Subgroups — C₃₁×#20492 #21477251

Order 7936.

1122 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#435	C₂	1	2	yes	maximal
2	C₂×C₃₁×#405	C₂	1	2	yes	maximal, complemented
3	C₃₁×#2293	C₂	1	1	yes	maximal, characteristic
4	C₃₁×#1771	C₂	1	2	yes	maximal, complemented
5	C₄×C₃₁×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#1753	C₂	1	2	yes	maximal, complemented
7	C₈×C₂²⋊C₄×C₃₁	C₂	1	2	yes	maximal, complemented
8	C₃₁×#1750	C₂	1	2	yes	maximal, complemented
9	C₄×C₃₁×#97	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×M₁₆×C₃₁	C₂²	1	2	yes	—
11	C₂³×C₈×C₃₁	C₂²	1	2	yes	—
12	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
13	C₂×C₃₁×#117	C₂²	1	2	yes	—
14	C₃₁×#435	C₄	1	16	yes	complemented
15	C₂×C₃₁×C₄⋊C₈	C₂²	1	2	yes	—
16	C₂×C₃₁×C₂²⋊C₈	C₂²	1	2	yes	—
17	C₂×C₃₁×C₂²⋊C₈	C₂²	1	2	yes	—
18	C₃₁×#405	—	2	8	no	—
19	C₂×C₃₁×#97	C₂²	1	2	yes	—
20	C₂×C₃₁×#97	C₂²	1	1	yes	characteristic
21	C₂×C₃₁×#97	C₂²	1	2	yes	—
22	C₂×C₃₁×#97	C₂²	1	1	yes	characteristic
23	C₂×C₄×C₈×C₃₁	C₂²	1	2	yes	—
24	C₂×C₄×C₈×C₃₁	C₂²	1	2	yes	—
25	C₂×C₄×C₈×C₃₁	C₂²	1	2	yes	—
26	C₃₁×#390	C₄	1	2	yes	—
27	C₃₁×#389	C₄	1	2	yes	—
28	C₃₁×#388	C₄	1	4	yes	—
29	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
30	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
31	C₄³×C₃₁	C₂²	1	1	yes	characteristic
32	C₃₁×#336	C₂²	1	2	yes	—
33	C₃₁×#336	C₂²	1	2	yes	—
34	C₃₁×#336	C₂²	1	1	yes	characteristic
35	C₃₁×#336	C₂²	1	1	yes	characteristic
36	C₂²×D₄×C₃₁	C₂×C₄	1	1	yes	characteristic
37	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
38	C₂×M₁₆×C₃₁	—	2	4	no	—
39	C₂×M₁₆×C₃₁	—	2	4	no	—
40	C₂×M₁₆×C₃₁	C₂×C₄	1	8	yes	—
41	C₂²×C₈×C₃₁	—	2	4	no	—
42	C₂²×C₈×C₃₁	—	2	4	no	—
43	C₂²×C₈×C₃₁	C₂×C₄	1	8	yes	—
44	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
45	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
46	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
47	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
48	C₄×D₄×C₃₁	C₂×C₄	1	8	yes	—
49	C₃₁×#117	—	2	4	no	—
50	C₃₁×#117	—	2	4	no	—
51	C₂×C₄⋊C₄×C₃₁	C₂×C₄	1	4	yes	—
52	C₂×C₄⋊C₄×C₃₁	C₂×C₄	1	2	yes	—
53	C₂×C₄⋊C₄×C₃₁	C₂×C₄	1	1	yes	characteristic
54	C₂×C₂²⋊C₄×C₃₁	C₂×C₄	1	4	yes	—
55	C₂×C₂²⋊C₄×C₃₁	C₂×C₄	1	4	yes	—
56	C₂×C₂²⋊C₄×C₃₁	C₂×C₄	1	2	yes	—
57	C₂×C₄²×C₃₁	C₂×C₄	1	2	yes	—
58	C₂×C₄²×C₃₁	C₂×C₄	1	2	yes	—
59	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
60	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
61	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
62	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
63	C₃₁×C₄⋊C₈	C₂×C₄	1	8	yes	—
64	C₃₁×C₂²⋊C₈	C₂×C₄	1	8	yes	—
65	C₃₁×C₂²⋊C₈	C₂×C₄	1	8	yes	—
66	C₃₁×#97	—	2	4	no	—
67	C₃₁×#97	—	2	2	no	—
68	C₃₁×#97	C₂×C₄	1	8	yes	—
69	C₃₁×#97	D₄	1	4	yes	complemented
70	C₄×C₈×C₃₁	—	2	4	no	—
71	C₄×C₈×C₃₁	—	2	4	no	—
72	C₄×C₈×C₃₁	—	2	4	no	—
73	C₃₁×#95	C₂×C₄	1	4	yes	—
74	C₃₁×#95	C₂×C₄	1	2	yes	—
75	C₂⁴×C₃₁	C₂²×C₄	1	2	yes	—
76	C₂×D₄×C₃₁	—	4	2	no	—
77	C₂×D₄×C₃₁	C₄²	1	4	yes	—
78	C₂²×C₄×C₃₁	—	2	2	no	—
79	C₂²×C₄×C₃₁	—	2	2	no	—
80	C₂²×C₄×C₃₁	—	2	2	no	—
81	C₂²×C₄×C₃₁	—	2	2	no	—
82	C₂²×C₄×C₃₁	C₂²×C₄	1	4	yes	—
83	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
84	C₂²×C₄×C₃₁	C₂²×C₄	1	2	yes	—
85	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
86	C₂²×C₄×C₃₁	C₂²×C₄	1	4	yes	—
87	C₂²×C₄×C₃₁	C₂²×C₄	1	4	yes	—
88	C₂²×C₄×C₃₁	C₂²×C₄	1	2	yes	—
89	C₂²×C₄×C₃₁	C₂²×C₄	1	2	yes	—
90	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
91	M₁₆×C₃₁	—	2	16	no	—
92	C₂×C₈×C₃₁	—	2	2	no	—
93	C₂×C₈×C₃₁	—	2	2	no	—
94	C₂×C₈×C₃₁	—	2	2	no	—
95	C₂×C₈×C₃₁	—	2	2	no	—
96	C₂×C₈×C₃₁	—	2	2	no	—
97	C₂×C₈×C₃₁	—	2	2	no	—
98	C₂×C₈×C₃₁	—	2	16	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	4	yes	—
102	C₂×C₈×C₃₁	C₂²×C₄	1	4	yes	—
103	C₂×C₈×C₃₁	C₂×D₄	1	4	yes	—
104	C₂×C₈×C₃₁	#41	1	4	yes	—
105	C₄⋊C₄×C₃₁	—	2	8	no	—
106	C₄⋊C₄×C₃₁	—	4	2	no	—
107	C₄⋊C₄×C₃₁	C₄²	1	4	yes	—
108	C₂²⋊C₄×C₃₁	—	2	8	no	—
109	C₂²⋊C₄×C₃₁	—	2	8	no	—
110	C₂²⋊C₄×C₃₁	C₄²	1	8	yes	—
111	C₄²×C₃₁	—	2	4	no	—
112	C₄²×C₃₁	—	2	2	no	—
113	C₄²×C₃₁	—	2	2	no	—
114	C₄²×C₃₁	—	2	2	no	—
115	C₄²×C₃₁	—	4	2	no	—
116	C₄²×C₃₁	C₂²×C₄	1	4	yes	—
117	C₄²×C₃₁	C₂×D₄	1	2	yes	—
118	C₄²×C₃₁	#41	1	2	yes	—
119	#20492	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
120	C₂³×C₃₁	—	2	2	no	—
121	C₂³×C₃₁	—	2	2	no	—
122	C₂³×C₃₁	—	2	4	no	—
123	C₂³×C₃₁	—	2	4	no	—
124	C₂³×C₃₁	C₂×C₄²	1	4	yes	—
125	C₂³×C₃₁	C₂³×C₄	1	1	yes	characteristic
126	D₄×C₃₁	—	4	4	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	4	no	—
136	C₂×C₄×C₃₁	—	2	4	no	—
137	C₂×C₄×C₃₁	—	2	4	no	—
138	C₂×C₄×C₃₁	—	2	4	no	—
139	C₂×C₄×C₃₁	—	2	4	no	—
140	C₂×C₄×C₃₁	—	2	4	no	—
141	C₂×C₄×C₃₁	—	2	4	no	—
142	C₂×C₄×C₃₁	C₂×C₄²	1	2	yes	—
143	C₂×C₄×C₃₁	C₂×C₄²	1	2	yes	—
144	C₂×C₄×C₃₁	C₂×C₄²	1	4	yes	—
145	C₂×C₄×C₃₁	C₄×D₄	1	4	yes	—
146	C₂×C₄×C₃₁	#131	1	4	yes	—
147	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
148	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
149	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
150	C₂×C₄×C₃₁	C₂×#41	1	1	yes	characteristic
151	C₈×C₃₁	—	2	4	no	—
152	C₈×C₃₁	—	2	4	no	—
153	C₈×C₃₁	—	2	4	no	—
154	C₈×C₃₁	C₄×D₄	1	8	yes	—
155	C₂×#435	C₂×C₃₁	1	2	yes	—
156	C₂×#405	C₂×C₃₁	1	2	yes	complemented
157	#2293	C₂×C₃₁	1	1	yes	characteristic
158	#1771	C₂×C₃₁	1	2	yes	complemented
159	C₄×C₄⋊C₈	C₂×C₃₁	1	1	yes	characteristic, complemented
160	#1753	C₂×C₃₁	1	2	yes	complemented
161	C₈×C₂²⋊C₄	C₂×C₃₁	1	2	yes	complemented
162	#1750	C₂×C₃₁	1	2	yes	complemented
163	C₄×#97	C₂×C₃₁	1	1	yes	characteristic, complemented
164	C₂²×C₃₁	—	2	4	no	—
165	C₂²×C₃₁	—	2	4	no	—
166	C₂²×C₃₁	—	2	4	no	—
167	C₂²×C₃₁	—	4	4	no	—
168	C₂²×C₃₁	—	4	4	no	—
169	C₂²×C₃₁	C₂²×C₄²	1	1	yes	characteristic
170	C₂²×C₃₁	C₂×C₄×D₄	1	1	yes	characteristic
171	C₂²×C₃₁	C₄×#41	1	1	yes	characteristic
172	C₂²×C₃₁	C₂×#131	1	2	yes	—
173	C₂²×C₃₁	#568	1	2	yes	—
174	C₄×C₃₁	—	2	2	no	—
175	C₄×C₃₁	—	2	2	no	—
176	C₄×C₃₁	—	2	4	no	—
177	C₄×C₃₁	—	2	4	no	—
178	C₄×C₃₁	—	2	4	no	—
179	C₄×C₃₁	—	4	4	no	—
180	C₄×C₃₁	C₂×C₄×D₄	1	2	yes	—
181	C₄×C₃₁	C₄×#41	1	2	yes	—
182	C₂²×M₁₆	C₂²×C₃₁	1	2	yes	—
183	C₂³×C₈	C₂²×C₃₁	1	2	yes	—
184	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
185	C₂×#117	C₂²×C₃₁	1	2	yes	—
186	#435	C₄×C₃₁	1	16	yes	complemented
187	C₂×C₄⋊C₈	C₂²×C₃₁	1	2	yes	—
188	C₂×C₂²⋊C₈	C₂²×C₃₁	1	2	yes	—
189	C₂×C₂²⋊C₈	C₂²×C₃₁	1	2	yes	—
190	#405	—	2	8	no	—
191	C₂×#97	C₂²×C₃₁	1	2	yes	—
192	C₂×#97	C₂²×C₃₁	1	1	yes	characteristic
193	C₂×#97	C₂²×C₃₁	1	2	yes	—
194	C₂×#97	C₂²×C₃₁	1	1	yes	characteristic
195	C₂×C₄×C₈	C₂²×C₃₁	1	2	yes	—
196	C₂×C₄×C₈	C₂²×C₃₁	1	2	yes	—
197	C₂×C₄×C₈	C₂²×C₃₁	1	2	yes	—
198	#390	C₄×C₃₁	1	2	yes	—
199	#389	C₄×C₃₁	1	2	yes	—
200	#388	C₄×C₃₁	1	4	yes	—
201	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
202	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
203	C₄³	C₂²×C₃₁	1	1	yes	characteristic
204	#336	C₂²×C₃₁	1	2	yes	—
205	#336	C₂²×C₃₁	1	2	yes	—
206	#336	C₂²×C₃₁	1	1	yes	characteristic
207	#336	C₂²×C₃₁	1	1	yes	characteristic
208	C₂×C₃₁	—	4	4	no	—
209	C₂×C₃₁	C₄²×D₄	1	1	yes	characteristic
210	C₂×C₃₁	#2873	1	1	yes	characteristic
211	C₂×C₃₁	C₄×#131	1	1	yes	characteristic
212	C₂×C₃₁	#2935	1	2	yes	—
213	C₂×C₃₁	#2968	1	2	yes	—
214	C₂²×D₄	C₂×C₄×C₃₁	1	1	yes	characteristic
215	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
216	C₂×M₁₆	—	2	4	no	—
217	C₂×M₁₆	—	2	4	no	—
218	C₂×M₁₆	C₂×C₄×C₃₁	1	8	yes	—
219	C₂²×C₈	—	2	4	no	—
220	C₂²×C₈	—	2	4	no	—
221	C₂²×C₈	C₂×C₄×C₃₁	1	8	yes	—
222	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
223	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
224	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
225	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
226	C₄×D₄	C₂×C₄×C₃₁	1	8	yes	—
227	#117	—	2	4	no	—
228	#117	—	2	4	no	—
229	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	4	yes	—
230	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	2	yes	—
231	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	1	yes	characteristic
232	C₂×C₂²⋊C₄	C₂×C₄×C₃₁	1	4	yes	—
233	C₂×C₂²⋊C₄	C₂×C₄×C₃₁	1	4	yes	—
234	C₂×C₂²⋊C₄	C₂×C₄×C₃₁	1	2	yes	—
235	C₂×C₄²	C₂×C₄×C₃₁	1	2	yes	—
236	C₂×C₄²	C₂×C₄×C₃₁	1	2	yes	—
237	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
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	8	yes	—
242	C₂²⋊C₈	C₂×C₄×C₃₁	1	8	yes	—
243	C₂²⋊C₈	C₂×C₄×C₃₁	1	8	yes	—
244	#97	—	2	4	no	—
245	#97	—	2	2	no	—
246	#97	C₂×C₄×C₃₁	1	8	yes	—
247	#97	D₄×C₃₁	1	4	yes	complemented
248	C₄×C₈	—	2	4	no	—
249	C₄×C₈	—	2	4	no	—
250	C₄×C₈	—	2	4	no	—
251	#95	C₂×C₄×C₃₁	1	4	yes	—
252	#95	C₂×C₄×C₃₁	1	2	yes	—
253	C₃₁	#20492	1	1	yes	characteristic, direct product factor, Sylow
254	C₂⁴	C₂²×C₄×C₃₁	1	2	yes	—
255	C₂×D₄	—	4	2	no	—
256	C₂×D₄	C₄²×C₃₁	1	4	yes	—
257	C₂²×C₄	—	2	2	no	—
258	C₂²×C₄	—	2	2	no	—
259	C₂²×C₄	—	2	2	no	—
260	C₂²×C₄	—	2	2	no	—
261	C₂²×C₄	C₂²×C₄×C₃₁	1	4	yes	—
262	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
263	C₂²×C₄	C₂²×C₄×C₃₁	1	2	yes	—
264	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
265	C₂²×C₄	C₂²×C₄×C₃₁	1	4	yes	—
266	C₂²×C₄	C₂²×C₄×C₃₁	1	4	yes	—
267	C₂²×C₄	C₂²×C₄×C₃₁	1	2	yes	—
268	C₂²×C₄	C₂²×C₄×C₃₁	1	2	yes	—
269	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
270	M₁₆	—	2	16	no	—
271	C₂×C₈	—	2	2	no	—
272	C₂×C₈	—	2	2	no	—
273	C₂×C₈	—	2	2	no	—
274	C₂×C₈	—	2	2	no	—
275	C₂×C₈	—	2	2	no	—
276	C₂×C₈	—	2	2	no	—
277	C₂×C₈	—	2	16	no	—
278	C₂×C₈	C₂²×C₄×C₃₁	1	4	yes	—
279	C₂×C₈	C₂²×C₄×C₃₁	1	4	yes	—
280	C₂×C₈	C₂²×C₄×C₃₁	1	4	yes	—
281	C₂×C₈	C₂²×C₄×C₃₁	1	4	yes	—
282	C₂×C₈	C₂×D₄×C₃₁	1	4	yes	—
283	C₂×C₈	#41×C₃₁	1	4	yes	—
284	C₄⋊C₄	—	2	8	no	—
285	C₄⋊C₄	—	4	2	no	—
286	C₄⋊C₄	C₄²×C₃₁	1	4	yes	—
287	C₂²⋊C₄	—	2	8	no	—
288	C₂²⋊C₄	—	2	8	no	—
289	C₂²⋊C₄	C₄²×C₃₁	1	8	yes	—
290	C₄²	—	2	4	no	—
291	C₄²	—	2	2	no	—
292	C₄²	—	2	2	no	—
293	C₄²	—	2	2	no	—
294	C₄²	—	4	2	no	—
295	C₄²	C₂²×C₄×C₃₁	1	4	yes	—
296	C₄²	C₂×D₄×C₃₁	1	2	yes	—
297	C₄²	#41×C₃₁	1	2	yes	—
298	C₂³	—	2	2	no	—
299	C₂³	—	2	2	no	—
300	C₂³	—	2	4	no	—
301	C₂³	—	2	4	no	—
302	C₂³	C₂×C₄²×C₃₁	1	4	yes	—
303	C₂³	C₂³×C₄×C₃₁	1	1	yes	characteristic
304	D₄	—	4	4	no	—
305	C₂×C₄	—	2	2	no	—
306	C₂×C₄	—	2	2	no	—
307	C₂×C₄	—	2	2	no	—
308	C₂×C₄	—	2	2	no	—
309	C₂×C₄	—	2	2	no	—
310	C₂×C₄	—	2	2	no	—
311	C₂×C₄	—	2	2	no	—
312	C₂×C₄	—	2	2	no	—
313	C₂×C₄	—	2	4	no	—
314	C₂×C₄	—	2	4	no	—
315	C₂×C₄	—	2	4	no	—
316	C₂×C₄	—	2	4	no	—
317	C₂×C₄	—	2	4	no	—
318	C₂×C₄	—	2	4	no	—
319	C₂×C₄	—	2	4	no	—
320	C₂×C₄	C₂×C₄²×C₃₁	1	2	yes	—
321	C₂×C₄	C₂×C₄²×C₃₁	1	2	yes	—
322	C₂×C₄	C₂×C₄²×C₃₁	1	4	yes	—
323	C₂×C₄	C₄×D₄×C₃₁	1	4	yes	—
324	C₂×C₄	C₃₁×#131	1	4	yes	—
325	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
326	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
327	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
328	C₂×C₄	C₂×#41×C₃₁	1	1	yes	characteristic
329	C₈	—	2	4	no	—
330	C₈	—	2	4	no	—
331	C₈	—	2	4	no	—
332	C₈	C₄×D₄×C₃₁	1	8	yes	—
333	C₂²	—	2	4	no	—
334	C₂²	—	2	4	no	—
335	C₂²	—	2	4	no	—
336	C₂²	—	4	4	no	—
337	C₂²	—	4	4	no	—
338	C₂²	C₂²×C₄²×C₃₁	1	1	yes	characteristic
339	C₂²	C₂×C₄×D₄×C₃₁	1	1	yes	characteristic
340	C₂²	C₄×#41×C₃₁	1	1	yes	characteristic
341	C₂²	C₂×C₃₁×#131	1	2	yes	—
342	C₂²	C₃₁×#568	1	2	yes	—
343	C₄	—	2	2	no	—
344	C₄	—	2	2	no	—
345	C₄	—	2	4	no	—
346	C₄	—	2	4	no	—
347	C₄	—	2	4	no	—
348	C₄	—	4	4	no	—
349	C₄	C₂×C₄×D₄×C₃₁	1	2	yes	—
350	C₄	C₄×#41×C₃₁	1	2	yes	—
351	C₂	—	4	4	no	—
352	C₂	C₄²×D₄×C₃₁	1	1	yes	characteristic
353	C₂	C₃₁×#2873	1	1	yes	characteristic
354	C₂	C₄×C₃₁×#131	1	1	yes	characteristic
355	C₂	C₃₁×#2935	1	2	yes	—
356	C₂	C₃₁×#2968	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	C₂²×D₄×C₃₁	C₂×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
2. C₂×C₃₁×#405	C₂	semidirect
4. C₃₁×#1771	C₂	semidirect
5. C₄×C₃₁×C₄⋊C₈	C₂	semidirect
6. C₃₁×#1753	C₂	semidirect
7. C₈×C₂²⋊C₄×C₃₁	C₂	semidirect
8. C₃₁×#1750	C₂	semidirect
9. C₄×C₃₁×#97	C₂	semidirect
14. C₃₁×#435	C₄	semidirect
69. C₃₁×#97	D₄	semidirect
119. #20492	C₃₁	direct (N × H)
156. C₂×#405	C₂×C₃₁	semidirect
158. #1771	C₂×C₃₁	semidirect
159. C₄×C₄⋊C₈	C₂×C₃₁	semidirect
160. #1753	C₂×C₃₁	semidirect
161. C₈×C₂²⋊C₄	C₂×C₃₁	semidirect
162. #1750	C₂×C₃₁	semidirect
163. C₄×#97	C₂×C₃₁	semidirect
186. #435	C₄×C₃₁	semidirect
247. #97	D₄×C₃₁	semidirect
253. C₃₁	#20492	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×#435	2
C₂×C₃₁×#405	2
C₃₁×#2293	2
C₃₁×#1771	2
C₄×C₃₁×C₄⋊C₈	2
C₃₁×#1753	2
C₈×C₂²⋊C₄×C₃₁	2
C₃₁×#1750	2
C₄×C₃₁×#97	2
#20492	31

Subgroups — C31×#20492 #21477251

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#20492 #21477251