Subgroups — C₃₁×#18075 #21474834

Order 7936.

592 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3168	C₂	1	1	yes	maximal, characteristic
2	C₃₁×#2969	C₂	1	2	yes	maximal, complemented
3	C₃₁×#1594	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#1593	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#1588	C₂	1	2	yes	maximal, complemented
6	C₃₁×#1585	C₂	1	2	yes	maximal, complemented
7	C₃₁×#1580	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#1579	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#1564	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#1482	C₂	1	2	yes	maximal, complemented
11	C₃₁×#1451	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#529	C₂²	1	2	yes	—
13	C₃₁×#499	C₄	1	1	yes	characteristic
14	C₃₁×#495	C₄	1	1	yes	characteristic
15	C₃₁×#488	C₄	1	2	yes	—
16	C₃₁×#467	C₄	1	1	yes	characteristic
17	C₃₁×#466	C₄	1	1	yes	characteristic
18	C₃₁×#465	C₄	1	2	yes	—
19	C₃₁×#446	C₂²	1	2	yes	—
20	C₈×Q₈×C₃₁	C₂²	1	2	yes	—
21	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
22	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	—
23	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic
24	C₃₁×#436	—	2	2	no	—
25	C₃₁×#436	C₂²	1	2	yes	—
26	C₃₁×#435	—	2	2	no	—
27	C₈×D₄×C₃₁	C₂²	1	2	yes	—
28	C₃₁×#433	—	2	2	no	—
29	C₃₁×#431	C₂²	1	2	yes	—
30	C₃₁×#431	C₂²	1	1	yes	characteristic
31	C₃₁×#405	—	2	2	no	—
32	C₄×M₁₆×C₃₁	C₂²	1	1	yes	characteristic
33	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
34	C₃₁×#335	C₂²	1	2	yes	—
35	C₃₁×#334	C₂²	1	1	yes	characteristic
36	C₃₁×#334	C₂²	1	1	yes	characteristic
37	C₃₁×Q₈⋊C₈	C₂²	1	2	yes	—
38	C₃₁×Q₈⋊C₈	C₂²	1	2	yes	—
39	C₃₁×D₄⋊C₈	C₂²	1	2	yes	—
40	C₃₁×D₄⋊C₈	C₂²	1	2	yes	—
41	C₃₁×#322	C₂²	1	1	yes	characteristic
42	C₃₁×#322	C₂²	1	1	yes	characteristic
43	C₃₁×#322	C₂²	1	1	yes	characteristic
44	C₃₁×#322	C₂²	1	1	yes	characteristic
45	C₂×Q₁₆×C₃₁	C₂×C₄	1	1	yes	characteristic
46	C₂×SD₁₆×C₃₁	C₂×C₄	1	2	yes	—
47	C₂×D₈×C₃₁	C₂×C₄	1	1	yes	characteristic
48	C₂×M₁₆×C₃₁	—	2	2	no	—
49	C₂×M₁₆×C₃₁	D₄	1	2	yes	—
50	C₂²×C₈×C₃₁	—	2	2	no	—
51	C₂²×C₈×C₃₁	C₂×C₄	1	1	yes	characteristic
52	C₂²×C₈×C₃₁	C₂×C₄	1	1	yes	characteristic
53	C₃₁×#126	—	2	2	no	—
54	C₃₁×#125	C₂×C₄	1	2	yes	—
55	C₃₁×#124	C₂×C₄	1	2	yes	—
56	C₃₁×#123	—	2	2	no	—
57	C₃₁×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
58	C₃₁×#121	C₂×C₄	1	2	yes	—
59	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
60	C₄×D₄×C₃₁	—	2	2	no	—
61	C₄×D₄×C₃₁	C₂³	1	2	yes	—
62	C₃₁×#117	—	2	2	no	—
63	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
64	C₃₁×#107	C₂×C₄	1	1	yes	characteristic
65	C₃₁×#107	C₂×C₄	1	1	yes	characteristic
66	C₃₁×#106	C₂×C₄	1	2	yes	—
67	C₃₁×C₄⋊C₈	—	2	2	no	—
68	C₃₁×C₄⋊C₈	—	2	2	no	—
69	C₃₁×C₄⋊C₈	—	2	1	no	—
70	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
71	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
72	C₃₁×#103	C₂×C₄	1	2	yes	—
73	C₃₁×#103	C₂×C₄	1	2	yes	—
74	C₃₁×#102	C₂×C₄	1	2	yes	—
75	C₃₁×#102	C₂×C₄	1	2	yes	—
76	C₃₁×C₂²⋊C₈	—	2	2	no	—
77	C₃₁×C₂²⋊C₈	—	2	1	no	—
78	C₃₁×C₂²⋊C₈	—	2	2	no	—
79	C₃₁×C₂²⋊C₈	—	2	2	no	—
80	C₃₁×#97	—	2	2	no	—
81	C₃₁×#97	D₄	1	2	yes	—
82	C₄×C₈×C₃₁	—	2	2	no	—
83	C₄×C₈×C₃₁	—	2	2	no	—
84	C₄×C₈×C₃₁	C₂×C₄	1	1	yes	characteristic
85	C₄×C₈×C₃₁	C₂×C₄	1	1	yes	characteristic
86	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
87	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
88	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
89	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
90	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
91	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
92	C₂×Q₈×C₃₁	C₂²×C₄	1	2	yes	—
93	C₂×D₄×C₃₁	—	2	2	no	—
94	C₂×D₄×C₃₁	C₂²×C₄	1	2	yes	—
95	C₂²×C₄×C₃₁	—	2	2	no	—
96	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
97	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₃₁	#41	1	1	yes	characteristic
99	Q₁₆×C₃₁	—	2	2	no	—
100	SD₁₆×C₃₁	—	4	2	no	—
101	D₈×C₃₁	—	2	2	no	—
102	M₁₆×C₃₁	—	4	2	no	—
103	M₁₆×C₃₁	—	4	4	no	—
104	C₂×C₈×C₃₁	—	2	2	no	—
105	C₂×C₈×C₃₁	—	2	2	no	—
106	C₂×C₈×C₃₁	—	2	2	no	—
107	C₂×C₈×C₃₁	—	2	1	no	—
108	C₂×C₈×C₃₁	—	2	1	no	—
109	C₂×C₈×C₃₁	—	4	1	no	—
110	C₂×C₈×C₃₁	—	4	4	no	—
111	C₂×C₈×C₃₁	C₂²×C₄	1	1	yes	characteristic
112	C₂×C₈×C₃₁	C₂²×C₄	1	1	yes	characteristic
113	C₂×C₈×C₃₁	C₂²×C₄	1	1	yes	characteristic
114	C₂×C₈×C₃₁	C₂²×C₄	1	1	yes	characteristic
115	C₂×C₈×C₃₁	C₂×D₄	1	2	yes	—
116	C₂×C₈×C₃₁	C₂×D₄	1	2	yes	—
117	C₄⋊C₄×C₃₁	—	2	2	no	—
118	C₄⋊C₄×C₃₁	—	2	2	no	—
119	C₄⋊C₄×C₃₁	—	2	2	no	—
120	C₄⋊C₄×C₃₁	—	2	2	no	—
121	C₄⋊C₄×C₃₁	C₂²×C₄	1	2	yes	—
122	C₄⋊C₄×C₃₁	C₂²×C₄	1	2	yes	—
123	C₂²⋊C₄×C₃₁	—	2	2	no	—
124	C₂²⋊C₄×C₃₁	—	2	2	no	—
125	C₂²⋊C₄×C₃₁	—	2	2	no	—
126	C₂²⋊C₄×C₃₁	—	2	2	no	—
127	C₂²⋊C₄×C₃₁	—	2	2	no	—
128	C₄²×C₃₁	—	2	2	no	—
129	C₄²×C₃₁	C₂²×C₄	1	1	yes	characteristic
130	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
131	C₄²×C₃₁	#41	1	1	yes	characteristic
132	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
133	#18075	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
134	C₂³×C₃₁	—	2	2	no	—
135	C₂³×C₃₁	C₄×D₄	1	1	yes	characteristic
136	Q₈×C₃₁	—	2	2	no	—
137	Q₈×C₃₁	—	2	2	no	—
138	D₄×C₃₁	—	2	2	no	—
139	D₄×C₃₁	—	2	2	no	—
140	D₄×C₃₁	—	8	2	no	—
141	C₂×C₄×C₃₁	—	2	1	no	—
142	C₂×C₄×C₃₁	—	2	1	no	—
143	C₂×C₄×C₃₁	—	2	2	no	—
144	C₂×C₄×C₃₁	—	2	2	no	—
145	C₂×C₄×C₃₁	—	2	2	no	—
146	C₂×C₄×C₃₁	—	2	2	no	—
147	C₂×C₄×C₃₁	—	4	1	no	—
148	C₂×C₄×C₃₁	—	4	2	no	—
149	C₂×C₄×C₃₁	—	4	2	no	—
150	C₂×C₄×C₃₁	C₄×D₄	1	1	yes	characteristic
151	C₂×C₄×C₃₁	C₄×D₄	1	1	yes	characteristic
152	C₂×C₄×C₃₁	C₄×D₄	1	1	yes	characteristic
153	C₂×C₄×C₃₁	C₂³×C₄	1	1	yes	characteristic
154	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
155	C₂×C₄×C₃₁	C₂×#41	1	1	yes	characteristic
156	C₈×C₃₁	—	2	1	no	—
157	C₈×C₃₁	—	2	1	no	—
158	C₈×C₃₁	—	2	1	no	—
159	C₈×C₃₁	—	2	2	no	—
160	C₈×C₃₁	—	2	2	no	—
161	C₈×C₃₁	—	4	1	no	—
162	C₈×C₃₁	—	4	1	no	—
163	C₈×C₃₁	—	4	2	no	—
164	C₈×C₃₁	—	4	2	no	—
165	C₈×C₃₁	#131	1	2	yes	—
166	#3168	C₂×C₃₁	1	1	yes	characteristic
167	#2969	C₂×C₃₁	1	2	yes	complemented
168	#1594	C₂×C₃₁	1	1	yes	characteristic, complemented
169	#1593	C₂×C₃₁	1	1	yes	characteristic, complemented
170	#1588	C₂×C₃₁	1	2	yes	complemented
171	#1585	C₂×C₃₁	1	2	yes	complemented
172	#1580	C₂×C₃₁	1	1	yes	characteristic, complemented
173	#1579	C₂×C₃₁	1	1	yes	characteristic, complemented
174	#1564	C₂×C₃₁	1	1	yes	characteristic, complemented
175	#1482	C₂×C₃₁	1	2	yes	complemented
176	#1451	C₂×C₃₁	1	1	yes	characteristic, complemented
177	C₂²×C₃₁	—	2	1	no	—
178	C₂²×C₃₁	—	2	1	no	—
179	C₂²×C₃₁	—	2	1	no	—
180	C₂²×C₃₁	—	4	2	no	—
181	C₂²×C₃₁	—	4	2	no	—
182	C₂²×C₃₁	—	4	2	no	—
183	C₂²×C₃₁	C₂×C₄×D₄	1	1	yes	characteristic
184	C₄×C₃₁	—	2	1	no	—
185	C₄×C₃₁	—	2	1	no	—
186	C₄×C₃₁	—	2	1	no	—
187	C₄×C₃₁	—	2	1	no	—
188	C₄×C₃₁	—	4	2	no	—
189	C₄×C₃₁	—	4	2	no	—
190	C₄×C₃₁	—	4	2	no	—
191	C₄×C₃₁	C₂×#131	1	1	yes	characteristic
192	C₄×C₃₁	#568	1	1	yes	characteristic
193	C₄×C₃₁	#575	1	2	yes	—
194	#529	C₂²×C₃₁	1	2	yes	—
195	#499	C₄×C₃₁	1	1	yes	characteristic
196	#495	C₄×C₃₁	1	1	yes	characteristic
197	#488	C₄×C₃₁	1	2	yes	—
198	#467	C₄×C₃₁	1	1	yes	characteristic
199	#466	C₄×C₃₁	1	1	yes	characteristic
200	#465	C₄×C₃₁	1	2	yes	—
201	#446	C₂²×C₃₁	1	2	yes	—
202	C₈×Q₈	C₂²×C₃₁	1	2	yes	—
203	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
204	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	—
205	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic
206	#436	—	2	2	no	—
207	#436	C₂²×C₃₁	1	2	yes	—
208	#435	—	2	2	no	—
209	C₈×D₄	C₂²×C₃₁	1	2	yes	—
210	#433	—	2	2	no	—
211	#431	C₂²×C₃₁	1	2	yes	—
212	#431	C₂²×C₃₁	1	1	yes	characteristic
213	#405	—	2	2	no	—
214	C₄×M₁₆	C₂²×C₃₁	1	1	yes	characteristic
215	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
216	#335	C₂²×C₃₁	1	2	yes	—
217	#334	C₂²×C₃₁	1	1	yes	characteristic
218	#334	C₂²×C₃₁	1	1	yes	characteristic
219	Q₈⋊C₈	C₂²×C₃₁	1	2	yes	—
220	Q₈⋊C₈	C₂²×C₃₁	1	2	yes	—
221	D₄⋊C₈	C₂²×C₃₁	1	2	yes	—
222	D₄⋊C₈	C₂²×C₃₁	1	2	yes	—
223	#322	C₂²×C₃₁	1	1	yes	characteristic
224	#322	C₂²×C₃₁	1	1	yes	characteristic
225	#322	C₂²×C₃₁	1	1	yes	characteristic
226	#322	C₂²×C₃₁	1	1	yes	characteristic
227	C₂×C₃₁	—	4	1	no	—
228	C₂×C₃₁	—	8	2	no	—
229	C₂×C₃₁	#2935	1	1	yes	characteristic
230	C₂×C₃₁	#2943	1	1	yes	characteristic
231	C₂×C₃₁	#2957	1	1	yes	characteristic
232	C₂×Q₁₆	C₂×C₄×C₃₁	1	1	yes	characteristic
233	C₂×SD₁₆	C₂×C₄×C₃₁	1	2	yes	—
234	C₂×D₈	C₂×C₄×C₃₁	1	1	yes	characteristic
235	C₂×M₁₆	—	2	2	no	—
236	C₂×M₁₆	D₄×C₃₁	1	2	yes	—
237	C₂²×C₈	—	2	2	no	—
238	C₂²×C₈	C₂×C₄×C₃₁	1	1	yes	characteristic
239	C₂²×C₈	C₂×C₄×C₃₁	1	1	yes	characteristic
240	#126	—	2	2	no	—
241	#125	C₂×C₄×C₃₁	1	2	yes	—
242	#124	C₂×C₄×C₃₁	1	2	yes	—
243	#123	—	2	2	no	—
244	C₂²⋊Q₈	C₂×C₄×C₃₁	1	2	yes	—
245	#121	C₂×C₄×C₃₁	1	2	yes	—
246	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
247	C₄×D₄	—	2	2	no	—
248	C₄×D₄	C₂³×C₃₁	1	2	yes	—
249	#117	—	2	2	no	—
250	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
251	#107	C₂×C₄×C₃₁	1	1	yes	characteristic
252	#107	C₂×C₄×C₃₁	1	1	yes	characteristic
253	#106	C₂×C₄×C₃₁	1	2	yes	—
254	C₄⋊C₈	—	2	2	no	—
255	C₄⋊C₈	—	2	2	no	—
256	C₄⋊C₈	—	2	1	no	—
257	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
258	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
259	#103	C₂×C₄×C₃₁	1	2	yes	—
260	#103	C₂×C₄×C₃₁	1	2	yes	—
261	#102	C₂×C₄×C₃₁	1	2	yes	—
262	#102	C₂×C₄×C₃₁	1	2	yes	—
263	C₂²⋊C₈	—	2	2	no	—
264	C₂²⋊C₈	—	2	1	no	—
265	C₂²⋊C₈	—	2	2	no	—
266	C₂²⋊C₈	—	2	2	no	—
267	#97	—	2	2	no	—
268	#97	D₄×C₃₁	1	2	yes	—
269	C₄×C₈	—	2	2	no	—
270	C₄×C₈	—	2	2	no	—
271	C₄×C₈	C₂×C₄×C₃₁	1	1	yes	characteristic
272	C₄×C₈	C₂×C₄×C₃₁	1	1	yes	characteristic
273	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
274	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
275	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
276	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
277	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
278	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
279	C₃₁	#18075	1	1	yes	characteristic, direct product factor, Sylow
280	C₂×Q₈	C₂²×C₄×C₃₁	1	2	yes	—
281	C₂×D₄	—	2	2	no	—
282	C₂×D₄	C₂²×C₄×C₃₁	1	2	yes	—
283	C₂²×C₄	—	2	2	no	—
284	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
285	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
286	C₂²×C₄	#41×C₃₁	1	1	yes	characteristic
287	Q₁₆	—	2	2	no	—
288	SD₁₆	—	4	2	no	—
289	D₈	—	2	2	no	—
290	M₁₆	—	4	2	no	—
291	M₁₆	—	4	4	no	—
292	C₂×C₈	—	2	2	no	—
293	C₂×C₈	—	2	2	no	—
294	C₂×C₈	—	2	2	no	—
295	C₂×C₈	—	2	1	no	—
296	C₂×C₈	—	2	1	no	—
297	C₂×C₈	—	4	1	no	—
298	C₂×C₈	—	4	4	no	—
299	C₂×C₈	C₂²×C₄×C₃₁	1	1	yes	characteristic
300	C₂×C₈	C₂²×C₄×C₃₁	1	1	yes	characteristic
301	C₂×C₈	C₂²×C₄×C₃₁	1	1	yes	characteristic
302	C₂×C₈	C₂²×C₄×C₃₁	1	1	yes	characteristic
303	C₂×C₈	C₂×D₄×C₃₁	1	2	yes	—
304	C₂×C₈	C₂×D₄×C₃₁	1	2	yes	—
305	C₄⋊C₄	—	2	2	no	—
306	C₄⋊C₄	—	2	2	no	—
307	C₄⋊C₄	—	2	2	no	—
308	C₄⋊C₄	—	2	2	no	—
309	C₄⋊C₄	C₂²×C₄×C₃₁	1	2	yes	—
310	C₄⋊C₄	C₂²×C₄×C₃₁	1	2	yes	—
311	C₂²⋊C₄	—	2	2	no	—
312	C₂²⋊C₄	—	2	2	no	—
313	C₂²⋊C₄	—	2	2	no	—
314	C₂²⋊C₄	—	2	2	no	—
315	C₂²⋊C₄	—	2	2	no	—
316	C₄²	—	2	2	no	—
317	C₄²	C₂²×C₄×C₃₁	1	1	yes	characteristic
318	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
319	C₄²	#41×C₃₁	1	1	yes	characteristic
320	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
321	C₂³	—	2	2	no	—
322	C₂³	C₄×D₄×C₃₁	1	1	yes	characteristic
323	Q₈	—	2	2	no	—
324	Q₈	—	2	2	no	—
325	D₄	—	2	2	no	—
326	D₄	—	2	2	no	—
327	D₄	—	8	2	no	—
328	C₂×C₄	—	2	1	no	—
329	C₂×C₄	—	2	1	no	—
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	2	2	no	—
333	C₂×C₄	—	2	2	no	—
334	C₂×C₄	—	4	1	no	—
335	C₂×C₄	—	4	2	no	—
336	C₂×C₄	—	4	2	no	—
337	C₂×C₄	C₄×D₄×C₃₁	1	1	yes	characteristic
338	C₂×C₄	C₄×D₄×C₃₁	1	1	yes	characteristic
339	C₂×C₄	C₄×D₄×C₃₁	1	1	yes	characteristic
340	C₂×C₄	C₂³×C₄×C₃₁	1	1	yes	characteristic
341	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
342	C₂×C₄	C₂×#41×C₃₁	1	1	yes	characteristic
343	C₈	—	2	1	no	—
344	C₈	—	2	1	no	—
345	C₈	—	2	1	no	—
346	C₈	—	2	2	no	—
347	C₈	—	2	2	no	—
348	C₈	—	4	1	no	—
349	C₈	—	4	1	no	—
350	C₈	—	4	2	no	—
351	C₈	—	4	2	no	—
352	C₈	C₃₁×#131	1	2	yes	—
353	C₂²	—	2	1	no	—
354	C₂²	—	2	1	no	—
355	C₂²	—	2	1	no	—
356	C₂²	—	4	2	no	—
357	C₂²	—	4	2	no	—
358	C₂²	—	4	2	no	—
359	C₂²	C₂×C₄×D₄×C₃₁	1	1	yes	characteristic
360	C₄	—	2	1	no	—
361	C₄	—	2	1	no	—
362	C₄	—	2	1	no	—
363	C₄	—	2	1	no	—
364	C₄	—	4	2	no	—
365	C₄	—	4	2	no	—
366	C₄	—	4	2	no	—
367	C₄	C₂×C₃₁×#131	1	1	yes	characteristic
368	C₄	C₃₁×#568	1	1	yes	characteristic
369	C₄	C₃₁×#575	1	2	yes	—
370	C₂	—	4	1	no	—
371	C₂	—	8	2	no	—
372	C₂	C₃₁×#2935	1	1	yes	characteristic
373	C₂	C₃₁×#2943	1	1	yes	characteristic
374	C₂	C₃₁×#2957	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₃₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₃₁
Frattini, cosocle	C₄²	C₂⁴×C₃₁
socle	C₂²×C₃₁	C₂×C₄×D₄
prime radical	C₃₁×#466	C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₃₁ ◁ C₄×M₁₆×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃₁×#2969	C₂	semidirect
3. C₃₁×#1594	C₂	semidirect
4. C₃₁×#1593	C₂	semidirect
5. C₃₁×#1588	C₂	semidirect
6. C₃₁×#1585	C₂	semidirect
7. C₃₁×#1580	C₂	semidirect
8. C₃₁×#1579	C₂	semidirect
9. C₃₁×#1564	C₂	semidirect
10. C₃₁×#1482	C₂	semidirect
11. C₃₁×#1451	C₂	semidirect
133. #18075	C₃₁	direct (N × H)
167. #2969	C₂×C₃₁	semidirect
168. #1594	C₂×C₃₁	semidirect
169. #1593	C₂×C₃₁	semidirect
170. #1588	C₂×C₃₁	semidirect
171. #1585	C₂×C₃₁	semidirect
172. #1580	C₂×C₃₁	semidirect
173. #1579	C₂×C₃₁	semidirect
174. #1564	C₂×C₃₁	semidirect
175. #1482	C₂×C₃₁	semidirect
176. #1451	C₂×C₃₁	semidirect
279. C₃₁	#18075	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×#3168	2
C₃₁×#2969	2
C₃₁×#1594	2
C₃₁×#1593	2
C₃₁×#1588	2
C₃₁×#1585	2
C₃₁×#1580	2
C₃₁×#1579	2
C₃₁×#1564	2
C₃₁×#1482	2
C₃₁×#1451	2
#18075	31

Subgroups — C31×#18075 #21474834

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#18075 #21474834