Subgroups — C₃₁×#11328 #21468087

Order 7936.

958 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃₁×#107	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃₁×#389	C₂	1	2	yes	maximal
3	C₂×C₃₁×#340	C₂	1	2	yes	maximal
4	C₂×C₃₁×#340	C₂	1	1	yes	maximal, characteristic
5	C₂×C₃₁×#336	C₂	1	1	yes	maximal, characteristic
6	C₂³×C₈×C₃₁	C₂²	1	1	yes	characteristic
7	C₂³×C₈×C₃₁	C₂²	1	1	yes	characteristic
8	C₂²×C₄⋊C₄×C₃₁	—	2	2	no	—
9	C₂²×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
10	C₂²×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
11	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
12	C₂×C₃₁×#107	—	2	2	no	—
13	C₂×C₃₁×#107	—	2	4	no	—
14	C₃₁×#389	—	2	4	no	—
15	C₃₁×#389	—	2	4	no	—
16	C₂×C₃₁×#95	—	2	2	no	—
17	C₃₁×#340	—	2	4	no	—
18	C₃₁×#340	C₄	1	4	yes	complemented
19	C₃₁×#336	—	2	2	no	—
20	C₂³×C₄×C₃₁	—	2	2	no	—
21	C₂³×C₄×C₃₁	—	2	2	no	—
22	C₂³×C₄×C₃₁	D₄	1	1	yes	characteristic
23	C₂³×C₄×C₃₁	D₄	1	1	yes	characteristic
24	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
25	C₂²×C₈×C₃₁	—	2	2	no	—
26	C₂²×C₈×C₃₁	—	2	2	no	—
27	C₂²×C₈×C₃₁	—	2	1	no	—
28	C₂²×C₈×C₃₁	—	2	2	no	—
29	C₂²×C₈×C₃₁	—	2	2	no	—
30	C₂²×C₈×C₃₁	—	2	1	no	—
31	C₂²×C₈×C₃₁	C₂×C₄	1	2	yes	—
32	C₂²×C₈×C₃₁	D₄	1	2	yes	—
33	C₂²×C₈×C₃₁	Q₈	1	2	yes	—
34	C₂²×C₈×C₃₁	Q₈	1	2	yes	—
35	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
36	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
37	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
38	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
39	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
40	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
41	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
42	C₂×C₄⋊C₄×C₃₁	—	2	8	no	—
43	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
44	C₂×C₄⋊C₄×C₃₁	—	4	4	no	—
45	C₂×C₄⋊C₄×C₃₁	—	4	4	no	—
46	C₂×C₄⋊C₄×C₃₁	C₂×C₄	1	4	yes	—
47	C₂×C₄⋊C₄×C₃₁	D₄	1	4	yes	—
48	C₂×C₄⋊C₄×C₃₁	D₄	1	4	yes	—
49	C₂×C₄⋊C₄×C₃₁	Q₈	1	4	yes	—
50	C₂×C₄²×C₃₁	—	2	1	no	—
51	C₂×C₄²×C₃₁	—	2	2	no	—
52	C₂×C₄²×C₃₁	—	2	2	no	—
53	C₂×C₄²×C₃₁	—	2	1	no	—
54	C₃₁×#107	—	2	8	no	—
55	C₃₁×#95	—	2	8	no	—
56	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
57	C₂²×C₄×C₃₁	—	2	4	no	—
58	C₂²×C₄×C₃₁	—	2	2	no	—
59	C₂²×C₄×C₃₁	—	2	4	no	—
60	C₂²×C₄×C₃₁	—	2	2	no	—
61	C₂²×C₄×C₃₁	—	2	1	no	—
62	C₂²×C₄×C₃₁	—	2	1	no	—
63	C₂²×C₄×C₃₁	—	2	4	no	—
64	C₂²×C₄×C₃₁	—	2	1	no	—
65	C₂²×C₄×C₃₁	—	2	1	no	—
66	C₂²×C₄×C₃₁	—	2	2	no	—
67	C₂²×C₄×C₃₁	—	2	2	no	—
68	C₂²×C₄×C₃₁	—	2	4	no	—
69	C₂²×C₄×C₃₁	—	4	2	no	—
70	C₂²×C₄×C₃₁	—	4	2	no	—
71	C₂²×C₄×C₃₁	—	4	2	no	—
72	C₂²×C₄×C₃₁	—	4	2	no	—
73	C₂²×C₄×C₃₁	—	4	2	no	—
74	C₂²×C₄×C₃₁	—	4	2	no	—
75	C₂²×C₄×C₃₁	—	4	2	no	—
76	C₂²×C₄×C₃₁	—	4	2	no	—
77	C₂²×C₄×C₃₁	—	4	2	no	—
78	C₂²×C₄×C₃₁	—	4	2	no	—
79	C₂²×C₄×C₃₁	D₈	1	2	yes	—
80	C₂²×C₄×C₃₁	Q₁₆	1	2	yes	—
81	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
82	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
83	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
84	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
85	C₂²×C₄×C₃₁	C₂×Q₈	1	1	yes	characteristic
86	C₂²×C₄×C₃₁	C₂×Q₈	1	2	yes	—
87	C₂²×C₄×C₃₁	C₂×Q₈	1	1	yes	characteristic
88	C₂²×C₄×C₃₁	#41	1	2	yes	—
89	C₂²×C₄×C₃₁	#41	1	1	yes	characteristic
90	C₂²×C₄×C₃₁	#41	1	1	yes	characteristic
91	C₂×C₈×C₃₁	—	2	4	no	—
92	C₂×C₈×C₃₁	—	2	2	no	—
93	C₂×C₈×C₃₁	—	2	4	no	—
94	C₂×C₈×C₃₁	—	2	2	no	—
95	C₂×C₈×C₃₁	—	2	4	no	—
96	C₂×C₈×C₃₁	—	2	2	no	—
97	C₂×C₈×C₃₁	—	4	1	no	—
98	C₂×C₈×C₃₁	—	4	2	no	—
99	C₂×C₈×C₃₁	—	4	1	no	—
100	C₂×C₈×C₃₁	C₄⋊C₄	1	4	yes	complemented
101	C₄⋊C₄×C₃₁	—	2	4	no	—
102	C₄⋊C₄×C₃₁	—	2	4	no	—
103	C₄⋊C₄×C₃₁	—	2	4	no	—
104	C₄⋊C₄×C₃₁	—	2	4	no	—
105	C₄⋊C₄×C₃₁	—	2	4	no	—
106	C₄⋊C₄×C₃₁	—	4	16	no	—
107	C₄⋊C₄×C₃₁	—	4	2	no	—
108	C₄⋊C₄×C₃₁	—	4	2	no	—
109	C₄⋊C₄×C₃₁	C₄⋊C₄	1	8	yes	complemented
110	C₄²×C₃₁	—	4	1	no	—
111	C₄²×C₃₁	—	4	2	no	—
112	C₄²×C₃₁	—	4	1	no	—
113	#11328	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
114	C₂³×C₃₁	C₄×D₄	1	1	yes	characteristic
115	C₂³×C₃₁	#120	1	2	yes	—
116	C₂³×C₃₁	#121	1	1	yes	characteristic
117	C₂³×C₃₁	C₂²⋊Q₈	1	2	yes	—
118	C₂³×C₃₁	C₄⋊Q₈	1	1	yes	characteristic
119	C₂³×C₃₁	C₂×D₈	1	1	yes	characteristic
120	C₂³×C₃₁	C₂×Q₁₆	1	1	yes	characteristic
121	C₂³×C₃₁	#135	1	1	yes	characteristic
122	C₂³×C₃₁	#135	1	1	yes	characteristic
123	C₂³×C₃₁	AGL(1,ℤ/8)	1	2	yes	—
124	C₂³×C₃₁	#137	1	2	yes	—
125	C₂×C₄×C₃₁	—	2	8	no	—
126	C₂×C₄×C₃₁	—	2	4	no	—
127	C₂×C₄×C₃₁	—	2	4	no	—
128	C₂×C₄×C₃₁	—	2	2	no	—
129	C₂×C₄×C₃₁	—	2	2	no	—
130	C₂×C₄×C₃₁	—	4	1	no	—
131	C₂×C₄×C₃₁	—	4	1	no	—
132	C₂×C₄×C₃₁	—	4	4	no	—
133	C₂×C₄×C₃₁	—	4	4	no	—
134	C₂×C₄×C₃₁	—	4	4	no	—
135	C₂×C₄×C₃₁	—	4	2	no	—
136	C₂×C₄×C₃₁	—	4	2	no	—
137	C₂×C₄×C₃₁	—	4	4	no	—
138	C₂×C₄×C₃₁	—	4	1	no	—
139	C₂×C₄×C₃₁	—	4	1	no	—
140	C₂×C₄×C₃₁	—	4	4	no	—
141	C₂×C₄×C₃₁	—	4	4	no	—
142	C₂×C₄×C₃₁	—	4	4	no	—
143	C₂×C₄×C₃₁	—	4	4	no	—
144	C₂×C₄×C₃₁	—	4	4	no	—
145	C₂×C₄×C₃₁	—	8	2	no	—
146	C₂×C₄×C₃₁	—	8	2	no	—
147	C₂×C₄×C₃₁	—	8	2	no	—
148	C₂×C₄×C₃₁	—	8	2	no	—
149	C₂×C₄×C₃₁	C₂×C₄⋊C₄	1	1	yes	characteristic
150	C₂×C₄×C₃₁	C₂×C₄⋊C₄	1	2	yes	—
151	C₂×C₄×C₃₁	C₄×D₄	1	2	yes	—
152	C₂×C₄×C₃₁	C₄×Q₈	1	1	yes	characteristic
153	C₂×C₄×C₃₁	#120	1	1	yes	characteristic
154	C₂×C₄×C₃₁	#121	1	2	yes	—
155	C₂×C₄×C₃₁	C₂²⋊Q₈	1	2	yes	—
156	C₂×C₄×C₃₁	C₂²⋊Q₈	1	2	yes	—
157	C₂×C₄×C₃₁	C₂²⋊Q₈	1	2	yes	—
158	C₂×C₄×C₃₁	C₂²⋊Q₈	1	1	yes	characteristic
159	C₂×C₄×C₃₁	#123	1	1	yes	characteristic
160	C₂×C₄×C₃₁	#123	1	2	yes	—
161	C₂×C₄×C₃₁	#125	1	2	yes	—
162	C₂×C₄×C₃₁	#125	1	1	yes	characteristic
163	C₂×C₄×C₃₁	#127	1	1	yes	characteristic
164	C₂×C₄×C₃₁	C₄⋊Q₈	1	1	yes	characteristic
165	C₂×C₄×C₃₁	C₄⋊Q₈	1	2	yes	—
166	C₂×C₄×C₃₁	C₄⋊Q₈	1	2	yes	—
167	C₈×C₃₁	—	2	4	no	—
168	C₈×C₃₁	—	4	2	no	—
169	C₂²×#107	C₂×C₃₁	1	1	yes	characteristic
170	C₂×#389	C₂×C₃₁	1	2	yes	—
171	C₂×#340	C₂×C₃₁	1	2	yes	—
172	C₂×#340	C₂×C₃₁	1	1	yes	characteristic
173	C₂×#336	C₂×C₃₁	1	1	yes	characteristic
174	C₂²×C₃₁	#385	1	2	yes	—
175	C₂²×C₃₁	#389	1	1	yes	characteristic
176	C₂²×C₃₁	#392	1	1	yes	characteristic
177	C₂²×C₃₁	#395	1	2	yes	—
178	C₂²×C₃₁	#398	1	1	yes	characteristic
179	C₂²×C₃₁	C₄×D₈	1	1	yes	characteristic
180	C₂²×C₃₁	C₄×Q₁₆	1	1	yes	characteristic
181	C₂²×C₃₁	#440	1	2	yes	—
182	C₂²×C₃₁	#447	1	2	yes	—
183	C₂²×C₃₁	#449	1	2	yes	—
184	C₂²×C₃₁	#451	1	2	yes	—
185	C₂²×C₃₁	#452	1	2	yes	—
186	C₂²×C₃₁	#466	1	1	yes	characteristic
187	C₂²×C₃₁	#467	1	1	yes	characteristic
188	C₂²×C₃₁	#469	1	1	yes	characteristic
189	C₂²×C₃₁	#470	1	1	yes	characteristic
190	C₂²×C₃₁	#474	1	2	yes	—
191	C₂²×C₃₁	#477	1	2	yes	—
192	C₂²×C₃₁	#478	1	2	yes	—
193	C₂²×C₃₁	#479	1	2	yes	—
194	C₂²×C₃₁	#499	1	1	yes	characteristic
195	C₂²×C₃₁	#500	1	1	yes	characteristic
196	C₂²×C₃₁	#501	1	2	yes	—
197	C₄×C₃₁	—	4	8	no	—
198	C₄×C₃₁	—	4	2	no	—
199	C₄×C₃₁	—	4	2	no	—
200	C₄×C₃₁	—	8	4	no	—
201	C₄×C₃₁	#384	1	1	yes	characteristic
202	C₄×C₃₁	#385	1	1	yes	characteristic
203	C₄×C₃₁	#389	1	2	yes	—
204	C₄×C₃₁	#395	1	1	yes	characteristic
205	C₄×C₃₁	#398	1	2	yes	—
206	C₄×C₃₁	#399	1	1	yes	characteristic
207	C₂³×C₈	C₂²×C₃₁	1	1	yes	characteristic
208	C₂³×C₈	C₂²×C₃₁	1	1	yes	characteristic
209	C₂²×C₄⋊C₄	—	2	2	no	—
210	C₂²×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
211	C₂²×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
212	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
213	C₂×#107	—	2	2	no	—
214	C₂×#107	—	2	4	no	—
215	#389	—	2	4	no	—
216	#389	—	2	4	no	—
217	C₂×#95	—	2	2	no	—
218	#340	—	2	4	no	—
219	#340	C₄×C₃₁	1	4	yes	complemented
220	#336	—	2	2	no	—
221	C₂×C₃₁	#1444	1	1	yes	characteristic
222	C₂×C₃₁	#1862	1	2	yes	—
223	C₂×C₃₁	#1863	1	2	yes	—
224	C₂×C₃₁	#1942	1	1	yes	characteristic
225	C₂×C₃₁	#1944	1	1	yes	characteristic
226	C₂×C₃₁	#1999	1	1	yes	characteristic
227	C₂×C₃₁	#2001	1	1	yes	characteristic
228	C₂×C₃₁	#2057	1	2	yes	—
229	C₂×C₃₁	#2059	1	2	yes	—
230	C₂×C₃₁	#2086	1	1	yes	characteristic
231	C₂×C₃₁	#2087	1	1	yes	characteristic
232	C₂³×C₄	—	2	2	no	—
233	C₂³×C₄	—	2	2	no	—
234	C₂³×C₄	D₄×C₃₁	1	1	yes	characteristic
235	C₂³×C₄	D₄×C₃₁	1	1	yes	characteristic
236	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
237	C₂²×C₈	—	2	2	no	—
238	C₂²×C₈	—	2	2	no	—
239	C₂²×C₈	—	2	1	no	—
240	C₂²×C₈	—	2	2	no	—
241	C₂²×C₈	—	2	2	no	—
242	C₂²×C₈	—	2	1	no	—
243	C₂²×C₈	C₂×C₄×C₃₁	1	2	yes	—
244	C₂²×C₈	D₄×C₃₁	1	2	yes	—
245	C₂²×C₈	Q₈×C₃₁	1	2	yes	—
246	C₂²×C₈	Q₈×C₃₁	1	2	yes	—
247	C₂×C₄⋊C₄	—	2	2	no	—
248	C₂×C₄⋊C₄	—	2	2	no	—
249	C₂×C₄⋊C₄	—	2	2	no	—
250	C₂×C₄⋊C₄	—	2	2	no	—
251	C₂×C₄⋊C₄	—	2	2	no	—
252	C₂×C₄⋊C₄	—	2	2	no	—
253	C₂×C₄⋊C₄	—	2	2	no	—
254	C₂×C₄⋊C₄	—	2	8	no	—
255	C₂×C₄⋊C₄	—	2	2	no	—
256	C₂×C₄⋊C₄	—	4	4	no	—
257	C₂×C₄⋊C₄	—	4	4	no	—
258	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	4	yes	—
259	C₂×C₄⋊C₄	D₄×C₃₁	1	4	yes	—
260	C₂×C₄⋊C₄	D₄×C₃₁	1	4	yes	—
261	C₂×C₄⋊C₄	Q₈×C₃₁	1	4	yes	—
262	C₂×C₄²	—	2	1	no	—
263	C₂×C₄²	—	2	2	no	—
264	C₂×C₄²	—	2	2	no	—
265	C₂×C₄²	—	2	1	no	—
266	#107	—	2	8	no	—
267	#95	—	2	8	no	—
268	C₃₁	#11328	1	1	yes	characteristic, direct product factor, Sylow
269	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
270	C₂²×C₄	—	2	4	no	—
271	C₂²×C₄	—	2	2	no	—
272	C₂²×C₄	—	2	4	no	—
273	C₂²×C₄	—	2	2	no	—
274	C₂²×C₄	—	2	1	no	—
275	C₂²×C₄	—	2	1	no	—
276	C₂²×C₄	—	2	4	no	—
277	C₂²×C₄	—	2	1	no	—
278	C₂²×C₄	—	2	1	no	—
279	C₂²×C₄	—	2	2	no	—
280	C₂²×C₄	—	2	2	no	—
281	C₂²×C₄	—	2	4	no	—
282	C₂²×C₄	—	4	2	no	—
283	C₂²×C₄	—	4	2	no	—
284	C₂²×C₄	—	4	2	no	—
285	C₂²×C₄	—	4	2	no	—
286	C₂²×C₄	—	4	2	no	—
287	C₂²×C₄	—	4	2	no	—
288	C₂²×C₄	—	4	2	no	—
289	C₂²×C₄	—	4	2	no	—
290	C₂²×C₄	—	4	2	no	—
291	C₂²×C₄	—	4	2	no	—
292	C₂²×C₄	D₈×C₃₁	1	2	yes	—
293	C₂²×C₄	Q₁₆×C₃₁	1	2	yes	—
294	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
295	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
296	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
297	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
298	C₂²×C₄	C₂×Q₈×C₃₁	1	1	yes	characteristic
299	C₂²×C₄	C₂×Q₈×C₃₁	1	2	yes	—
300	C₂²×C₄	C₂×Q₈×C₃₁	1	1	yes	characteristic
301	C₂²×C₄	#41×C₃₁	1	2	yes	—
302	C₂²×C₄	#41×C₃₁	1	1	yes	characteristic
303	C₂²×C₄	#41×C₃₁	1	1	yes	characteristic
304	C₂×C₈	—	2	4	no	—
305	C₂×C₈	—	2	2	no	—
306	C₂×C₈	—	2	4	no	—
307	C₂×C₈	—	2	2	no	—
308	C₂×C₈	—	2	2	no	—
309	C₂×C₈	—	2	4	no	—
310	C₂×C₈	—	4	2	no	—
311	C₂×C₈	—	4	1	no	—
312	C₂×C₈	—	4	1	no	—
313	C₂×C₈	C₄⋊C₄×C₃₁	1	4	yes	complemented
314	C₄⋊C₄	—	2	4	no	—
315	C₄⋊C₄	—	2	4	no	—
316	C₄⋊C₄	—	2	4	no	—
317	C₄⋊C₄	—	2	4	no	—
318	C₄⋊C₄	—	2	4	no	—
319	C₄⋊C₄	—	4	16	no	—
320	C₄⋊C₄	—	4	2	no	—
321	C₄⋊C₄	—	4	2	no	—
322	C₄⋊C₄	C₄⋊C₄×C₃₁	1	8	yes	complemented
323	C₄²	—	4	1	no	—
324	C₄²	—	4	2	no	—
325	C₄²	—	4	1	no	—
326	C₂³	C₄×D₄×C₃₁	1	1	yes	characteristic
327	C₂³	C₃₁×#120	1	2	yes	—
328	C₂³	C₃₁×#121	1	1	yes	characteristic
329	C₂³	C₃₁×C₂²⋊Q₈	1	2	yes	—
330	C₂³	C₃₁×C₄⋊Q₈	1	1	yes	characteristic
331	C₂³	C₂×D₈×C₃₁	1	1	yes	characteristic
332	C₂³	C₂×Q₁₆×C₃₁	1	1	yes	characteristic
333	C₂³	C₃₁×#135	1	1	yes	characteristic
334	C₂³	C₃₁×#135	1	1	yes	characteristic
335	C₂³	C₃₁×AGL(1,ℤ/8)	1	2	yes	—
336	C₂³	C₃₁×#137	1	2	yes	—
337	C₂×C₄	—	2	4	no	—
338	C₂×C₄	—	2	4	no	—
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	2	2	no	—
341	C₂×C₄	—	2	8	no	—
342	C₂×C₄	—	4	4	no	—
343	C₂×C₄	—	4	4	no	—
344	C₂×C₄	—	4	4	no	—
345	C₂×C₄	—	4	2	no	—
346	C₂×C₄	—	4	2	no	—
347	C₂×C₄	—	4	4	no	—
348	C₂×C₄	—	4	1	no	—
349	C₂×C₄	—	4	1	no	—
350	C₂×C₄	—	4	4	no	—
351	C₂×C₄	—	4	4	no	—
352	C₂×C₄	—	4	1	no	—
353	C₂×C₄	—	4	1	no	—
354	C₂×C₄	—	4	4	no	—
355	C₂×C₄	—	4	4	no	—
356	C₂×C₄	—	4	4	no	—
357	C₂×C₄	—	8	2	no	—
358	C₂×C₄	—	8	2	no	—
359	C₂×C₄	—	8	2	no	—
360	C₂×C₄	—	8	2	no	—
361	C₂×C₄	C₂×C₄⋊C₄×C₃₁	1	1	yes	characteristic
362	C₂×C₄	C₂×C₄⋊C₄×C₃₁	1	2	yes	—
363	C₂×C₄	C₄×D₄×C₃₁	1	2	yes	—
364	C₂×C₄	C₄×Q₈×C₃₁	1	1	yes	characteristic
365	C₂×C₄	C₃₁×#120	1	1	yes	characteristic
366	C₂×C₄	C₃₁×#121	1	2	yes	—
367	C₂×C₄	C₃₁×C₂²⋊Q₈	1	2	yes	—
368	C₂×C₄	C₃₁×C₂²⋊Q₈	1	1	yes	characteristic
369	C₂×C₄	C₃₁×C₂²⋊Q₈	1	2	yes	—
370	C₂×C₄	C₃₁×C₂²⋊Q₈	1	2	yes	—
371	C₂×C₄	C₃₁×#123	1	2	yes	—
372	C₂×C₄	C₃₁×#123	1	1	yes	characteristic
373	C₂×C₄	C₃₁×#125	1	1	yes	characteristic
374	C₂×C₄	C₃₁×#125	1	2	yes	—
375	C₂×C₄	C₃₁×#127	1	1	yes	characteristic
376	C₂×C₄	C₃₁×C₄⋊Q₈	1	1	yes	characteristic
377	C₂×C₄	C₃₁×C₄⋊Q₈	1	2	yes	—
378	C₂×C₄	C₃₁×C₄⋊Q₈	1	2	yes	—
379	C₈	—	2	4	no	—
380	C₈	—	4	2	no	—
381	C₂²	C₃₁×#385	1	2	yes	—
382	C₂²	C₃₁×#389	1	1	yes	characteristic
383	C₂²	C₃₁×#392	1	1	yes	characteristic
384	C₂²	C₃₁×#395	1	2	yes	—
385	C₂²	C₃₁×#398	1	1	yes	characteristic
386	C₂²	C₄×D₈×C₃₁	1	1	yes	characteristic
387	C₂²	C₄×Q₁₆×C₃₁	1	1	yes	characteristic
388	C₂²	C₃₁×#440	1	2	yes	—
389	C₂²	C₃₁×#447	1	2	yes	—
390	C₂²	C₃₁×#449	1	2	yes	—
391	C₂²	C₃₁×#451	1	2	yes	—
392	C₂²	C₃₁×#452	1	2	yes	—
393	C₂²	C₃₁×#466	1	1	yes	characteristic
394	C₂²	C₃₁×#467	1	1	yes	characteristic
395	C₂²	C₃₁×#469	1	1	yes	characteristic
396	C₂²	C₃₁×#470	1	1	yes	characteristic
397	C₂²	C₃₁×#474	1	2	yes	—
398	C₂²	C₃₁×#477	1	2	yes	—
399	C₂²	C₃₁×#478	1	2	yes	—
400	C₂²	C₃₁×#479	1	2	yes	—
401	C₂²	C₃₁×#499	1	1	yes	characteristic
402	C₂²	C₃₁×#500	1	1	yes	characteristic
403	C₂²	C₃₁×#501	1	2	yes	—
404	C₄	—	4	8	no	—
405	C₄	—	4	2	no	—
406	C₄	—	4	2	no	—
407	C₄	—	8	4	no	—
408	C₄	C₃₁×#384	1	1	yes	characteristic
409	C₄	C₃₁×#385	1	1	yes	characteristic
410	C₄	C₃₁×#389	1	2	yes	—
411	C₄	C₃₁×#395	1	1	yes	characteristic
412	C₄	C₃₁×#398	1	2	yes	—
413	C₄	C₃₁×#399	1	1	yes	characteristic
414	C₂	C₃₁×#1444	1	1	yes	characteristic
415	C₂	C₃₁×#1862	1	2	yes	—
416	C₂	C₃₁×#1863	1	2	yes	—
417	C₂	C₃₁×#1942	1	1	yes	characteristic
418	C₂	C₃₁×#1944	1	1	yes	characteristic
419	C₂	C₃₁×#1999	1	1	yes	characteristic
420	C₂	C₃₁×#2001	1	1	yes	characteristic
421	C₂	C₃₁×#2057	1	2	yes	—
422	C₂	C₃₁×#2059	1	2	yes	—
423	C₂	C₃₁×#2086	1	1	yes	characteristic
424	C₂	C₃₁×#2087	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
18. C₃₁×#340	C₄	semidirect
100. C₂×C₈×C₃₁	C₄⋊C₄	semidirect
109. C₄⋊C₄×C₃₁	C₄⋊C₄	semidirect
113. #11328	C₃₁	direct (N × H)
219. #340	C₄×C₃₁	semidirect
268. C₃₁	#11328	direct (N × H)
313. C₂×C₈	C₄⋊C₄×C₃₁	semidirect
322. C₄⋊C₄	C₄⋊C₄×C₃₁	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₃₁×#107	2
C₂×C₃₁×#389	2
C₂×C₃₁×#340	2
C₂×C₃₁×#336	2
#11328	31

Subgroups — C31×#11328 #21468087

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#11328 #21468087