Subgroups — C₃₁×#21022 #21477781

Order 7936.

906 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#424	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×M₁₆×C₃₁	C₂	1	1	yes	maximal, characteristic
3	C₃₁×#2296	C₂	1	1	yes	maximal, characteristic
4	C₃₁×#1917	C₂	1	4	yes	maximal, complemented
5	C₃₁×#1916	C₂	1	4	yes	maximal, complemented
6	C₃₁×#1729	C₂	1	1	yes	maximal, characteristic
7	C₃₁×#1729	C₂	1	1	yes	maximal, characteristic
8	C₃₁×#1729	C₂	1	1	yes	maximal, characteristic
9	C₂×C₃₁×#336	C₂	1	1	yes	maximal, characteristic
10	C₂²×M₁₆×C₃₁	C₂²	1	1	yes	characteristic
11	C₂²×M₁₆×C₃₁	C₂²	1	1	yes	characteristic
12	C₂³×C₈×C₃₁	C₂²	1	1	yes	characteristic
13	C₂³×C₈×C₃₁	C₂²	1	1	yes	characteristic
14	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
15	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
16	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
17	C₃₁×#424	—	2	4	no	—
18	C₂×C₃₁×C₄⋊C₈	C₂²	1	4	yes	—
19	C₄×M₁₆×C₃₁	—	2	4	no	—
20	C₂×C₃₁×#97	C₂²	1	2	yes	—
21	C₂×C₄×C₈×C₃₁	C₂²	1	2	yes	—
22	C₃₁×#389	C₄	1	2	yes	—
23	C₃₁×#389	C₄	1	2	yes	—
24	C₃₁×#385	C₄	1	4	yes	—
25	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
26	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
27	C₃₁×#336	C₂²	1	2	yes	—
28	C₃₁×#336	C₂²	1	4	yes	—
29	C₃₁×#336	C₂²	1	4	yes	—
30	C₃₁×#336	C₂²	1	4	yes	—
31	C₃₁×#336	C₂²	1	2	yes	—
32	C₂³×C₄×C₃₁	C₂×C₄	1	2	yes	—
33	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
34	C₂×M₁₆×C₃₁	—	2	2	no	—
35	C₂×M₁₆×C₃₁	—	2	2	no	—
36	C₂×M₁₆×C₃₁	—	2	2	no	—
37	C₂×M₁₆×C₃₁	—	2	2	no	—
38	C₂×M₁₆×C₃₁	D₄	1	4	yes	—
39	C₂×M₁₆×C₃₁	Q₈	1	4	yes	—
40	C₂²×C₈×C₃₁	—	2	2	no	—
41	C₂²×C₈×C₃₁	—	2	2	no	—
42	C₂²×C₈×C₃₁	—	2	2	no	—
43	C₂²×C₈×C₃₁	—	2	2	no	—
44	C₂²×C₈×C₃₁	—	2	2	no	—
45	C₂²×C₈×C₃₁	—	2	2	no	—
46	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
47	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
48	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
49	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
50	C₃₁×#117	—	2	2	no	—
51	C₃₁×#117	—	2	2	no	—
52	C₃₁×#117	—	2	2	no	—
53	C₃₁×#117	—	2	2	no	—
54	C₂×C₄⋊C₄×C₃₁	C₂×C₄	1	1	yes	characteristic
55	C₂×C₄⋊C₄×C₃₁	C₂×C₄	1	1	yes	characteristic
56	C₂×C₄⋊C₄×C₃₁	C₂×C₄	1	2	yes	—
57	C₂×C₄⋊C₄×C₃₁	C₂×C₄	1	4	yes	—
58	C₂×C₄⋊C₄×C₃₁	C₂×C₄	1	4	yes	—
59	C₂×C₂²⋊C₄×C₃₁	C₂×C₄	1	2	yes	—
60	C₂×C₂²⋊C₄×C₃₁	C₂×C₄	1	2	yes	—
61	C₂×C₄²×C₃₁	—	2	2	no	—
62	C₂×C₄²×C₃₁	—	2	2	no	—
63	C₂×C₄²×C₃₁	C₂×C₄	1	2	yes	—
64	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
65	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
66	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
67	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
68	C₃₁×C₄⋊C₈	—	2	8	no	—
69	C₃₁×#97	—	2	4	no	—
70	C₄×C₈×C₃₁	—	2	4	no	—
71	C₃₁×#95	C₂×C₄	1	4	yes	—
72	C₃₁×#95	C₂×C₄	1	4	yes	—
73	C₂⁴×C₃₁	C₂²×C₄	1	1	yes	characteristic
74	C₂²×C₄×C₃₁	—	2	4	no	—
75	C₂²×C₄×C₃₁	—	2	4	no	—
76	C₂²×C₄×C₃₁	—	4	2	no	—
77	C₂²×C₄×C₃₁	C₂²×C₄	1	2	yes	—
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	2	yes	—
82	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
83	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
84	C₂²×C₄×C₃₁	C₂×Q₈	1	2	yes	—
85	C₂²×C₄×C₃₁	#41	1	2	yes	—
86	C₂²×C₄×C₃₁	#41	1	2	yes	—
87	C₂²×C₄×C₃₁	#41	1	2	yes	—
88	C₂²×C₄×C₃₁	#41	1	2	yes	—
89	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
90	M₁₆×C₃₁	—	2	8	no	—
91	M₁₆×C₃₁	—	2	8	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	2	no	—
99	C₂×C₈×C₃₁	—	2	2	no	—
100	C₂×C₈×C₃₁	—	2	2	no	—
101	C₂×C₈×C₃₁	—	2	2	no	—
102	C₂×C₈×C₃₁	—	4	4	no	—
103	C₂×C₈×C₃₁	—	4	4	no	—
104	C₂×C₈×C₃₁	C₂×D₄	1	4	yes	—
105	C₂×C₈×C₃₁	C₂×Q₈	1	4	yes	—
106	C₄⋊C₄×C₃₁	—	2	2	no	—
107	C₄⋊C₄×C₃₁	—	2	2	no	—
108	C₄⋊C₄×C₃₁	—	2	4	no	—
109	C₄⋊C₄×C₃₁	—	2	8	no	—
110	C₄⋊C₄×C₃₁	—	4	4	no	—
111	C₂²⋊C₄×C₃₁	—	2	4	no	—
112	C₂²⋊C₄×C₃₁	—	2	4	no	—
113	C₄²×C₃₁	—	2	4	no	—
114	C₄²×C₃₁	—	2	1	no	—
115	C₄²×C₃₁	—	2	1	no	—
116	C₄²×C₃₁	—	2	2	no	—
117	C₄²×C₃₁	—	2	1	no	—
118	C₄²×C₃₁	—	2	1	no	—
119	C₄²×C₃₁	—	2	2	no	—
120	C₄²×C₃₁	—	2	2	no	—
121	C₄²×C₃₁	—	2	2	no	—
122	#21022	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
123	C₂³×C₃₁	—	2	2	no	—
124	C₂³×C₃₁	—	2	2	no	—
125	C₂³×C₃₁	#117	1	2	yes	—
126	C₂³×C₃₁	C₄×D₄	1	2	yes	—
127	C₂³×C₃₁	C₄×Q₈	1	2	yes	—
128	C₂³×C₃₁	C₂³×C₄	1	1	yes	characteristic
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	4	no	—
135	C₂×C₄×C₃₁	—	2	4	no	—
136	C₂×C₄×C₃₁	—	2	4	no	—
137	C₂×C₄×C₃₁	—	2	2	no	—
138	C₂×C₄×C₃₁	—	2	2	no	—
139	C₂×C₄×C₃₁	—	2	4	no	—
140	C₂×C₄×C₃₁	—	2	4	no	—
141	C₂×C₄×C₃₁	—	4	8	no	—
142	C₂×C₄×C₃₁	#117	1	2	yes	—
143	C₂×C₄×C₃₁	C₄×D₄	1	2	yes	—
144	C₂×C₄×C₃₁	C₄×Q₈	1	2	yes	—
145	C₂×C₄×C₃₁	C₂²⋊Q₈	1	4	yes	—
146	C₂×C₄×C₃₁	#123	1	4	yes	—
147	C₂×C₄×C₃₁	#125	1	4	yes	—
148	C₂×C₄×C₃₁	#126	1	4	yes	—
149	C₂×C₄×C₃₁	#131	1	4	yes	—
150	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
151	C₂×C₄×C₃₁	C₂²×Q₈	1	1	yes	characteristic
152	C₂×C₄×C₃₁	C₂×#41	1	1	yes	characteristic
153	C₂×C₄×C₃₁	C₂×#41	1	1	yes	characteristic
154	C₂×C₄×C₃₁	C₂×#41	1	1	yes	characteristic
155	C₂×C₄×C₃₁	C₂×#41	1	1	yes	characteristic
156	C₈×C₃₁	—	2	4	no	—
157	C₈×C₃₁	—	2	4	no	—
158	C₈×C₃₁	—	4	2	no	—
159	C₈×C₃₁	—	4	2	no	—
160	C₂×#424	C₂×C₃₁	1	1	yes	characteristic
161	C₂×C₄×M₁₆	C₂×C₃₁	1	1	yes	characteristic
162	#2296	C₂×C₃₁	1	1	yes	characteristic
163	#1917	C₂×C₃₁	1	4	yes	complemented
164	#1916	C₂×C₃₁	1	4	yes	complemented
165	#1729	C₂×C₃₁	1	1	yes	characteristic
166	#1729	C₂×C₃₁	1	1	yes	characteristic
167	#1729	C₂×C₃₁	1	1	yes	characteristic
168	C₂×#336	C₂×C₃₁	1	1	yes	characteristic
169	C₂²×C₃₁	—	2	2	no	—
170	C₂²×C₃₁	—	2	2	no	—
171	C₂²×C₃₁	—	2	4	no	—
172	C₂²×C₃₁	—	2	4	no	—
173	C₂²×C₃₁	#387	1	4	yes	—
174	C₂²×C₃₁	C₂×#117	1	1	yes	characteristic
175	C₂²×C₃₁	C₂×C₄×D₄	1	1	yes	characteristic
176	C₂²×C₃₁	C₂×C₄×Q₈	1	1	yes	characteristic
177	C₂²×C₃₁	C₂×#131	1	2	yes	—
178	C₂²×C₃₁	#568	1	2	yes	—
179	C₄×C₃₁	—	2	4	no	—
180	C₄×C₃₁	—	4	2	no	—
181	C₄×C₃₁	—	4	2	no	—
182	C₄×C₃₁	—	4	4	no	—
183	C₄×C₃₁	—	4	2	no	—
184	C₄×C₃₁	#387	1	4	yes	—
185	C₄×C₃₁	C₂×C₂²⋊Q₈	1	1	yes	characteristic
186	C₄×C₃₁	C₂×#123	1	1	yes	characteristic
187	C₄×C₃₁	C₂×#125	1	1	yes	characteristic
188	C₄×C₃₁	C₂×#126	1	1	yes	characteristic
189	C₂²×M₁₆	C₂²×C₃₁	1	1	yes	characteristic
190	C₂²×M₁₆	C₂²×C₃₁	1	1	yes	characteristic
191	C₂³×C₈	C₂²×C₃₁	1	1	yes	characteristic
192	C₂³×C₈	C₂²×C₃₁	1	1	yes	characteristic
193	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
194	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
195	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
196	#424	—	2	4	no	—
197	C₂×C₄⋊C₈	C₂²×C₃₁	1	4	yes	—
198	C₄×M₁₆	—	2	4	no	—
199	C₂×#97	C₂²×C₃₁	1	2	yes	—
200	C₂×C₄×C₈	C₂²×C₃₁	1	2	yes	—
201	#389	C₄×C₃₁	1	2	yes	—
202	#389	C₄×C₃₁	1	2	yes	—
203	#385	C₄×C₃₁	1	4	yes	—
204	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
205	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
206	#336	C₂²×C₃₁	1	2	yes	—
207	#336	C₂²×C₃₁	1	4	yes	—
208	#336	C₂²×C₃₁	1	4	yes	—
209	#336	C₂²×C₃₁	1	4	yes	—
210	#336	C₂²×C₃₁	1	2	yes	—
211	C₂×C₃₁	—	2	4	no	—
212	C₂×C₃₁	C₂×#387	1	1	yes	characteristic
213	C₂×C₃₁	#2922	1	1	yes	characteristic
214	C₂×C₃₁	#2923	1	1	yes	characteristic
215	C₂×C₃₁	#2933	1	2	yes	—
216	C₂×C₃₁	#2962	1	2	yes	—
217	C₂³×C₄	C₂×C₄×C₃₁	1	2	yes	—
218	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
219	C₂×M₁₆	—	2	2	no	—
220	C₂×M₁₆	—	2	2	no	—
221	C₂×M₁₆	—	2	2	no	—
222	C₂×M₁₆	—	2	2	no	—
223	C₂×M₁₆	D₄×C₃₁	1	4	yes	—
224	C₂×M₁₆	Q₈×C₃₁	1	4	yes	—
225	C₂²×C₈	—	2	2	no	—
226	C₂²×C₈	—	2	2	no	—
227	C₂²×C₈	—	2	2	no	—
228	C₂²×C₈	—	2	2	no	—
229	C₂²×C₈	—	2	2	no	—
230	C₂²×C₈	—	2	2	no	—
231	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
232	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
233	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
234	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
235	#117	—	2	2	no	—
236	#117	—	2	2	no	—
237	#117	—	2	2	no	—
238	#117	—	2	2	no	—
239	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	1	yes	characteristic
240	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	1	yes	characteristic
241	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	2	yes	—
242	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	4	yes	—
243	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	4	yes	—
244	C₂×C₂²⋊C₄	C₂×C₄×C₃₁	1	2	yes	—
245	C₂×C₂²⋊C₄	C₂×C₄×C₃₁	1	2	yes	—
246	C₂×C₄²	—	2	2	no	—
247	C₂×C₄²	—	2	2	no	—
248	C₂×C₄²	C₂×C₄×C₃₁	1	2	yes	—
249	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
250	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
251	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
252	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
253	C₄⋊C₈	—	2	8	no	—
254	#97	—	2	4	no	—
255	C₄×C₈	—	2	4	no	—
256	#95	C₂×C₄×C₃₁	1	4	yes	—
257	#95	C₂×C₄×C₃₁	1	4	yes	—
258	C₃₁	#21022	1	1	yes	characteristic, direct product factor, Sylow
259	C₂⁴	C₂²×C₄×C₃₁	1	1	yes	characteristic
260	C₂²×C₄	—	2	4	no	—
261	C₂²×C₄	—	2	4	no	—
262	C₂²×C₄	—	4	2	no	—
263	C₂²×C₄	C₂²×C₄×C₃₁	1	2	yes	—
264	C₂²×C₄	C₂²×C₄×C₃₁	1	2	yes	—
265	C₂²×C₄	C₂²×C₄×C₃₁	1	2	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	1	yes	characteristic
269	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
270	C₂²×C₄	C₂×Q₈×C₃₁	1	2	yes	—
271	C₂²×C₄	#41×C₃₁	1	2	yes	—
272	C₂²×C₄	#41×C₃₁	1	2	yes	—
273	C₂²×C₄	#41×C₃₁	1	2	yes	—
274	C₂²×C₄	#41×C₃₁	1	2	yes	—
275	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
276	M₁₆	—	2	8	no	—
277	M₁₆	—	2	8	no	—
278	C₂×C₈	—	2	2	no	—
279	C₂×C₈	—	2	2	no	—
280	C₂×C₈	—	2	2	no	—
281	C₂×C₈	—	2	2	no	—
282	C₂×C₈	—	2	2	no	—
283	C₂×C₈	—	2	2	no	—
284	C₂×C₈	—	2	2	no	—
285	C₂×C₈	—	2	2	no	—
286	C₂×C₈	—	2	2	no	—
287	C₂×C₈	—	2	2	no	—
288	C₂×C₈	—	4	4	no	—
289	C₂×C₈	—	4	4	no	—
290	C₂×C₈	C₂×D₄×C₃₁	1	4	yes	—
291	C₂×C₈	C₂×Q₈×C₃₁	1	4	yes	—
292	C₄⋊C₄	—	2	2	no	—
293	C₄⋊C₄	—	2	2	no	—
294	C₄⋊C₄	—	2	4	no	—
295	C₄⋊C₄	—	2	8	no	—
296	C₄⋊C₄	—	4	4	no	—
297	C₂²⋊C₄	—	2	4	no	—
298	C₂²⋊C₄	—	2	4	no	—
299	C₄²	—	2	4	no	—
300	C₄²	—	2	1	no	—
301	C₄²	—	2	1	no	—
302	C₄²	—	2	2	no	—
303	C₄²	—	2	1	no	—
304	C₄²	—	2	1	no	—
305	C₄²	—	2	2	no	—
306	C₄²	—	2	2	no	—
307	C₄²	—	2	2	no	—
308	C₂³	—	2	2	no	—
309	C₂³	—	2	2	no	—
310	C₂³	C₃₁×#117	1	2	yes	—
311	C₂³	C₄×D₄×C₃₁	1	2	yes	—
312	C₂³	C₄×Q₈×C₃₁	1	2	yes	—
313	C₂³	C₂³×C₄×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	4	no	—
320	C₂×C₄	—	2	4	no	—
321	C₂×C₄	—	2	4	no	—
322	C₂×C₄	—	2	2	no	—
323	C₂×C₄	—	2	2	no	—
324	C₂×C₄	—	2	4	no	—
325	C₂×C₄	—	2	4	no	—
326	C₂×C₄	—	4	8	no	—
327	C₂×C₄	C₃₁×#117	1	2	yes	—
328	C₂×C₄	C₄×D₄×C₃₁	1	2	yes	—
329	C₂×C₄	C₄×Q₈×C₃₁	1	2	yes	—
330	C₂×C₄	C₃₁×C₂²⋊Q₈	1	4	yes	—
331	C₂×C₄	C₃₁×#123	1	4	yes	—
332	C₂×C₄	C₃₁×#125	1	4	yes	—
333	C₂×C₄	C₃₁×#126	1	4	yes	—
334	C₂×C₄	C₃₁×#131	1	4	yes	—
335	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
336	C₂×C₄	C₂²×Q₈×C₃₁	1	1	yes	characteristic
337	C₂×C₄	C₂×#41×C₃₁	1	1	yes	characteristic
338	C₂×C₄	C₂×#41×C₃₁	1	1	yes	characteristic
339	C₂×C₄	C₂×#41×C₃₁	1	1	yes	characteristic
340	C₂×C₄	C₂×#41×C₃₁	1	1	yes	characteristic
341	C₈	—	2	4	no	—
342	C₈	—	2	4	no	—
343	C₈	—	4	2	no	—
344	C₈	—	4	2	no	—
345	C₂²	—	2	2	no	—
346	C₂²	—	2	2	no	—
347	C₂²	—	2	4	no	—
348	C₂²	—	2	4	no	—
349	C₂²	C₃₁×#387	1	4	yes	—
350	C₂²	C₂×C₃₁×#117	1	1	yes	characteristic
351	C₂²	C₂×C₄×D₄×C₃₁	1	1	yes	characteristic
352	C₂²	C₂×C₄×Q₈×C₃₁	1	1	yes	characteristic
353	C₂²	C₂×C₃₁×#131	1	2	yes	—
354	C₂²	C₃₁×#568	1	2	yes	—
355	C₄	—	2	4	no	—
356	C₄	—	4	2	no	—
357	C₄	—	4	2	no	—
358	C₄	—	4	2	no	—
359	C₄	—	4	4	no	—
360	C₄	C₃₁×#387	1	4	yes	—
361	C₄	C₂×C₃₁×C₂²⋊Q₈	1	1	yes	characteristic
362	C₄	C₂×C₃₁×#123	1	1	yes	characteristic
363	C₄	C₂×C₃₁×#125	1	1	yes	characteristic
364	C₄	C₂×C₃₁×#126	1	1	yes	characteristic
365	C₂	—	2	4	no	—
366	C₂	C₂×C₃₁×#387	1	1	yes	characteristic
367	C₂	C₃₁×#2922	1	1	yes	characteristic
368	C₂	C₃₁×#2923	1	1	yes	characteristic
369	C₂	C₃₁×#2933	1	2	yes	—
370	C₂	C₃₁×#2962	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₃₁	C₂⁴
commutator	C₂³	C₂³×C₄×C₃₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₃₁
socle	C₂³×C₃₁	C₂³×C₄
prime radical	C₂⁴×C₃₁	C₂²×C₄
LCS	G ▷ C₂³ ▷ 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×#1917	C₂	semidirect
5. C₃₁×#1916	C₂	semidirect
122. #21022	C₃₁	direct (N × H)
163. #1917	C₂×C₃₁	semidirect
164. #1916	C₂×C₃₁	semidirect
258. C₃₁	#21022	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×#424	2
C₂×C₄×M₁₆×C₃₁	2
C₃₁×#2296	2
C₃₁×#1917	2
C₃₁×#1916	2
C₃₁×#1729	2
C₂×C₃₁×#336	2
#21022	31

Subgroups — C31×#21022 #21477781

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#21022 #21477781