Subgroups — C₃₁×#22320 #21479079

Order 7936.

652 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#2396	C₂	1	1	yes	maximal, characteristic
2	C₃₁×#1984	C₂	1	2	yes	maximal, complemented
3	C₃₁×#1924	C₂	1	2	yes	maximal
4	C₃₁×#1923	C₂	1	2	yes	maximal
5	C₃₁×#1917	C₂	1	2	yes	maximal, complemented
6	C₃₁×#1916	C₂	1	2	yes	maximal, complemented
7	C₃₁×#1818	C₂	1	1	yes	maximal, characteristic
8	C₃₁×#1771	C₂	1	2	yes	maximal, complemented
9	C₃₁×#1750	C₂	1	1	yes	maximal, characteristic
10	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
11	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
12	C₂×C₃₁×C₄⋊C₈	C₂²	1	2	yes	—
13	C₂×C₃₁×C₄⋊C₈	C₂²	1	2	yes	—
14	C₂×C₃₁×C₂²⋊C₈	C₂²	1	2	yes	—
15	C₂×C₃₁×C₂²⋊C₈	C₂²	1	1	yes	characteristic
16	C₂×C₃₁×C₂²⋊C₈	C₂²	1	1	yes	characteristic
17	C₂×C₃₁×#97	C₂²	1	2	yes	—
18	C₂×C₃₁×#97	C₂²	1	1	yes	characteristic
19	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
20	C₂×C₄×C₈×C₃₁	C₂²	1	2	yes	—
21	C₃₁×#400	C₄	1	1	yes	characteristic
22	C₃₁×#399	C₄	1	1	yes	characteristic
23	C₃₁×#398	C₄	1	2	yes	—
24	C₃₁×#396	C₄	1	2	yes	—
25	C₃₁×#395	C₄	1	1	yes	characteristic
26	C₃₁×#393	C₄	1	1	yes	characteristic
27	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
28	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
29	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
30	C₃₁×#336	C₂²	1	2	yes	—
31	C₃₁×#336	C₂²	1	2	yes	—
32	C₃₁×#336	C₂²	1	2	yes	—
33	C₃₁×#336	C₂²	1	2	yes	—
34	C₃₁×#336	C₂²	1	2	yes	—
35	C₃₁×#336	C₂²	1	2	yes	—
36	C₃₁×#336	C₂²	1	2	yes	—
37	C₂²×Q₈×C₃₁	C₂×C₄	1	1	yes	characteristic
38	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
39	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
40	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
41	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
42	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
43	C₄×Q₈×C₃₁	—	4	1	no	—
44	C₄×Q₈×C₃₁	—	4	1	no	—
45	C₃₁×#117	—	4	1	no	—
46	C₃₁×#117	—	4	1	no	—
47	C₂×C₄⋊C₄×C₃₁	C₂×C₄	1	2	yes	—
48	C₂×C₄⋊C₄×C₃₁	C₂×C₄	1	1	yes	characteristic
49	C₂×C₄⋊C₄×C₃₁	C₂×C₄	1	2	yes	—
50	C₂×C₄⋊C₄×C₃₁	C₂×C₄	1	2	yes	—
51	C₂×C₄⋊C₄×C₃₁	C₂×C₄	1	1	yes	characteristic
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	2	yes	—
55	C₂×C₂²⋊C₄×C₃₁	C₂×C₄	1	1	yes	characteristic
56	C₂×C₂²⋊C₄×C₃₁	C₂×C₄	1	2	yes	—
57	C₂×C₂²⋊C₄×C₃₁	C₂×C₄	1	1	yes	characteristic
58	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
59	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
60	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
61	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
62	C₃₁×C₄⋊C₈	—	2	4	no	—
63	C₃₁×C₄⋊C₈	—	4	2	no	—
64	C₃₁×C₂²⋊C₈	—	2	4	no	—
65	C₃₁×C₂²⋊C₈	—	4	1	no	—
66	C₃₁×C₂²⋊C₈	—	4	1	no	—
67	C₃₁×#97	—	2	4	no	—
68	C₃₁×#97	—	4	1	no	—
69	C₄×C₈×C₃₁	—	4	1	no	—
70	C₄×C₈×C₃₁	—	4	2	no	—
71	C₃₁×#95	C₂×C₄	1	2	yes	—
72	C₃₁×#95	C₂×C₄	1	1	yes	characteristic
73	C₃₁×#95	C₂×C₄	1	2	yes	—
74	C₃₁×#95	C₂×C₄	1	2	yes	—
75	C₃₁×#95	C₂×C₄	1	2	yes	—
76	C₃₁×#95	C₂×C₄	1	1	yes	characteristic
77	C₂⁴×C₃₁	C₂²×C₄	1	1	yes	characteristic
78	C₂×Q₈×C₃₁	—	2	4	no	—
79	C₂×Q₈×C₃₁	—	4	1	no	—
80	C₂²×C₄×C₃₁	—	2	2	no	—
81	C₂²×C₄×C₃₁	—	2	1	no	—
82	C₂²×C₄×C₃₁	—	2	1	no	—
83	C₂²×C₄×C₃₁	—	2	2	no	—
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	2	yes	—
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	2	yes	—
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	2	yes	—
93	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
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	—	2	2	no	—
103	C₂×C₈×C₃₁	—	2	2	no	—
104	C₂×C₈×C₃₁	—	2	2	no	—
105	C₂×C₈×C₃₁	#41	1	4	yes	—
106	C₄⋊C₄×C₃₁	—	2	4	no	—
107	C₄⋊C₄×C₃₁	—	4	2	no	—
108	C₄⋊C₄×C₃₁	—	4	2	no	—
109	C₄⋊C₄×C₃₁	—	4	1	no	—
110	C₄⋊C₄×C₃₁	—	4	1	no	—
111	C₄⋊C₄×C₃₁	—	4	2	no	—
112	C₄⋊C₄×C₃₁	—	4	1	no	—
113	C₂²⋊C₄×C₃₁	—	2	4	no	—
114	C₂²⋊C₄×C₃₁	—	4	2	no	—
115	C₂²⋊C₄×C₃₁	—	4	1	no	—
116	C₂²⋊C₄×C₃₁	—	4	1	no	—
117	C₄²×C₃₁	—	2	2	no	—
118	C₄²×C₃₁	—	2	2	no	—
119	C₄²×C₃₁	—	2	1	no	—
120	C₄²×C₃₁	—	2	2	no	—
121	C₄²×C₃₁	—	2	1	no	—
122	C₄²×C₃₁	—	2	2	no	—
123	C₄²×C₃₁	—	2	1	no	—
124	C₄²×C₃₁	—	2	1	no	—
125	#22320	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
126	C₂³×C₃₁	—	2	1	no	—
127	C₂³×C₃₁	—	2	1	no	—
128	C₂³×C₃₁	—	2	1	no	—
129	C₂³×C₃₁	—	2	2	no	—
130	C₂³×C₃₁	—	2	2	no	—
131	C₂³×C₃₁	C₂³×C₄	1	1	yes	characteristic
132	Q₈×C₃₁	—	4	4	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	—	2	1	no	—
138	C₂×C₄×C₃₁	—	2	1	no	—
139	C₂×C₄×C₃₁	—	2	1	no	—
140	C₂×C₄×C₃₁	—	2	1	no	—
141	C₂×C₄×C₃₁	—	2	1	no	—
142	C₂×C₄×C₃₁	—	2	2	no	—
143	C₂×C₄×C₃₁	—	2	1	no	—
144	C₂×C₄×C₃₁	—	2	1	no	—
145	C₂×C₄×C₃₁	—	2	2	no	—
146	C₂×C₄×C₃₁	—	2	2	no	—
147	C₂×C₄×C₃₁	—	2	2	no	—
148	C₂×C₄×C₃₁	—	2	2	no	—
149	C₂×C₄×C₃₁	—	2	2	no	—
150	C₂×C₄×C₃₁	—	2	2	no	—
151	C₂×C₄×C₃₁	—	2	2	no	—
152	C₂×C₄×C₃₁	—	2	2	no	—
153	C₂×C₄×C₃₁	—	2	2	no	—
154	C₂×C₄×C₃₁	—	2	2	no	—
155	C₂×C₄×C₃₁	—	4	2	no	—
156	C₂×C₄×C₃₁	—	4	2	no	—
157	C₂×C₄×C₃₁	#131	1	4	yes	—
158	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
159	C₂×C₄×C₃₁	H(5,𝔽₂)	1	1	yes	characteristic
160	C₂×C₄×C₃₁	H(5,𝔽₂)	1	1	yes	characteristic
161	C₂×C₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
162	C₈×C₃₁	—	2	4	no	—
163	C₈×C₃₁	—	4	2	no	—
164	C₈×C₃₁	—	4	2	no	—
165	C₈×C₃₁	—	4	2	no	—
166	#2396	C₂×C₃₁	1	1	yes	characteristic
167	#1984	C₂×C₃₁	1	2	yes	complemented
168	#1924	C₂×C₃₁	1	2	yes	—
169	#1923	C₂×C₃₁	1	2	yes	—
170	#1917	C₂×C₃₁	1	2	yes	complemented
171	#1916	C₂×C₃₁	1	2	yes	complemented
172	#1818	C₂×C₃₁	1	1	yes	characteristic
173	#1771	C₂×C₃₁	1	2	yes	complemented
174	#1750	C₂×C₃₁	1	1	yes	characteristic
175	C₂²×C₃₁	—	4	1	no	—
176	C₂²×C₃₁	—	4	2	no	—
177	C₂²×C₃₁	—	4	1	no	—
178	C₂²×C₃₁	—	4	1	no	—
179	C₂²×C₃₁	—	4	2	no	—
180	C₂²×C₃₁	C₄×#41	1	1	yes	characteristic
181	C₂²×C₃₁	#518	1	1	yes	characteristic
182	C₂²×C₃₁	#519	1	1	yes	characteristic
183	C₂²×C₃₁	C₂×#131	1	2	yes	—
184	C₂²×C₃₁	#568	1	2	yes	—
185	C₄×C₃₁	—	2	4	no	—
186	C₄×C₃₁	—	4	1	no	—
187	C₄×C₃₁	—	4	2	no	—
188	C₄×C₃₁	—	4	2	no	—
189	C₄×C₃₁	—	4	1	no	—
190	C₄×C₃₁	—	4	1	no	—
191	C₄×C₃₁	—	4	1	no	—
192	C₄×C₃₁	—	4	1	no	—
193	C₄×C₃₁	—	4	2	no	—
194	C₄×C₃₁	#539	1	2	yes	—
195	C₄×C₃₁	#542	1	2	yes	—
196	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
197	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
198	C₂×C₄⋊C₈	C₂²×C₃₁	1	2	yes	—
199	C₂×C₄⋊C₈	C₂²×C₃₁	1	2	yes	—
200	C₂×C₂²⋊C₈	C₂²×C₃₁	1	2	yes	—
201	C₂×C₂²⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
202	C₂×C₂²⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
203	C₂×#97	C₂²×C₃₁	1	2	yes	—
204	C₂×#97	C₂²×C₃₁	1	1	yes	characteristic
205	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
206	C₂×C₄×C₈	C₂²×C₃₁	1	2	yes	—
207	#400	C₄×C₃₁	1	1	yes	characteristic
208	#399	C₄×C₃₁	1	1	yes	characteristic
209	#398	C₄×C₃₁	1	2	yes	—
210	#396	C₄×C₃₁	1	2	yes	—
211	#395	C₄×C₃₁	1	1	yes	characteristic
212	#393	C₄×C₃₁	1	1	yes	characteristic
213	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
214	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
215	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
216	#336	C₂²×C₃₁	1	2	yes	—
217	#336	C₂²×C₃₁	1	2	yes	—
218	#336	C₂²×C₃₁	1	2	yes	—
219	#336	C₂²×C₃₁	1	2	yes	—
220	#336	C₂²×C₃₁	1	2	yes	—
221	#336	C₂²×C₃₁	1	2	yes	—
222	#336	C₂²×C₃₁	1	2	yes	—
223	C₂×C₃₁	—	8	1	no	—
224	C₂×C₃₁	#2332	1	1	yes	characteristic
225	C₂×C₃₁	#2969	1	2	yes	—
226	C₂×C₃₁	#2977	1	1	yes	characteristic
227	C₂×C₃₁	#2980	1	1	yes	characteristic
228	C₂×C₃₁	#2985	1	2	yes	—
229	C₂²×Q₈	C₂×C₄×C₃₁	1	1	yes	characteristic
230	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
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	C₄×Q₈	—	4	1	no	—
236	C₄×Q₈	—	4	1	no	—
237	#117	—	4	1	no	—
238	#117	—	4	1	no	—
239	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	2	yes	—
240	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	1	yes	characteristic
241	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	1	yes	characteristic
242	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	2	yes	—
243	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	1	yes	characteristic
244	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	2	yes	—
245	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	2	yes	—
246	C₂×C₂²⋊C₄	C₂×C₄×C₃₁	1	2	yes	—
247	C₂×C₂²⋊C₄	C₂×C₄×C₃₁	1	1	yes	characteristic
248	C₂×C₂²⋊C₄	C₂×C₄×C₃₁	1	1	yes	characteristic
249	C₂×C₂²⋊C₄	C₂×C₄×C₃₁	1	2	yes	—
250	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
251	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
252	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
253	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
254	C₄⋊C₈	—	2	4	no	—
255	C₄⋊C₈	—	4	2	no	—
256	C₂²⋊C₈	—	2	4	no	—
257	C₂²⋊C₈	—	4	1	no	—
258	C₂²⋊C₈	—	4	1	no	—
259	#97	—	2	4	no	—
260	#97	—	4	1	no	—
261	C₄×C₈	—	4	1	no	—
262	C₄×C₈	—	4	2	no	—
263	#95	C₂×C₄×C₃₁	1	2	yes	—
264	#95	C₂×C₄×C₃₁	1	2	yes	—
265	#95	C₂×C₄×C₃₁	1	2	yes	—
266	#95	C₂×C₄×C₃₁	1	1	yes	characteristic
267	#95	C₂×C₄×C₃₁	1	1	yes	characteristic
268	#95	C₂×C₄×C₃₁	1	2	yes	—
269	C₃₁	#22320	1	1	yes	characteristic, direct product factor, Sylow
270	C₂⁴	C₂²×C₄×C₃₁	1	1	yes	characteristic
271	C₂×Q₈	—	2	4	no	—
272	C₂×Q₈	—	4	1	no	—
273	C₂²×C₄	—	2	2	no	—
274	C₂²×C₄	—	2	1	no	—
275	C₂²×C₄	—	2	1	no	—
276	C₂²×C₄	—	2	2	no	—
277	C₂²×C₄	C₂²×C₄×C₃₁	1	2	yes	—
278	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
279	C₂²×C₄	C₂²×C₄×C₃₁	1	2	yes	—
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	2	yes	—
283	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
284	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
285	C₂²×C₄	C₂²×C₄×C₃₁	1	2	yes	—
286	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
287	C₂×C₈	—	2	2	no	—
288	C₂×C₈	—	2	2	no	—
289	C₂×C₈	—	2	2	no	—
290	C₂×C₈	—	2	2	no	—
291	C₂×C₈	—	2	2	no	—
292	C₂×C₈	—	2	2	no	—
293	C₂×C₈	—	2	2	no	—
294	C₂×C₈	—	2	2	no	—
295	C₂×C₈	—	2	2	no	—
296	C₂×C₈	—	2	2	no	—
297	C₂×C₈	—	2	2	no	—
298	C₂×C₈	#41×C₃₁	1	4	yes	—
299	C₄⋊C₄	—	2	4	no	—
300	C₄⋊C₄	—	4	2	no	—
301	C₄⋊C₄	—	4	2	no	—
302	C₄⋊C₄	—	4	1	no	—
303	C₄⋊C₄	—	4	1	no	—
304	C₄⋊C₄	—	4	2	no	—
305	C₄⋊C₄	—	4	1	no	—
306	C₂²⋊C₄	—	2	4	no	—
307	C₂²⋊C₄	—	4	2	no	—
308	C₂²⋊C₄	—	4	1	no	—
309	C₂²⋊C₄	—	4	1	no	—
310	C₄²	—	2	2	no	—
311	C₄²	—	2	2	no	—
312	C₄²	—	2	1	no	—
313	C₄²	—	2	2	no	—
314	C₄²	—	2	1	no	—
315	C₄²	—	2	2	no	—
316	C₄²	—	2	1	no	—
317	C₄²	—	2	1	no	—
318	C₂³	—	2	1	no	—
319	C₂³	—	2	1	no	—
320	C₂³	—	2	1	no	—
321	C₂³	—	2	2	no	—
322	C₂³	—	2	2	no	—
323	C₂³	C₂³×C₄×C₃₁	1	1	yes	characteristic
324	Q₈	—	4	4	no	—
325	C₂×C₄	—	2	2	no	—
326	C₂×C₄	—	2	2	no	—
327	C₂×C₄	—	2	2	no	—
328	C₂×C₄	—	2	2	no	—
329	C₂×C₄	—	2	1	no	—
330	C₂×C₄	—	2	1	no	—
331	C₂×C₄	—	2	1	no	—
332	C₂×C₄	—	2	1	no	—
333	C₂×C₄	—	2	1	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	2	1	no	—
336	C₂×C₄	—	2	1	no	—
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	2	2	no	—
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	2	2	no	—
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	2	2	no	—
343	C₂×C₄	—	2	2	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	4	2	no	—
348	C₂×C₄	—	4	2	no	—
349	C₂×C₄	C₃₁×#131	1	4	yes	—
350	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
351	C₂×C₄	C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
352	C₂×C₄	C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
353	C₂×C₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
354	C₈	—	2	4	no	—
355	C₈	—	4	2	no	—
356	C₈	—	4	2	no	—
357	C₈	—	4	2	no	—
358	C₂²	—	4	1	no	—
359	C₂²	—	4	2	no	—
360	C₂²	—	4	1	no	—
361	C₂²	—	4	1	no	—
362	C₂²	—	4	2	no	—
363	C₂²	C₄×#41×C₃₁	1	1	yes	characteristic
364	C₂²	C₃₁×#518	1	1	yes	characteristic
365	C₂²	C₃₁×#519	1	1	yes	characteristic
366	C₂²	C₂×C₃₁×#131	1	2	yes	—
367	C₂²	C₃₁×#568	1	2	yes	—
368	C₄	—	2	4	no	—
369	C₄	—	4	1	no	—
370	C₄	—	4	2	no	—
371	C₄	—	4	2	no	—
372	C₄	—	4	1	no	—
373	C₄	—	4	1	no	—
374	C₄	—	4	1	no	—
375	C₄	—	4	1	no	—
376	C₄	—	4	2	no	—
377	C₄	C₃₁×#539	1	2	yes	—
378	C₄	C₃₁×#542	1	2	yes	—
379	C₂	—	8	1	no	—
380	C₂	C₃₁×#2332	1	1	yes	characteristic
381	C₂	C₃₁×#2969	1	2	yes	—
382	C₂	C₃₁×#2977	1	1	yes	characteristic
383	C₂	C₃₁×#2980	1	1	yes	characteristic
384	C₂	C₃₁×#2985	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
2. C₃₁×#1984	C₂	semidirect
5. C₃₁×#1917	C₂	semidirect
6. C₃₁×#1916	C₂	semidirect
8. C₃₁×#1771	C₂	semidirect
125. #22320	C₃₁	direct (N × H)
167. #1984	C₂×C₃₁	semidirect
170. #1917	C₂×C₃₁	semidirect
171. #1916	C₂×C₃₁	semidirect
173. #1771	C₂×C₃₁	semidirect
269. C₃₁	#22320	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×#2396	2
C₃₁×#1984	2
C₃₁×#1924	2
C₃₁×#1923	2
C₃₁×#1917	2
C₃₁×#1916	2
C₃₁×#1818	2
C₃₁×#1771	2
C₃₁×#1750	2
#22320	31

Subgroups — C31×#22320 #21479079

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#22320 #21479079