Subgroups — C₃₁×#20550 #21477309

Order 7936.

994 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#431	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃₁×#423	C₂	1	1	yes	maximal, characteristic
3	C₄×C₃₁×#117	C₂	1	1	yes	maximal, characteristic
4	C₃₁×#1770	C₂	1	2	yes	maximal, complemented
5	C₈×C₄⋊C₄×C₃₁	C₂	1	2	yes	maximal, complemented
6	C₃₁×#1767	C₂	1	2	yes	maximal, complemented
7	C₄×C₃₁×C₄⋊C₈	C₂	1	2	yes	maximal, complemented
8	C₃₁×#1753	C₂	1	4	yes	maximal
9	C₂²×M₁₆×C₃₁	C₂²	1	2	yes	—
10	C₂×C₃₁×#117	C₄	1	2	yes	—
11	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
12	C₃₁×#431	C₄	1	8	yes	complemented
13	C₃₁×#423	C₄	1	8	yes	complemented
14	C₂×C₃₁×C₄⋊C₈	C₂²	1	2	yes	—
15	C₂×C₃₁×C₄⋊C₈	C₂²	1	2	yes	—
16	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
17	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
18	C₂×C₃₁×C₂²⋊C₈	C₂²	1	2	yes	—
19	C₂×C₃₁×#97	C₂²	1	4	yes	—
20	C₂×C₄×C₈×C₃₁	C₂²	1	4	yes	—
21	C₂×C₄×C₈×C₃₁	C₂²	1	2	yes	—
22	C₄×C₄⋊C₄×C₃₁	C₄	1	2	yes	—
23	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
24	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
25	C₄×C₂²⋊C₄×C₃₁	C₄	1	2	yes	—
26	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
27	C₃₁×#376	C₄	1	2	yes	—
28	C₄³×C₃₁	C₂²	1	2	yes	—
29	C₃₁×#336	C₂²	1	4	yes	—
30	C₃₁×#336	C₂²	1	4	yes	—
31	C₂³×C₄×C₃₁	C₂×C₄	1	1	yes	characteristic
32	C₂³×C₄×C₃₁	C₂×C₄	1	1	yes	characteristic
33	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
34	C₂×M₁₆×C₃₁	—	4	2	no	—
35	C₂×M₁₆×C₃₁	—	4	2	no	—
36	C₂×M₁₆×C₃₁	C₂×C₄	1	8	yes	—
37	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
38	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
39	C₂²×C₈×C₃₁	C₂³	1	4	yes	—
40	C₃₁×#117	—	2	8	no	—
41	C₂×C₄⋊C₄×C₃₁	C₂×C₄	1	2	yes	—
42	C₂×C₄⋊C₄×C₃₁	C₂×C₄	1	2	yes	—
43	C₂×C₂²⋊C₄×C₃₁	C₂×C₄	1	4	yes	—
44	C₂×C₄²×C₃₁	C₂×C₄	1	4	yes	—
45	C₂×C₄²×C₃₁	C₂×C₄	1	4	yes	—
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	4	yes	—
49	C₂×C₄²×C₃₁	C₂×C₄	1	4	yes	—
50	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
51	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
52	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
53	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
54	C₃₁×C₄⋊C₈	C₂×C₄	1	8	yes	—
55	C₃₁×C₄⋊C₈	C₂×C₄	1	8	yes	—
56	C₃₁×C₄⋊C₈	C₂×C₄	1	4	yes	—
57	C₃₁×C₄⋊C₈	C₂×C₄	1	4	yes	—
58	C₃₁×C₂²⋊C₈	C₂×C₄	1	8	yes	—
59	C₃₁×#97	—	4	4	no	—
60	C₄×C₈×C₃₁	—	4	4	no	—
61	C₄×C₈×C₃₁	C₂×C₄	1	8	yes	—
62	C₃₁×#95	C₂×C₄	1	2	yes	—
63	C₃₁×#95	C₂×C₄	1	2	yes	—
64	C₃₁×#95	C₂×C₄	1	4	yes	—
65	C₂⁴×C₃₁	C₂²×C₄	1	1	yes	characteristic
66	C₂²×C₄×C₃₁	—	2	4	no	—
67	C₂²×C₄×C₃₁	—	2	4	no	—
68	C₂²×C₄×C₃₁	—	2	1	no	—
69	C₂²×C₄×C₃₁	—	2	1	no	—
70	C₂²×C₄×C₃₁	—	2	1	no	—
71	C₂²×C₄×C₃₁	—	2	1	no	—
72	C₂²×C₄×C₃₁	C₄²	1	4	yes	—
73	C₂²×C₄×C₃₁	C₄²	1	4	yes	—
74	C₂²×C₄×C₃₁	C₂²×C₄	1	4	yes	—
75	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
76	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
77	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
78	C₂²×C₄×C₃₁	C₂²×C₄	1	2	yes	—
79	C₂²×C₄×C₃₁	C₂²×C₄	1	2	yes	—
80	C₂²×C₄×C₃₁	C₂²×C₄	1	4	yes	—
81	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
82	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
83	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
84	M₁₆×C₃₁	—	4	8	no	—
85	C₂×C₈×C₃₁	—	2	2	no	—
86	C₂×C₈×C₃₁	—	2	4	no	—
87	C₂×C₈×C₃₁	—	2	2	no	—
88	C₂×C₈×C₃₁	—	2	4	no	—
89	C₂×C₈×C₃₁	—	2	2	no	—
90	C₂×C₈×C₃₁	—	2	2	no	—
91	C₂×C₈×C₃₁	C₂²×C₄	1	4	yes	—
92	C₂×C₈×C₃₁	C₂²×C₄	1	4	yes	—
93	C₂×C₈×C₃₁	C₂²×C₄	1	8	yes	—
94	C₄⋊C₄×C₃₁	—	2	4	no	—
95	C₄⋊C₄×C₃₁	M₁₆	1	8	yes	complemented
96	C₂²⋊C₄×C₃₁	—	2	8	no	—
97	C₄²×C₃₁	—	2	8	no	—
98	C₄²×C₃₁	—	2	8	no	—
99	C₄²×C₃₁	—	2	2	no	—
100	C₄²×C₃₁	—	2	2	no	—
101	C₄²×C₃₁	—	2	2	no	—
102	C₄²×C₃₁	—	2	2	no	—
103	C₄²×C₃₁	C₄²	1	4	yes	—
104	C₄²×C₃₁	C₄²	1	4	yes	—
105	C₄²×C₃₁	C₂²×C₄	1	2	yes	—
106	C₄²×C₃₁	C₂²×C₄	1	2	yes	—
107	C₄²×C₃₁	C₂²×C₄	1	2	yes	—
108	C₄²×C₃₁	C₂²×C₄	1	2	yes	—
109	#20550	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
110	C₂³×C₃₁	—	2	1	no	—
111	C₂³×C₃₁	—	2	1	no	—
112	C₂³×C₃₁	—	2	2	no	—
113	C₂³×C₃₁	—	2	2	no	—
114	C₂³×C₃₁	C₂×C₄²	1	2	yes	—
115	C₂³×C₃₁	C₂³×C₄	1	1	yes	characteristic
116	C₂×C₄×C₃₁	—	2	4	no	—
117	C₂×C₄×C₃₁	—	2	1	no	—
118	C₂×C₄×C₃₁	—	2	1	no	—
119	C₂×C₄×C₃₁	—	2	2	no	—
120	C₂×C₄×C₃₁	—	2	4	no	—
121	C₂×C₄×C₃₁	—	2	2	no	—
122	C₂×C₄×C₃₁	—	2	2	no	—
123	C₂×C₄×C₃₁	—	2	2	no	—
124	C₂×C₄×C₃₁	—	2	2	no	—
125	C₂×C₄×C₃₁	—	2	2	no	—
126	C₂×C₄×C₃₁	—	2	8	no	—
127	C₂×C₄×C₃₁	—	2	8	no	—
128	C₂×C₄×C₃₁	—	2	4	no	—
129	C₂×C₄×C₃₁	—	2	4	no	—
130	C₂×C₄×C₃₁	—	2	4	no	—
131	C₂×C₄×C₃₁	C₂×C₄²	1	2	yes	—
132	C₂×C₄×C₃₁	C₂×C₄²	1	2	yes	—
133	C₂×C₄×C₃₁	C₂×C₄²	1	2	yes	—
134	C₂×C₄×C₃₁	C₂×C₄²	1	2	yes	—
135	C₂×C₄×C₃₁	C₂×C₄²	1	2	yes	—
136	C₂×C₄×C₃₁	C₂×M₁₆	1	8	yes	—
137	C₂×C₄×C₃₁	C₂×M₁₆	1	4	yes	—
138	C₂×C₄×C₃₁	#131	1	4	yes	—
139	C₂×C₄×C₃₁	C₂³×C₄	1	1	yes	characteristic
140	C₂×C₄×C₃₁	C₂³×C₄	1	1	yes	characteristic
141	C₂×C₄×C₃₁	H(5,𝔽₂)	1	1	yes	characteristic
142	C₂×C₄×C₃₁	H(5,𝔽₂)	1	1	yes	characteristic
143	C₂×C₄×C₃₁	2₋¹⁺⁴	1	1	yes	characteristic
144	C₂×C₄×C₃₁	2₋¹⁺⁴	1	1	yes	characteristic
145	C₈×C₃₁	—	2	8	no	—
146	C₈×C₃₁	—	2	4	no	—
147	C₈×C₃₁	—	2	4	no	—
148	C₂×#431	C₂×C₃₁	1	1	yes	characteristic
149	C₂×#423	C₂×C₃₁	1	1	yes	characteristic
150	C₄×#117	C₂×C₃₁	1	1	yes	characteristic
151	#1770	C₂×C₃₁	1	2	yes	complemented
152	C₈×C₄⋊C₄	C₂×C₃₁	1	2	yes	complemented
153	#1767	C₂×C₃₁	1	2	yes	complemented
154	C₄×C₄⋊C₈	C₂×C₃₁	1	2	yes	complemented
155	#1753	C₂×C₃₁	1	4	yes	—
156	C₂²×C₃₁	—	2	2	no	—
157	C₂²×C₃₁	—	2	2	no	—
158	C₂²×C₃₁	—	2	2	no	—
159	C₂²×C₃₁	—	4	2	no	—
160	C₂²×C₃₁	—	4	2	no	—
161	C₂²×C₃₁	C₂²×C₄²	1	1	yes	characteristic
162	C₂²×C₃₁	#520	1	1	yes	characteristic
163	C₂²×C₃₁	#520	1	1	yes	characteristic
164	C₂²×C₃₁	C₂²×M₁₆	1	2	yes	—
165	C₂²×C₃₁	C₂×#131	1	2	yes	—
166	C₄×C₃₁	—	2	2	no	—
167	C₄×C₃₁	—	2	2	no	—
168	C₄×C₃₁	—	2	8	no	—
169	C₄×C₃₁	—	2	2	no	—
170	C₄×C₃₁	—	4	4	no	—
171	C₄×C₃₁	C₄×M₁₆	1	4	yes	—
172	C₄×C₃₁	#405	1	4	yes	—
173	C₄×C₃₁	#518	1	1	yes	characteristic
174	C₄×C₃₁	#519	1	1	yes	characteristic
175	C₄×C₃₁	#520	1	1	yes	characteristic
176	C₄×C₃₁	#520	1	1	yes	characteristic
177	C₂²×M₁₆	C₂²×C₃₁	1	2	yes	—
178	C₂×#117	C₄×C₃₁	1	2	yes	—
179	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
180	#431	C₄×C₃₁	1	8	yes	complemented
181	#423	C₄×C₃₁	1	8	yes	complemented
182	C₂×C₄⋊C₈	C₂²×C₃₁	1	2	yes	—
183	C₂×C₄⋊C₈	C₂²×C₃₁	1	2	yes	—
184	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
185	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
186	C₂×C₂²⋊C₈	C₂²×C₃₁	1	2	yes	—
187	C₂×#97	C₂²×C₃₁	1	4	yes	—
188	C₂×C₄×C₈	C₂²×C₃₁	1	4	yes	—
189	C₂×C₄×C₈	C₂²×C₃₁	1	2	yes	—
190	C₄×C₄⋊C₄	C₄×C₃₁	1	2	yes	—
191	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
192	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
193	C₄×C₂²⋊C₄	C₄×C₃₁	1	2	yes	—
194	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
195	#376	C₄×C₃₁	1	2	yes	—
196	C₄³	C₂²×C₃₁	1	2	yes	—
197	#336	C₂²×C₃₁	1	4	yes	—
198	#336	C₂²×C₃₁	1	4	yes	—
199	C₂×C₃₁	—	4	2	no	—
200	C₂×C₃₁	#2274	1	1	yes	characteristic
201	C₂×C₃₁	C₂×C₄×M₁₆	1	1	yes	characteristic
202	C₂×C₃₁	C₂×#405	1	1	yes	characteristic
203	C₂×C₃₁	#2990	1	2	yes	—
204	C₂×C₃₁	#2991	1	2	yes	—
205	C₂³×C₄	C₂×C₄×C₃₁	1	1	yes	characteristic
206	C₂³×C₄	C₂×C₄×C₃₁	1	1	yes	characteristic
207	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
208	C₂×M₁₆	—	4	2	no	—
209	C₂×M₁₆	—	4	2	no	—
210	C₂×M₁₆	C₂×C₄×C₃₁	1	8	yes	—
211	C₂²×C₈	C₂³×C₃₁	1	4	yes	—
212	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
213	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
214	#117	—	2	8	no	—
215	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	2	yes	—
216	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	2	yes	—
217	C₂×C₂²⋊C₄	C₂×C₄×C₃₁	1	4	yes	—
218	C₂×C₄²	C₂×C₄×C₃₁	1	4	yes	—
219	C₂×C₄²	C₂×C₄×C₃₁	1	4	yes	—
220	C₂×C₄²	C₂×C₄×C₃₁	1	1	yes	characteristic
221	C₂×C₄²	C₂×C₄×C₃₁	1	1	yes	characteristic
222	C₂×C₄²	C₂×C₄×C₃₁	1	4	yes	—
223	C₂×C₄²	C₂×C₄×C₃₁	1	4	yes	—
224	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
225	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
226	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
227	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
228	C₄⋊C₈	C₂×C₄×C₃₁	1	8	yes	—
229	C₄⋊C₈	C₂×C₄×C₃₁	1	8	yes	—
230	C₄⋊C₈	C₂×C₄×C₃₁	1	4	yes	—
231	C₄⋊C₈	C₂×C₄×C₃₁	1	4	yes	—
232	C₂²⋊C₈	C₂×C₄×C₃₁	1	8	yes	—
233	#97	—	4	4	no	—
234	C₄×C₈	—	4	4	no	—
235	C₄×C₈	C₂×C₄×C₃₁	1	8	yes	—
236	#95	C₂×C₄×C₃₁	1	2	yes	—
237	#95	C₂×C₄×C₃₁	1	2	yes	—
238	#95	C₂×C₄×C₃₁	1	4	yes	—
239	C₃₁	#20550	1	1	yes	characteristic, direct product factor, Sylow
240	C₂⁴	C₂²×C₄×C₃₁	1	1	yes	characteristic
241	C₂²×C₄	—	2	4	no	—
242	C₂²×C₄	—	2	4	no	—
243	C₂²×C₄	—	2	1	no	—
244	C₂²×C₄	—	2	1	no	—
245	C₂²×C₄	—	2	1	no	—
246	C₂²×C₄	—	2	1	no	—
247	C₂²×C₄	C₄²×C₃₁	1	4	yes	—
248	C₂²×C₄	C₄²×C₃₁	1	4	yes	—
249	C₂²×C₄	C₂²×C₄×C₃₁	1	4	yes	—
250	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
251	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
252	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
253	C₂²×C₄	C₂²×C₄×C₃₁	1	2	yes	—
254	C₂²×C₄	C₂²×C₄×C₃₁	1	2	yes	—
255	C₂²×C₄	C₂²×C₄×C₃₁	1	4	yes	—
256	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
257	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
258	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
259	M₁₆	—	4	8	no	—
260	C₂×C₈	—	2	2	no	—
261	C₂×C₈	—	2	4	no	—
262	C₂×C₈	—	2	2	no	—
263	C₂×C₈	—	2	4	no	—
264	C₂×C₈	—	2	2	no	—
265	C₂×C₈	—	2	2	no	—
266	C₂×C₈	C₂²×C₄×C₃₁	1	4	yes	—
267	C₂×C₈	C₂²×C₄×C₃₁	1	4	yes	—
268	C₂×C₈	C₂²×C₄×C₃₁	1	8	yes	—
269	C₄⋊C₄	—	2	4	no	—
270	C₄⋊C₄	M₁₆×C₃₁	1	8	yes	complemented
271	C₂²⋊C₄	—	2	8	no	—
272	C₄²	—	2	8	no	—
273	C₄²	—	2	8	no	—
274	C₄²	—	2	2	no	—
275	C₄²	—	2	2	no	—
276	C₄²	—	2	2	no	—
277	C₄²	—	2	2	no	—
278	C₄²	C₄²×C₃₁	1	4	yes	—
279	C₄²	C₄²×C₃₁	1	4	yes	—
280	C₄²	C₂²×C₄×C₃₁	1	2	yes	—
281	C₄²	C₂²×C₄×C₃₁	1	2	yes	—
282	C₄²	C₂²×C₄×C₃₁	1	2	yes	—
283	C₄²	C₂²×C₄×C₃₁	1	2	yes	—
284	C₂³	—	2	1	no	—
285	C₂³	—	2	1	no	—
286	C₂³	—	2	2	no	—
287	C₂³	—	2	2	no	—
288	C₂³	C₂×C₄²×C₃₁	1	2	yes	—
289	C₂³	C₂³×C₄×C₃₁	1	1	yes	characteristic
290	C₂×C₄	—	2	4	no	—
291	C₂×C₄	—	2	1	no	—
292	C₂×C₄	—	2	1	no	—
293	C₂×C₄	—	2	2	no	—
294	C₂×C₄	—	2	4	no	—
295	C₂×C₄	—	2	2	no	—
296	C₂×C₄	—	2	8	no	—
297	C₂×C₄	—	2	8	no	—
298	C₂×C₄	—	2	2	no	—
299	C₂×C₄	—	2	2	no	—
300	C₂×C₄	—	2	2	no	—
301	C₂×C₄	—	2	2	no	—
302	C₂×C₄	—	2	4	no	—
303	C₂×C₄	—	2	4	no	—
304	C₂×C₄	—	2	4	no	—
305	C₂×C₄	C₂×C₄²×C₃₁	1	2	yes	—
306	C₂×C₄	C₂×C₄²×C₃₁	1	2	yes	—
307	C₂×C₄	C₂×C₄²×C₃₁	1	2	yes	—
308	C₂×C₄	C₂×C₄²×C₃₁	1	2	yes	—
309	C₂×C₄	C₂×C₄²×C₃₁	1	2	yes	—
310	C₂×C₄	C₂×M₁₆×C₃₁	1	8	yes	—
311	C₂×C₄	C₂×M₁₆×C₃₁	1	4	yes	—
312	C₂×C₄	C₃₁×#131	1	4	yes	—
313	C₂×C₄	C₂³×C₄×C₃₁	1	1	yes	characteristic
314	C₂×C₄	C₂³×C₄×C₃₁	1	1	yes	characteristic
315	C₂×C₄	C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
316	C₂×C₄	C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
317	C₂×C₄	C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
318	C₂×C₄	C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
319	C₈	—	2	8	no	—
320	C₈	—	2	4	no	—
321	C₈	—	2	4	no	—
322	C₂²	—	2	2	no	—
323	C₂²	—	2	2	no	—
324	C₂²	—	2	2	no	—
325	C₂²	—	4	2	no	—
326	C₂²	—	4	2	no	—
327	C₂²	C₂²×C₄²×C₃₁	1	1	yes	characteristic
328	C₂²	C₃₁×#520	1	1	yes	characteristic
329	C₂²	C₃₁×#520	1	1	yes	characteristic
330	C₂²	C₂²×M₁₆×C₃₁	1	2	yes	—
331	C₂²	C₂×C₃₁×#131	1	2	yes	—
332	C₄	—	2	2	no	—
333	C₄	—	2	2	no	—
334	C₄	—	2	8	no	—
335	C₄	—	2	2	no	—
336	C₄	—	4	4	no	—
337	C₄	C₄×M₁₆×C₃₁	1	4	yes	—
338	C₄	C₃₁×#405	1	4	yes	—
339	C₄	C₃₁×#518	1	1	yes	characteristic
340	C₄	C₃₁×#519	1	1	yes	characteristic
341	C₄	C₃₁×#520	1	1	yes	characteristic
342	C₄	C₃₁×#520	1	1	yes	characteristic
343	C₂	—	4	2	no	—
344	C₂	C₃₁×#2274	1	1	yes	characteristic
345	C₂	C₂×C₄×M₁₆×C₃₁	1	1	yes	characteristic
346	C₂	C₂×C₃₁×#405	1	1	yes	characteristic
347	C₂	C₃₁×#2990	1	2	yes	—
348	C₂	C₃₁×#2991	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
4. C₃₁×#1770	C₂	semidirect
5. C₈×C₄⋊C₄×C₃₁	C₂	semidirect
6. C₃₁×#1767	C₂	semidirect
7. C₄×C₃₁×C₄⋊C₈	C₂	semidirect
12. C₃₁×#431	C₄	semidirect
13. C₃₁×#423	C₄	semidirect
95. C₄⋊C₄×C₃₁	M₁₆	semidirect
109. #20550	C₃₁	direct (N × H)
151. #1770	C₂×C₃₁	semidirect
152. C₈×C₄⋊C₄	C₂×C₃₁	semidirect
153. #1767	C₂×C₃₁	semidirect
154. C₄×C₄⋊C₈	C₂×C₃₁	semidirect
180. #431	C₄×C₃₁	semidirect
181. #423	C₄×C₃₁	semidirect
239. C₃₁	#20550	direct (N × H)
270. C₄⋊C₄	M₁₆×C₃₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃₁×#431	2
C₂×C₃₁×#423	2
C₄×C₃₁×#117	2
C₃₁×#1770	2
C₈×C₄⋊C₄×C₃₁	2
C₃₁×#1767	2
C₄×C₃₁×C₄⋊C₈	2
C₃₁×#1753	2
#20550	31

Subgroups — C31×#20550 #21477309

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#20550 #21477309