Subgroups — C₃₁×#17324 #21474083

Order 7936.

742 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#2920	C₂	1	1	yes	maximal, characteristic
2	C₃₁×#2920	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃₁×#431	C₂	1	1	yes	maximal, characteristic
4	C₃₁×#1454	C₂	1	4	yes	maximal, complemented
5	C₃₁×#1453	C₂	1	4	yes	maximal, complemented
6	C₃₁×#1451	C₂	1	2	yes	maximal, complemented
7	C₈×M₁₆×C₃₁	C₂	1	2	yes	maximal, complemented
8	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
9	C₃₁×#432	C₄	1	2	yes	—
10	C₃₁×#432	C₄	1	2	yes	—
11	C₃₁×#432	C₄	1	2	yes	—
12	C₃₁×#432	C₄	1	2	yes	—
13	C₃₁×#431	C₄	1	2	yes	—
14	C₃₁×#431	C₄	1	2	yes	—
15	C₃₁×#431	C₂²	1	2	yes	—
16	C₃₁×#431	C₂²	1	2	yes	—
17	C₃₁×#431	C₂²	1	2	yes	—
18	C₃₁×#431	C₂²	1	2	yes	—
19	C₃₁×#431	C₂²	1	2	yes	—
20	C₃₁×#431	C₂²	1	2	yes	—
21	C₃₁×#423	C₄	1	2	yes	—
22	C₃₁×#423	C₄	1	2	yes	—
23	C₂×C₃₁×C₄⋊C₈	C₄	1	2	yes	—
24	C₃₁×#407	C₄	1	2	yes	—
25	C₃₁×#407	C₄	1	2	yes	—
26	C₂×C₃₁×C₂²⋊C₈	C₄	1	2	yes	—
27	C₄×M₁₆×C₃₁	C₂²	1	2	yes	—
28	C₄×M₁₆×C₃₁	C₂²	1	2	yes	—
29	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
30	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
31	C₃₁×#322	C₂²	1	4	yes	complemented
32	C₃₁×#322	C₂²	1	8	yes	complemented
33	C₈²×C₃₁	C₂²	1	4	yes	complemented
34	C₂³×C₄×C₃₁	C₂×C₄	1	1	yes	characteristic
35	C₂³×C₄×C₃₁	C₂×C₄	1	1	yes	characteristic
36	C₂³×C₄×C₃₁	C₂×C₄	1	1	yes	characteristic
37	C₂×M₁₆×C₃₁	C₂×C₄	1	4	yes	—
38	C₂×M₁₆×C₃₁	C₂×C₄	1	4	yes	—
39	C₂²×C₈×C₃₁	C₂×C₄	1	2	yes	—
40	C₂²×C₈×C₃₁	C₂×C₄	1	2	yes	—
41	C₂×C₄²×C₃₁	C₂×C₄	1	1	yes	characteristic
42	C₂×C₄²×C₃₁	C₂×C₄	1	1	yes	characteristic
43	C₂×C₄²×C₃₁	C₂×C₄	1	1	yes	characteristic
44	C₂×C₄²×C₃₁	C₂×C₄	1	1	yes	characteristic
45	C₂×C₄²×C₃₁	C₂×C₄	1	1	yes	characteristic
46	C₂×C₄²×C₃₁	C₂×C₄	1	1	yes	characteristic
47	C₂×C₄²×C₃₁	C₂×C₄	1	1	yes	characteristic
48	C₂×C₄²×C₃₁	C₂×C₄	1	1	yes	characteristic
49	C₂×C₄²×C₃₁	C₂×C₄	1	1	yes	characteristic
50	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
51	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
52	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
53	C₃₁×C₄⋊C₈	C₂×C₄	1	4	yes	—
54	C₃₁×C₄⋊C₈	C₂×C₄	1	4	yes	—
55	C₃₁×C₄⋊C₈	C₂×C₄	1	4	yes	—
56	C₃₁×C₄⋊C₈	C₂×C₄	1	4	yes	—
57	C₃₁×C₄⋊C₈	C₂×C₄	1	4	yes	—
58	C₃₁×C₄⋊C₈	C₂×C₄	1	4	yes	—
59	C₃₁×C₂²⋊C₈	C₂×C₄	1	4	yes	—
60	C₃₁×C₂²⋊C₈	C₂×C₄	1	4	yes	—
61	C₃₁×C₂²⋊C₈	C₂×C₄	1	4	yes	—
62	C₃₁×C₂²⋊C₈	C₂×C₄	1	4	yes	—
63	C₃₁×C₂²⋊C₈	C₂×C₄	1	4	yes	—
64	C₃₁×C₂²⋊C₈	C₂×C₄	1	4	yes	—
65	C₃₁×#97	C₂×C₄	1	4	yes	—
66	C₃₁×#97	C₂×C₄	1	4	yes	—
67	C₄×C₈×C₃₁	C₂×C₄	1	2	yes	—
68	C₄×C₈×C₃₁	C₂×C₄	1	2	yes	—
69	C₄×C₈×C₃₁	C₂³	1	2	yes	—
70	C₄×C₈×C₃₁	C₂³	1	2	yes	—
71	C₄×C₈×C₃₁	C₂³	1	4	yes	—
72	C₄×C₈×C₃₁	C₂³	1	4	yes	—
73	C₂⁴×C₃₁	C₄²	1	1	yes	characteristic
74	C₂²×C₄×C₃₁	—	2	4	no	—
75	C₂²×C₄×C₃₁	—	4	2	no	—
76	C₂²×C₄×C₃₁	—	4	2	no	—
77	C₂²×C₄×C₃₁	C₄²	1	1	yes	characteristic
78	C₂²×C₄×C₃₁	C₄²	1	1	yes	characteristic
79	C₂²×C₄×C₃₁	C₄²	1	1	yes	characteristic
80	C₂²×C₄×C₃₁	C₄²	1	1	yes	characteristic
81	C₂²×C₄×C₃₁	C₄²	1	1	yes	characteristic
82	C₂²×C₄×C₃₁	C₄²	1	1	yes	characteristic
83	C₂²×C₄×C₃₁	C₄²	1	1	yes	characteristic
84	C₂²×C₄×C₃₁	C₄²	1	1	yes	characteristic
85	C₂²×C₄×C₃₁	C₄²	1	1	yes	characteristic
86	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
87	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
88	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
89	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
90	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
91	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
92	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
93	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
94	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
95	M₁₆×C₃₁	—	2	8	no	—
96	M₁₆×C₃₁	—	4	4	no	—
97	C₂×C₈×C₃₁	—	4	2	no	—
98	C₂×C₈×C₃₁	—	4	2	no	—
99	C₂×C₈×C₃₁	C₂²×C₄	1	4	yes	—
100	C₂×C₈×C₃₁	C₂²×C₄	1	4	yes	—
101	C₂×C₈×C₃₁	C₂²×C₄	1	8	yes	—
102	C₂×C₈×C₃₁	C₂²×C₄	1	8	yes	—
103	C₄²×C₃₁	C₄²	1	1	yes	characteristic
104	C₄²×C₃₁	C₄²	1	1	yes	characteristic
105	C₄²×C₃₁	C₄²	1	1	yes	characteristic
106	C₄²×C₃₁	C₄²	1	1	yes	characteristic
107	C₄²×C₃₁	C₄²	1	1	yes	characteristic
108	C₄²×C₃₁	C₄²	1	1	yes	characteristic
109	C₄²×C₃₁	C₂²×C₄	1	1	yes	characteristic
110	C₄²×C₃₁	C₂²×C₄	1	1	yes	characteristic
111	C₄²×C₃₁	C₂²×C₄	1	1	yes	characteristic
112	C₄²×C₃₁	C₂²×C₄	1	1	yes	characteristic
113	C₄²×C₃₁	C₂²×C₄	1	1	yes	characteristic
114	C₄²×C₃₁	C₂²×C₄	1	1	yes	characteristic
115	C₄²×C₃₁	C₂²×C₄	1	1	yes	characteristic
116	C₄²×C₃₁	C₂²×C₄	1	1	yes	characteristic
117	C₄²×C₃₁	C₂²×C₄	1	1	yes	characteristic
118	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
119	#17324	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
120	C₂³×C₃₁	—	2	2	no	—
121	C₂³×C₃₁	—	4	1	no	—
122	C₂³×C₃₁	—	4	1	no	—
123	C₂³×C₃₁	C₂×C₄²	1	1	yes	characteristic
124	C₂³×C₃₁	C₂×C₄²	1	1	yes	characteristic
125	C₂³×C₃₁	C₂×C₄²	1	1	yes	characteristic
126	C₂×C₄×C₃₁	—	2	2	no	—
127	C₂×C₄×C₃₁	—	2	2	no	—
128	C₂×C₄×C₃₁	—	2	2	no	—
129	C₂×C₄×C₃₁	—	2	2	no	—
130	C₂×C₄×C₃₁	—	2	2	no	—
131	C₂×C₄×C₃₁	—	2	2	no	—
132	C₂×C₄×C₃₁	—	2	2	no	—
133	C₂×C₄×C₃₁	—	2	2	no	—
134	C₂×C₄×C₃₁	—	2	2	no	—
135	C₂×C₄×C₃₁	—	2	2	no	—
136	C₂×C₄×C₃₁	—	2	2	no	—
137	C₂×C₄×C₃₁	—	4	1	no	—
138	C₂×C₄×C₃₁	—	4	1	no	—
139	C₂×C₄×C₃₁	—	4	1	no	—
140	C₂×C₄×C₃₁	—	4	1	no	—
141	C₂×C₄×C₃₁	—	4	1	no	—
142	C₂×C₄×C₃₁	—	4	1	no	—
143	C₂×C₄×C₃₁	C₂×C₄²	1	1	yes	characteristic
144	C₂×C₄×C₃₁	C₂×C₄²	1	1	yes	characteristic
145	C₂×C₄×C₃₁	C₂×C₄²	1	1	yes	characteristic
146	C₂×C₄×C₃₁	C₂×C₄²	1	1	yes	characteristic
147	C₂×C₄×C₃₁	C₂×C₄²	1	1	yes	characteristic
148	C₂×C₄×C₃₁	C₂×C₄²	1	1	yes	characteristic
149	C₂×C₄×C₃₁	C₂×C₄²	1	1	yes	characteristic
150	C₂×C₄×C₃₁	C₂×C₄²	1	1	yes	characteristic
151	C₂×C₄×C₃₁	C₂×C₄²	1	1	yes	characteristic
152	C₂×C₄×C₃₁	#131	1	4	yes	—
153	C₂×C₄×C₃₁	C₂³×C₄	1	1	yes	characteristic
154	C₂×C₄×C₃₁	C₂³×C₄	1	1	yes	characteristic
155	C₂×C₄×C₃₁	C₂³×C₄	1	1	yes	characteristic
156	C₈×C₃₁	—	2	8	no	—
157	C₈×C₃₁	—	2	4	no	—
158	C₈×C₃₁	—	2	4	no	—
159	C₈×C₃₁	—	2	8	no	—
160	#2920	C₂×C₃₁	1	1	yes	characteristic
161	#2920	C₂×C₃₁	1	1	yes	characteristic
162	C₂×#431	C₂×C₃₁	1	1	yes	characteristic
163	#1454	C₂×C₃₁	1	4	yes	complemented
164	#1453	C₂×C₃₁	1	4	yes	complemented
165	#1451	C₂×C₃₁	1	2	yes	complemented
166	C₈×M₁₆	C₂×C₃₁	1	2	yes	complemented
167	C₂²×C₃₁	—	2	1	no	—
168	C₂²×C₃₁	—	2	1	no	—
169	C₂²×C₃₁	—	2	1	no	—
170	C₂²×C₃₁	—	2	1	no	—
171	C₂²×C₃₁	—	2	1	no	—
172	C₂²×C₃₁	—	2	1	no	—
173	C₂²×C₃₁	—	2	1	no	—
174	C₂²×C₃₁	—	2	1	no	—
175	C₂²×C₃₁	—	4	4	no	—
176	C₂²×C₃₁	#405	1	2	yes	—
177	C₂²×C₃₁	C₂²×C₄²	1	1	yes	characteristic
178	C₄×C₃₁	—	2	1	no	—
179	C₄×C₃₁	—	2	1	no	—
180	C₄×C₃₁	—	2	1	no	—
181	C₄×C₃₁	—	2	1	no	—
182	C₄×C₃₁	—	2	1	no	—
183	C₄×C₃₁	—	2	1	no	—
184	C₄×C₃₁	—	2	1	no	—
185	C₄×C₃₁	—	2	1	no	—
186	C₄×C₃₁	#405	1	2	yes	—
187	C₄×C₃₁	C₂×#131	1	2	yes	—
188	C₄×C₃₁	#568	1	2	yes	—
189	C₄×C₃₁	#568	1	2	yes	—
190	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
191	#432	C₄×C₃₁	1	2	yes	—
192	#432	C₄×C₃₁	1	2	yes	—
193	#432	C₄×C₃₁	1	2	yes	—
194	#432	C₄×C₃₁	1	2	yes	—
195	#431	C₄×C₃₁	1	2	yes	—
196	#431	C₄×C₃₁	1	2	yes	—
197	#431	C₂²×C₃₁	1	2	yes	—
198	#431	C₂²×C₃₁	1	2	yes	—
199	#431	C₂²×C₃₁	1	2	yes	—
200	#431	C₂²×C₃₁	1	2	yes	—
201	#431	C₂²×C₃₁	1	2	yes	—
202	#431	C₂²×C₃₁	1	2	yes	—
203	#423	C₄×C₃₁	1	2	yes	—
204	#423	C₄×C₃₁	1	2	yes	—
205	C₂×C₄⋊C₈	C₄×C₃₁	1	2	yes	—
206	#407	C₄×C₃₁	1	2	yes	—
207	#407	C₄×C₃₁	1	2	yes	—
208	C₂×C₂²⋊C₈	C₄×C₃₁	1	2	yes	—
209	C₄×M₁₆	C₂²×C₃₁	1	2	yes	—
210	C₄×M₁₆	C₂²×C₃₁	1	2	yes	—
211	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
212	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
213	#322	C₂²×C₃₁	1	4	yes	complemented
214	#322	C₂²×C₃₁	1	8	yes	complemented
215	C₈²	C₂²×C₃₁	1	4	yes	complemented
216	C₂×C₃₁	—	2	2	no	—
217	C₂×C₃₁	—	4	1	no	—
218	C₂×C₃₁	—	4	1	no	—
219	C₂×C₃₁	C₂×#405	1	1	yes	characteristic
220	C₂×C₃₁	#2873	1	1	yes	characteristic
221	C₂×C₃₁	#2873	1	1	yes	characteristic
222	C₂³×C₄	C₂×C₄×C₃₁	1	1	yes	characteristic
223	C₂³×C₄	C₂×C₄×C₃₁	1	1	yes	characteristic
224	C₂³×C₄	C₂×C₄×C₃₁	1	1	yes	characteristic
225	C₂×M₁₆	C₂×C₄×C₃₁	1	4	yes	—
226	C₂×M₁₆	C₂×C₄×C₃₁	1	4	yes	—
227	C₂²×C₈	C₂×C₄×C₃₁	1	2	yes	—
228	C₂²×C₈	C₂×C₄×C₃₁	1	2	yes	—
229	C₂×C₄²	C₂×C₄×C₃₁	1	1	yes	characteristic
230	C₂×C₄²	C₂×C₄×C₃₁	1	1	yes	characteristic
231	C₂×C₄²	C₂×C₄×C₃₁	1	1	yes	characteristic
232	C₂×C₄²	C₂×C₄×C₃₁	1	1	yes	characteristic
233	C₂×C₄²	C₂×C₄×C₃₁	1	1	yes	characteristic
234	C₂×C₄²	C₂×C₄×C₃₁	1	1	yes	characteristic
235	C₂×C₄²	C₂×C₄×C₃₁	1	1	yes	characteristic
236	C₂×C₄²	C₂×C₄×C₃₁	1	1	yes	characteristic
237	C₂×C₄²	C₂×C₄×C₃₁	1	1	yes	characteristic
238	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
239	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
240	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
241	C₄⋊C₈	C₂×C₄×C₃₁	1	4	yes	—
242	C₄⋊C₈	C₂×C₄×C₃₁	1	4	yes	—
243	C₄⋊C₈	C₂×C₄×C₃₁	1	4	yes	—
244	C₄⋊C₈	C₂×C₄×C₃₁	1	4	yes	—
245	C₄⋊C₈	C₂×C₄×C₃₁	1	4	yes	—
246	C₄⋊C₈	C₂×C₄×C₃₁	1	4	yes	—
247	C₂²⋊C₈	C₂×C₄×C₃₁	1	4	yes	—
248	C₂²⋊C₈	C₂×C₄×C₃₁	1	4	yes	—
249	C₂²⋊C₈	C₂×C₄×C₃₁	1	4	yes	—
250	C₂²⋊C₈	C₂×C₄×C₃₁	1	4	yes	—
251	C₂²⋊C₈	C₂×C₄×C₃₁	1	4	yes	—
252	C₂²⋊C₈	C₂×C₄×C₃₁	1	4	yes	—
253	#97	C₂×C₄×C₃₁	1	4	yes	—
254	#97	C₂×C₄×C₃₁	1	4	yes	—
255	C₄×C₈	C₂×C₄×C₃₁	1	2	yes	—
256	C₄×C₈	C₂×C₄×C₃₁	1	2	yes	—
257	C₄×C₈	C₂³×C₃₁	1	2	yes	—
258	C₄×C₈	C₂³×C₃₁	1	4	yes	—
259	C₄×C₈	C₂³×C₃₁	1	4	yes	—
260	C₄×C₈	C₂³×C₃₁	1	2	yes	—
261	C₃₁	#17324	1	1	yes	characteristic, direct product factor, Sylow
262	C₂⁴	C₄²×C₃₁	1	1	yes	characteristic
263	C₂²×C₄	—	2	4	no	—
264	C₂²×C₄	—	4	2	no	—
265	C₂²×C₄	—	4	2	no	—
266	C₂²×C₄	C₄²×C₃₁	1	1	yes	characteristic
267	C₂²×C₄	C₄²×C₃₁	1	1	yes	characteristic
268	C₂²×C₄	C₄²×C₃₁	1	1	yes	characteristic
269	C₂²×C₄	C₄²×C₃₁	1	1	yes	characteristic
270	C₂²×C₄	C₄²×C₃₁	1	1	yes	characteristic
271	C₂²×C₄	C₄²×C₃₁	1	1	yes	characteristic
272	C₂²×C₄	C₄²×C₃₁	1	1	yes	characteristic
273	C₂²×C₄	C₄²×C₃₁	1	1	yes	characteristic
274	C₂²×C₄	C₄²×C₃₁	1	1	yes	characteristic
275	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
276	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
277	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
278	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
279	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
280	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
281	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
282	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
283	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
284	M₁₆	—	2	8	no	—
285	M₁₆	—	4	4	no	—
286	C₂×C₈	—	4	2	no	—
287	C₂×C₈	—	4	2	no	—
288	C₂×C₈	C₂²×C₄×C₃₁	1	4	yes	—
289	C₂×C₈	C₂²×C₄×C₃₁	1	4	yes	—
290	C₂×C₈	C₂²×C₄×C₃₁	1	8	yes	—
291	C₂×C₈	C₂²×C₄×C₃₁	1	8	yes	—
292	C₄²	C₄²×C₃₁	1	1	yes	characteristic
293	C₄²	C₄²×C₃₁	1	1	yes	characteristic
294	C₄²	C₄²×C₃₁	1	1	yes	characteristic
295	C₄²	C₄²×C₃₁	1	1	yes	characteristic
296	C₄²	C₄²×C₃₁	1	1	yes	characteristic
297	C₄²	C₄²×C₃₁	1	1	yes	characteristic
298	C₄²	C₂²×C₄×C₃₁	1	1	yes	characteristic
299	C₄²	C₂²×C₄×C₃₁	1	1	yes	characteristic
300	C₄²	C₂²×C₄×C₃₁	1	1	yes	characteristic
301	C₄²	C₂²×C₄×C₃₁	1	1	yes	characteristic
302	C₄²	C₂²×C₄×C₃₁	1	1	yes	characteristic
303	C₄²	C₂²×C₄×C₃₁	1	1	yes	characteristic
304	C₄²	C₂²×C₄×C₃₁	1	1	yes	characteristic
305	C₄²	C₂²×C₄×C₃₁	1	1	yes	characteristic
306	C₄²	C₂²×C₄×C₃₁	1	1	yes	characteristic
307	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
308	C₂³	—	2	2	no	—
309	C₂³	—	4	1	no	—
310	C₂³	—	4	1	no	—
311	C₂³	C₂×C₄²×C₃₁	1	1	yes	characteristic
312	C₂³	C₂×C₄²×C₃₁	1	1	yes	characteristic
313	C₂³	C₂×C₄²×C₃₁	1	1	yes	characteristic
314	C₂×C₄	—	2	2	no	—
315	C₂×C₄	—	2	2	no	—
316	C₂×C₄	—	2	2	no	—
317	C₂×C₄	—	2	2	no	—
318	C₂×C₄	—	2	2	no	—
319	C₂×C₄	—	2	2	no	—
320	C₂×C₄	—	2	2	no	—
321	C₂×C₄	—	2	2	no	—
322	C₂×C₄	—	2	2	no	—
323	C₂×C₄	—	2	2	no	—
324	C₂×C₄	—	2	2	no	—
325	C₂×C₄	—	4	1	no	—
326	C₂×C₄	—	4	1	no	—
327	C₂×C₄	—	4	1	no	—
328	C₂×C₄	—	4	1	no	—
329	C₂×C₄	—	4	1	no	—
330	C₂×C₄	—	4	1	no	—
331	C₂×C₄	C₂×C₄²×C₃₁	1	1	yes	characteristic
332	C₂×C₄	C₂×C₄²×C₃₁	1	1	yes	characteristic
333	C₂×C₄	C₂×C₄²×C₃₁	1	1	yes	characteristic
334	C₂×C₄	C₂×C₄²×C₃₁	1	1	yes	characteristic
335	C₂×C₄	C₂×C₄²×C₃₁	1	1	yes	characteristic
336	C₂×C₄	C₂×C₄²×C₃₁	1	1	yes	characteristic
337	C₂×C₄	C₂×C₄²×C₃₁	1	1	yes	characteristic
338	C₂×C₄	C₂×C₄²×C₃₁	1	1	yes	characteristic
339	C₂×C₄	C₂×C₄²×C₃₁	1	1	yes	characteristic
340	C₂×C₄	C₃₁×#131	1	4	yes	—
341	C₂×C₄	C₂³×C₄×C₃₁	1	1	yes	characteristic
342	C₂×C₄	C₂³×C₄×C₃₁	1	1	yes	characteristic
343	C₂×C₄	C₂³×C₄×C₃₁	1	1	yes	characteristic
344	C₈	—	2	8	no	—
345	C₈	—	2	4	no	—
346	C₈	—	2	4	no	—
347	C₈	—	2	8	no	—
348	C₂²	—	2	1	no	—
349	C₂²	—	2	1	no	—
350	C₂²	—	2	1	no	—
351	C₂²	—	2	1	no	—
352	C₂²	—	2	1	no	—
353	C₂²	—	2	1	no	—
354	C₂²	—	2	1	no	—
355	C₂²	—	2	1	no	—
356	C₂²	—	4	4	no	—
357	C₂²	C₃₁×#405	1	2	yes	—
358	C₂²	C₂²×C₄²×C₃₁	1	1	yes	characteristic
359	C₄	—	2	1	no	—
360	C₄	—	2	1	no	—
361	C₄	—	2	1	no	—
362	C₄	—	2	1	no	—
363	C₄	—	2	1	no	—
364	C₄	—	2	1	no	—
365	C₄	—	2	1	no	—
366	C₄	—	2	1	no	—
367	C₄	C₃₁×#405	1	2	yes	—
368	C₄	C₂×C₃₁×#131	1	2	yes	—
369	C₄	C₃₁×#568	1	2	yes	—
370	C₄	C₃₁×#568	1	2	yes	—
371	C₂	—	2	2	no	—
372	C₂	—	4	1	no	—
373	C₂	—	4	1	no	—
374	C₂	C₂×C₃₁×#405	1	1	yes	characteristic
375	C₂	C₃₁×#2873	1	1	yes	characteristic
376	C₂	C₃₁×#2873	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
4. C₃₁×#1454	C₂	semidirect
5. C₃₁×#1453	C₂	semidirect
6. C₃₁×#1451	C₂	semidirect
7. C₈×M₁₆×C₃₁	C₂	semidirect
31. C₃₁×#322	C₂²	semidirect
32. C₃₁×#322	C₂²	semidirect
33. C₈²×C₃₁	C₂²	semidirect
119. #17324	C₃₁	direct (N × H)
163. #1454	C₂×C₃₁	semidirect
164. #1453	C₂×C₃₁	semidirect
165. #1451	C₂×C₃₁	semidirect
166. C₈×M₁₆	C₂×C₃₁	semidirect
213. #322	C₂²×C₃₁	semidirect
214. #322	C₂²×C₃₁	semidirect
215. C₈²	C₂²×C₃₁	semidirect
261. C₃₁	#17324	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×#2920	2
C₂×C₃₁×#431	2
C₃₁×#1454	2
C₃₁×#1453	2
C₃₁×#1451	2
C₈×M₁₆×C₃₁	2
#17324	31

Subgroups — C31×#17324 #21474083

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#17324 #21474083