃₁×#343	—	2	4	no	—
24	C₂×#41×C₃₁	—	2	2	no	—
25	C₂×#41×C₃₁	—	2	2	no	—
26	C₂×#41×C₃₁	—	2	2	no	—
27	C₂×#41×C₃₁	—	2	2	no	—
28	C₂×#41×C₃₁	C₂×C₄	1	2	yes	—
29	C₂×#41×C₃₁	C₂×C₄	1	2	yes	—
30	C₂×#41×C₃₁	D₄	1	2	yes	—
31	C₂×#41×C₃₁	D₄	1	2	yes	—
32	C₂²×Q₈×C₃₁	Q₈	1	1	yes	characteristic
33	C₂²×D₄×C₃₁	C₂×C₄	1	2	yes	—
34	C₂²×D₄×C₃₁	Q₈	1	1	yes	characteristic
35	C₂³×C₄×C₃₁	D₄	1	2	yes	—
36	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
37	C₃₁×#131	—	2	16	no	—
38	C₃₁×#131	—	2	16	no	—
39	C₂×M₁₆×C₃₁	—	2	4	no	—
40	C₂×M₁₆×C₃₁	—	2	8	no	—
41	C₂×M₁₆×C₃₁	—	2	8	no	—
42	C₂×M₁₆×C₃₁	—	2	2	no	—
43	C₂×M₁₆×C₃₁	—	2	2	no	—
44	C₂×M₁₆×C₃₁	—	2	2	no	—
45	C₂×M₁₆×C₃₁	—	2	1	no	—
46	C₂×M₁₆×C₃₁	—	2	1	no	—
47	C₂×M₁₆×C₃₁	—	2	1	no	—
48	C₂×M₁₆×C₃₁	—	2	2	no	—
49	C₂×M₁₆×C₃₁	—	2	2	no	—
50	C₂×M₁₆×C₃₁	—	2	2	no	—
51	C₂×M₁₆×C₃₁	—	2	2	no	—
52	C₂×M₁₆×C₃₁	C₂×C₄	1	2	yes	—
53	C₂×M₁₆×C₃₁	C₂×C₄	1	4	yes	—
54	C₂×M₁₆×C₃₁	D₄	1	4	yes	—
55	C₂×M₁₆×C₃₁	D₄	1	4	yes	—
56	C₂²×C₈×C₃₁	—	2	4	no	—
57	C₂²×C₈×C₃₁	—	2	2	no	—
58	C₂²×C₈×C₃₁	—	2	1	no	—
59	C₂²×C₈×C₃₁	C₂×C₄	1	2	yes	—
60	C₃₁×#117	—	2	2	no	—
61	C₃₁×#117	—	2	2	no	—
62	C₃₁×#117	—	2	2	no	—
63	C₃₁×#117	—	2	2	no	—
64	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
65	C₂×C₂²⋊C₄×C₃₁	C₂×C₄	1	4	yes	—
66	C₂×C₄²×C₃₁	—	2	2	no	—
67	C₃₁×#99	—	2	8	no	—
68	C₃₁×C₂²⋊C₈	—	2	8	no	—
69	C₂⁴×C₃₁	C₄⋊C₄	1	2	yes	—
70	C₂⁴×C₃₁	C₂²×C₄	1	1	yes	characteristic
71	#41×C₃₁	—	2	4	no	—
72	#41×C₃₁	—	2	4	no	—
73	#41×C₃₁	—	2	4	no	—
74	#41×C₃₁	—	2	4	no	—
75	#41×C₃₁	—	2	4	no	—
76	#41×C₃₁	—	2	4	no	—
77	#41×C₃₁	—	2	4	no	—
78	#41×C₃₁	—	2	4	no	—
79	C₂×Q₈×C₃₁	—	2	2	no	—
80	C₂×Q₈×C₃₁	—	2	2	no	—
81	C₂×Q₈×C₃₁	C₄⋊C₄	1	2	yes	—
82	C₂×Q₈×C₃₁	C₄⋊C₄	1	2	yes	—
83	C₂×D₄×C₃₁	—	2	4	no	—
84	C₂×D₄×C₃₁	—	2	4	no	—
85	C₂×D₄×C₃₁	—	2	2	no	—
86	C₂×D₄×C₃₁	—	2	2	no	—
87	C₂×D₄×C₃₁	C₄²	1	4	yes	—
88	C₂×D₄×C₃₁	C₂²⋊C₄	1	4	yes	—
89	C₂×D₄×C₃₁	C₄⋊C₄	1	2	yes	—
90	C₂×D₄×C₃₁	C₄⋊C₄	1	2	yes	—
91	C₂²×C₄×C₃₁	—	2	2	no	—
92	C₂²×C₄×C₃₁	—	2	2	no	—
93	C₂²×C₄×C₃₁	—	2	2	no	—
94	C₂²×C₄×C₃₁	—	2	2	no	—
95	C₂²×C₄×C₃₁	—	2	4	no	—
96	C₂²×C₄×C₃₁	C₂²⋊C₄	1	4	yes	—
97	C₂²×C₄×C₃₁	C₂²⋊C₄	1	4	yes	—
98	C₂²×C₄×C₃₁	C₄⋊C₄	1	2	yes	—
99	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
100	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
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	C₂×D₄	1	2	yes	—
105	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
106	C₂²×C₄×C₃₁	C₂×Q₈	1	1	yes	characteristic
107	C₂²×C₄×C₃₁	#41	1	2	yes	—
108	C₂²×C₄×C₃₁	#41	1	2	yes	—
109	M₁₆×C₃₁	—	2	16	no	—
110	M₁₆×C₃₁	—	2	4	no	—
111	M₁₆×C₃₁	—	2	4	no	—
112	M₁₆×C₃₁	—	2	4	no	—
113	M₁₆×C₃₁	—	2	4	no	—
114	M₁₆×C₃₁	—	4	1	no	—
115	M₁₆×C₃₁	—	4	1	no	—
116	M₁₆×C₃₁	—	4	2	no	—
117	M₁₆×C₃₁	—	4	1	no	—
118	M₁₆×C₃₁	—	4	1	no	—
119	M₁₆×C₃₁	C₂²⋊C₄	1	8	yes	—
120	C₂×C₈×C₃₁	—	2	16	no	—
121	C₂×C₈×C₃₁	—	2	4	no	—
122	C₂×C₈×C₃₁	—	2	4	no	—
123	C₂×C₈×C₃₁	—	2	4	no	—
124	C₂×C₈×C₃₁	—	2	2	no	—
125	C₂×C₈×C₃₁	—	2	2	no	—
126	C₂×C₈×C₃₁	—	2	4	no	—
127	C₂×C₈×C₃₁	—	4	2	no	—
128	C₄⋊C₄×C₃₁	—	4	2	no	—
129	C₄⋊C₄×C₃₁	—	4	2	no	—
130	C₂²⋊C₄×C₃₁	—	2	4	no	—
131	C₂²⋊C₄×C₃₁	—	2	4	no	—
132	C₄²×C₃₁	—	4	2	no	—
133	C₄²×C₃₁	—	4	2	no	—
134	#10757	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
135	C₂³×C₃₁	—	2	2	no	—
136	C₂³×C₃₁	—	2	2	no	—
137	C₂³×C₃₁	—	8	1	no	—
138	C₂³×C₃₁	—	8	2	no	—
139	C₂³×C₃₁	#95	1	4	yes	—
140	C₂³×C₃₁	C₂×C₄²	1	1	yes	characteristic
141	C₂³×C₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
142	C₂³×C₃₁	C₂×C₄⋊C₄	1	1	yes	characteristic
143	C₂³×C₃₁	C₄×D₄	1	2	yes	—
144	C₂³×C₃₁	C₄×D₄	1	2	yes	—
145	Q₈×C₃₁	—	2	4	no	—
146	Q₈×C₃₁	—	2	4	no	—
147	D₄×C₃₁	—	2	8	no	—
148	D₄×C₃₁	—	2	8	no	—
149	D₄×C₃₁	—	2	4	no	—
150	D₄×C₃₁	—	2	4	no	—
151	C₂×C₄×C₃₁	—	2	2	no	—
152	C₂×C₄×C₃₁	—	2	2	no	—
153	C₂×C₄×C₃₁	—	2	4	no	—
154	C₂×C₄×C₃₁	—	2	4	no	—
155	C₂×C₄×C₃₁	—	2	4	no	—
156	C₂×C₄×C₃₁	—	2	4	no	—
157	C₂×C₄×C₃₁	—	4	4	no	—
158	C₂×C₄×C₃₁	—	8	4	no	—
159	C₂×C₄×C₃₁	#95	1	4	yes	—
160	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	2	yes	—
161	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
162	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
163	C₂×C₄×C₃₁	C₂×C₄⋊C₄	1	1	yes	characteristic
164	C₂×C₄×C₃₁	C₂×C₄⋊C₄	1	1	yes	characteristic
165	C₂×C₄×C₃₁	#117	1	2	yes	—
166	C₂×C₄×C₃₁	C₄×D₄	1	2	yes	—
167	C₂×C₄×C₃₁	C₄×D₄	1	2	yes	—
168	C₂×C₄×C₃₁	#120	1	2	yes	—
169	C₂×C₄×C₃₁	#120	1	1	yes	characteristic
170	C₂×C₄×C₃₁	#120	1	1	yes	characteristic
171	C₂×C₄×C₃₁	#121	1	2	yes	—
172	C₂×C₄×C₃₁	#121	1	2	yes	—
173	C₂×C₄×C₃₁	C₂²⋊Q₈	1	2	yes	—
174	C₂×C₄×C₃₁	C₂²⋊Q₈	1	2	yes	—
175	C₂×C₄×C₃₁	#123	1	2	yes	—
176	C₂×C₄×C₃₁	#123	1	1	yes	characteristic
177	C₂×C₄×C₃₁	#123	1	1	yes	characteristic
178	C₈×C₃₁	—	2	8	no	—
179	C₈×C₃₁	—	4	2	no	—
180	C₈×C₃₁	—	4	2	no	—
181	C₂×#568	C₂×C₃₁	1	1	yes	characteristic
182	C₂×#410	C₂×C₃₁	1	1	yes	characteristic
183	#2879	C₂×C₃₁	1	1	yes	characteristic
184	C₂×#344	C₂×C₃₁	1	2	yes	complemented
185	#1742	C₂×C₃₁	1	2	yes	complemented
186	C₂²×C₃₁	—	2	4	no	—
187	C₂²×C₃₁	—	4	2	no	—
188	C₂²×C₃₁	—	4	1	no	—
189	C₂²×C₃₁	—	4	1	no	—
190	C₂²×C₃₁	—	4	1	no	—
191	C₂²×C₃₁	—	4	2	no	—
192	C₂²×C₃₁	—	4	4	no	—
193	C₂²×C₃₁	—	4	4	no	—
194	C₂²×C₃₁	—	8	2	no	—
195	C₂²×C₃₁	C₂×#95	1	1	yes	characteristic
196	C₂²×C₃₁	C₄×C₂²⋊C₄	1	2	yes	—
197	C₂²×C₃₁	#385	1	1	yes	characteristic
198	C₂²×C₃₁	#385	1	1	yes	characteristic
199	C₂²×C₃₁	#386	1	2	yes	—
200	C₄×C₃₁	—	2	4	no	—
201	C₄×C₃₁	—	8	4	no	—
202	C₄×C₃₁	#379	1	1	yes	characteristic
203	C₄×C₃₁	#380	1	2	yes	—
204	C₄×C₃₁	#381	1	1	yes	characteristic
205	C₄×C₃₁	#385	1	2	yes	—
206	C₄×C₃₁	#386	1	1	yes	characteristic
207	C₄×C₃₁	#386	1	1	yes	characteristic
208	C₂²×#41	C₂²×C₃₁	1	1	yes	characteristic
209	#568	—	2	2	no	—
210	#568	—	2	4	no	—
211	#568	C₄×C₃₁	1	4	yes	complemented
212	C₂×#131	—	2	4	no	—
213	C₂²×M₁₆	—	2	2	no	—
214	C₂²×M₁₆	C₂²×C₃₁	1	1	yes	characteristic
215	C₂²×M₁₆	C₂²×C₃₁	1	2	yes	—
216	C₂²×M₁₆	C₂²×C₃₁	1	1	yes	characteristic
217	C₂×#117	C₂²×C₃₁	1	2	yes	—
218	#410	—	2	2	no	—
219	#410	—	2	2	no	—
220	C₂×#99	C₄×C₃₁	1	4	yes	—
221	#408	—	2	2	no	—
222	#408	C₄×C₃₁	1	4	yes	complemented
223	#407	—	2	2	no	—
224	#344	—	2	4	no	—
225	#343	—	2	4	no	—
226	C₂×C₃₁	—	2	2	no	—
227	C₂×C₃₁	—	2	1	no	—
228	C₂×C₃₁	—	2	1	no	—
229	C₂×C₃₁	—	2	1	no	—
230	C₂×C₃₁	—	2	2	no	—
231	C₂×C₃₁	—	4	4	no	—
232	C₂×C₃₁	C₂²⋊#95	1	1	yes	characteristic
233	C₂×#41	—	2	2	no	—
234	C₂×#41	—	2	2	no	—
235	C₂×#41	—	2	2	no	—
236	C₂×#41	—	2	2	no	—
237	C₂×#41	C₂×C₄×C₃₁	1	2	yes	—
238	C₂×#41	C₂×C₄×C₃₁	1	2	yes	—
239	C₂×#41	D₄×C₃₁	1	2	yes	—
240	C₂×#41	D₄×C₃₁	1	2	yes	—
241	C₂²×Q₈	Q₈×C₃₁	1	1	yes	characteristic
242	C₂²×D₄	C₂×C₄×C₃₁	1	2	yes	—
243	C₂²×D₄	Q₈×C₃₁	1	1	yes	characteristic
244	C₂³×C₄	D₄×C₃₁	1	2	yes	—
245	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
246	#131	—	2	16	no	—
247	#131	—	2	16	no	—
248	C₂×M₁₆	—	2	4	no	—
249	C₂×M₁₆	—	2	8	no	—
250	C₂×M₁₆	—	2	8	no	—
251	C₂×M₁₆	—	2	2	no	—
252	C₂×M₁₆	—	2	2	no	—
253	C₂×M₁₆	—	2	2	no	—
254	C₂×M₁₆	—	2	2	no	—
255	C₂×M₁₆	—	2	1	no	—
256	C₂×M₁₆	—	2	1	no	—
257	C₂×M₁₆	—	2	1	no	—
258	C₂×M₁₆	—	2	2	no	—
259	C₂×M₁₆	—	2	2	no	—
260	C₂×M₁₆	—	2	2	no	—
261	C₂×M₁₆	C₂×C₄×C₃₁	1	2	yes	—
262	C₂×M₁₆	C₂×C₄×C₃₁	1	4	yes	—
263	C₂×M₁₆	D₄×C₃₁	1	4	yes	—
264	C₂×M₁₆	D₄×C₃₁	1	4	yes	—
265	C₂²×C₈	—	2	4	no	—
266	C₂²×C₈	—	2	2	no	—
267	C₂²×C₈	—	2	1	no	—
268	C₂²×C₈	C₂×C₄×C₃₁	1	2	yes	—
269	#117	—	2	2	no	—
270	#117	—	2	2	no	—
271	#117	—	2	2	no	—
272	#117	—	2	2	no	—
273	C₂×C₄⋊C₄	—	2	2	no	—
274	C₂×C₂²⋊C₄	C₂×C₄×C₃₁	1	4	yes	—
275	C₂×C₄²	—	2	2	no	—
276	#99	—	2	8	no	—
277	C₂²⋊C₈	—	2	8	no	—
278	C₃₁	#10757	1	1	yes	characteristic, direct product factor, Sylow
279	C₂⁴	C₄⋊C₄×C₃₁	1	2	yes	—
280	C₂⁴	C₂²×C₄×C₃₁	1	1	yes	characteristic
281	#41	—	2	4	no	—
282	#41	—	2	4	no	—
283	#41	—	2	4	no	—
284	#41	—	2	4	no	—
285	#41	—	2	4	no	—
286	#41	—	2	4	no	—
287	#41	—	2	4	no	—
288	#41	—	2	4	no	—
289	C₂×Q₈	—	2	2	no	—
290	C₂×Q₈	—	2	2	no	—
291	C₂×Q₈	C₄⋊C₄×C₃₁	1	2	yes	—
292	C₂×Q₈	C₄⋊C₄×C₃₁	1	2	yes	—
293	C₂×D₄	—	2	4	no	—
294	C₂×D₄	—	2	4	no	—
295	C₂×D₄	—	2	2	no	—
296	C₂×D₄	—	2	2	no	—
297	C₂×D₄	C₄²×C₃₁	1	4	yes	—
298	C₂×D₄	C₂²⋊C₄×C₃₁	1	4	yes	—
299	C₂×D₄	C₄⋊C₄×C₃₁	1	2	yes	—
300	C₂×D₄	C₄⋊C₄×C₃₁	1	2	yes	—
301	C₂²×C₄	—	2	2	no	—
302	C₂²×C₄	—	2	2	no	—
303	C₂²×C₄	—	2	2	no	—
304	C₂²×C₄	—	2	2	no	—
305	C₂²×C₄	—	2	4	no	—
306	C₂²×C₄	C₂²⋊C₄×C₃₁	1	4	yes	—
307	C₂²×C₄	C₂²⋊C₄×C₃₁	1	4	yes	—
308	C₂²×C₄	C₄⋊C₄×C₃₁	1	2	yes	—
309	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
310	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
311	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
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	2	yes	—
315	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
316	C₂²×C₄	C₂×Q₈×C₃₁	1	1	yes	characteristic
317	C₂²×C₄	#41×C₃₁	1	2	yes	—
318	C₂²×C₄	#41×C₃₁	1	2	yes	—
319	M₁₆	—	2	16	no	—
320	M₁₆	—	2	4	no	—
321	M₁₆	—	2	4	no	—
322	M₁₆	—	2	4	no	—
323	M₁₆	—	2	4	no	—
324	M₁₆	—	4	1	no	—
325	M₁₆	—	4	1	no	—
326	M₁₆	—	4	2	no	—
327	M₁₆	—	4	1	no	—
328	M₁₆	—	4	1	no	—
329	M₁₆	C₂²⋊C₄×C₃₁	1	8	yes	—
330	C₂×C₈	—	2	16	no	—
331	C₂×C₈	—	2	4	no	—
332	C₂×C₈	—	2	4	no	—
333	C₂×C₈	—	2	4	no	—
334	C₂×C₈	—	2	2	no	—
335	C₂×C₈	—	2	2	no	—
336	C₂×C₈	—	2	4	no	—
337	C₂×C₈	—	4	2	no	—
338	C₄⋊C₄	—	4	2	no	—
339	C₄⋊C₄	—	4	2	no	—
340	C₂²⋊C₄	—	2	4	no	—
341	C₂²⋊C₄	—	2	4	no	—
342	C₄²	—	4	2	no	—
343	C₄²	—	4	2	no	—
344	C₂³	—	2	2	no	—
345	C₂³	—	2	2	no	—
346	C₂³	—	8	1	no	—
347	C₂³	—	8	2	no	—
348	C₂³	C₃₁×#95	1	4	yes	—
349	C₂³	C₂×C₄²×C₃₁	1	1	yes	characteristic
350	C₂³	C₂×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
351	C₂³	C₂×C₄⋊C₄×C₃₁	1	1	yes	characteristic
352	C₂³	C₄×D₄×C₃₁	1	2	yes	—
353	C₂³	C₄×D₄×C₃₁	1	2	yes	—
354	Q₈	—	2	4	no	—
355	Q₈	—	2	4	no	—
356	D₄	—	2	8	no	—
357	D₄	—	2	8	no	—
358	D₄	—	2	4	no	—
359	D₄	—	2	4	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	2	4	no	—
363	C₂×C₄	—	2	4	no	—
364	C₂×C₄	—	2	4	no	—
365	C₂×C₄	—	2	4	no	—
366	C₂×C₄	—	4	4	no	—
367	C₂×C₄	—	8	4	no	—
368	C₂×C₄	C₃₁×#95	1	4	yes	—
369	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	2	yes	—
370	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
371	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
372	C₂×C₄	C₂×C₄⋊C₄×C₃₁	1	1	yes	characteristic
373	C₂×C₄	C₂×C₄⋊C₄×C₃₁	1	1	yes	characteristic
374	C₂×C₄	C₃₁×#117	1	2	yes	—
375	C₂×C₄	C₄×D₄×C₃₁	1	2	yes	—
376	C₂×C₄	C₄×D₄×C₃₁	1	2	yes	—
377	C₂×C₄	C₃₁×#120	1	2	yes	—
378	C₂×C₄	C₃₁×#120	1	1	yes	characteristic
379	C₂×C₄	C₃₁×#120	1	1	yes	characteristic
380	C₂×C₄	C₃₁×#121	1	2	yes	—
381	C₂×C₄	C₃₁×#121	1	2	yes	—
382	C₂×C₄	C₃₁×C₂²⋊Q₈	1	2	yes	—
383	C₂×C₄	C₃₁×C₂²⋊Q₈	1	2	yes	—
384	C₂×C₄	C₃₁×#123	1	2	yes	—
385	C₂×C₄	C₃₁×#123	1	1	yes	characteristic
386	C₂×C₄	C₃₁×#123	1	1	yes	characteristic
387	C₈	—	2	8	no	—
388	C₈	—	4	2	no	—
389	C₈	—	4	2	no	—
390	C₂²	—	2	4	no	—
391	C₂²	—	4	2	no	—
392	C₂²	—	4	1	no	—
393	C₂²	—	4	1	no	—
394	C₂²	—	4	1	no	—
395	C₂²	—	4	2	no	—
396	C₂²	—	4	4	no	—
397	C₂²	—	4	4	no	—
398	C₂²	—	8	2	no	—
399	C₂²	C₂×C₃₁×#95	1	1	yes	characteristic
400	C₂²	C₄×C₂²⋊C₄×C₃₁	1	2	yes	—
401	C₂²	C₃₁×#385	1	1	yes	characteristic
402	C₂²	C₃₁×#385	1	1	yes	characteristic
403	C₂²	C₃₁×#386	1	2	yes	—
404	C₄	—	2	4	no	—
405	C₄	—	8	4	no	—
406	C₄	C₃₁×#379	1	1	yes	characteristic
407	C₄	C₃₁×#380	1	2	yes	—
408	C₄	C₃₁×#381	1	1	yes	characteristic
409	C₄	C₃₁×#385	1	2	yes	—
410	C₄	C₃₁×#386	1	1	yes	characteristic
411	C₄	C₃₁×#386	1	1	yes	characteristic
412	C₂	—	2	2	no	—
413	C₂	—	2	1	no	—
414	C₂	—	2	1	no	—
415	C₂	—	2	1	no	—
416	C₂	—	2	2	no	—
417	C₂	—	4	4	no	—
418	C₂	C₃₁×C₂²⋊#95	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₃₁	#386
commutator	C₂³	C₂×C₄²×C₃₁
Frattini, cosocle	C₂³×C₄	C₂³×C₃₁
socle	C₂×C₃₁	C₂²⋊#95
prime radical	C₂²×#41×C₃₁	C₂²
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₃₁ ◁ C₂³×C₄×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₂×C₃₁×#344	C₂	semidirect
5. C₃₁×#1742	C₂	semidirect
9. C₃₁×#568	C₄	semidirect
20. C₃₁×#408	C₄	semidirect
134. #10757	C₃₁	direct (N × H)
184. C₂×#344	C₂×C₃₁	semidirect
185. #1742	C₂×C₃₁	semidirect
211. #568	C₄×C₃₁	semidirect
222. #408	C₄×C₃₁	semidirect
278. C₃₁	#10757	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃₁×#568	2
C₂×C₃₁×#410	2
C₃₁×#2879	2
C₂×C₃₁×#344	2
C₃₁×#1742	2
#10757	31

Subgroups — C31×#10757 #21467516

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#10757 #21467516