Subgroups — C₃₁×#2780 #16842713

Order 3968.

464 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#400	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#399	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#398	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#396	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#396	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#396	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#390	C₂	1	1	yes	maximal, characteristic
8	C₃₁×#389	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#387	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#386	C₂	1	1	yes	maximal, characteristic
11	C₃₁×#386	C₂	1	1	yes	maximal, characteristic
12	C₃₁×#385	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#385	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#385	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#380	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×D₄×C₃₁	C₂²	1	1	yes	characteristic
17	C₂³×C₄×C₃₁	C₂²	1	1	yes	characteristic
18	C₂³×C₄×C₃₁	C₂²	1	1	yes	characteristic
19	C₂×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
20	C₂×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
23	C₂×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
24	C₂×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
25	C₂×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
26	C₂×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
27	C₂×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
28	C₂×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
29	C₂×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
30	C₂×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
31	C₂×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
32	C₂×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
33	C₂×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
34	C₂×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
35	C₂×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
36	C₂×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
37	C₂×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
38	C₂×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
39	C₂×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
40	C₂×C₄²×C₃₁	C₂²	1	1	yes	characteristic
41	C₃₁×#95	C₂²	1	1	yes	characteristic
42	C₃₁×#95	C₂²	1	1	yes	characteristic
43	C₃₁×#95	C₂²	1	1	yes	characteristic
44	C₃₁×#95	C₂²	1	1	yes	characteristic
45	C₃₁×#95	C₂²	1	1	yes	characteristic
46	C₃₁×#95	C₂²	1	1	yes	characteristic
47	C₃₁×#95	C₂²	1	1	yes	characteristic
48	C₃₁×#95	C₂²	1	1	yes	characteristic
49	C₃₁×#95	C₂²	1	1	yes	characteristic
50	C₃₁×#95	C₂²	1	1	yes	characteristic
51	C₂⁴×C₃₁	C₂³	1	1	yes	characteristic
52	C₂⁴×C₃₁	C₂³	1	1	yes	characteristic
53	C₂×D₄×C₃₁	—	4	1	no	—
54	C₂×D₄×C₃₁	—	4	1	no	—
55	C₂×D₄×C₃₁	Q₈	1	4	yes	—
56	C₂²×C₄×C₃₁	—	2	2	no	—
57	C₂²×C₄×C₃₁	—	4	1	no	—
58	C₂²×C₄×C₃₁	—	4	1	no	—
59	C₂²×C₄×C₃₁	—	4	1	no	—
60	C₂²×C₄×C₃₁	—	4	1	no	—
61	C₂²×C₄×C₃₁	—	4	1	no	—
62	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
63	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
64	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
65	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
66	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
67	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
68	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
69	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
70	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
71	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
72	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
73	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
74	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
75	C₄⋊C₄×C₃₁	—	2	2	no	—
76	C₄⋊C₄×C₃₁	—	2	2	no	—
77	C₄⋊C₄×C₃₁	—	4	1	no	—
78	C₄⋊C₄×C₃₁	—	4	1	no	—
79	C₄⋊C₄×C₃₁	—	4	1	no	—
80	C₄⋊C₄×C₃₁	—	4	1	no	—
81	C₄⋊C₄×C₃₁	—	4	1	no	—
82	C₄⋊C₄×C₃₁	—	4	1	no	—
83	C₄⋊C₄×C₃₁	—	4	1	no	—
84	C₄⋊C₄×C₃₁	—	4	1	no	—
85	C₄⋊C₄×C₃₁	—	4	1	no	—
86	C₂²⋊C₄×C₃₁	—	2	2	no	—
87	C₂²⋊C₄×C₃₁	—	2	2	no	—
88	C₂²⋊C₄×C₃₁	—	2	2	no	—
89	C₂²⋊C₄×C₃₁	—	4	1	no	—
90	C₂²⋊C₄×C₃₁	—	4	1	no	—
91	C₂²⋊C₄×C₃₁	—	4	1	no	—
92	C₂²⋊C₄×C₃₁	—	4	1	no	—
93	C₂²⋊C₄×C₃₁	—	4	1	no	—
94	C₂²⋊C₄×C₃₁	—	4	1	no	—
95	C₂²⋊C₄×C₃₁	—	4	1	no	—
96	C₄²×C₃₁	—	4	1	no	—
97	C₂³×C₃₁	—	2	1	no	—
98	C₂³×C₃₁	—	2	1	no	—
99	C₂³×C₃₁	—	2	1	no	—
100	C₂³×C₃₁	—	2	1	no	—
101	C₂³×C₃₁	—	2	1	no	—
102	C₂³×C₃₁	—	2	1	no	—
103	C₂³×C₃₁	—	2	1	no	—
104	C₂³×C₃₁	—	2	1	no	—
105	C₂³×C₃₁	—	2	1	no	—
106	C₂³×C₃₁	—	2	1	no	—
107	C₂³×C₃₁	—	2	1	no	—
108	C₂³×C₃₁	—	2	1	no	—
109	C₂³×C₃₁	C₂×Q₈	1	2	yes	—
110	C₂³×C₃₁	C₂×Q₈	1	2	yes	—
111	C₂³×C₃₁	C₂⁴	1	1	yes	characteristic
112	D₄×C₃₁	—	4	4	no	—
113	C₂×C₄×C₃₁	—	2	1	no	—
114	C₂×C₄×C₃₁	—	2	1	no	—
115	C₂×C₄×C₃₁	—	2	1	no	—
116	C₂×C₄×C₃₁	—	2	1	no	—
117	C₂×C₄×C₃₁	—	2	1	no	—
118	C₂×C₄×C₃₁	—	2	1	no	—
119	C₂×C₄×C₃₁	—	2	1	no	—
120	C₂×C₄×C₃₁	—	2	1	no	—
121	C₂×C₄×C₃₁	—	2	1	no	—
122	C₂×C₄×C₃₁	—	2	1	no	—
123	C₂×C₄×C₃₁	—	2	1	no	—
124	C₂×C₄×C₃₁	—	2	1	no	—
125	C₂×C₄×C₃₁	—	2	1	no	—
126	C₂×C₄×C₃₁	—	2	1	no	—
127	C₂×C₄×C₃₁	—	2	1	no	—
128	C₂×C₄×C₃₁	—	2	1	no	—
129	C₂×C₄×C₃₁	—	2	1	no	—
130	C₂×C₄×C₃₁	—	2	1	no	—
131	C₂×C₄×C₃₁	—	2	1	no	—
132	C₂×C₄×C₃₁	—	2	1	no	—
133	C₂×C₄×C₃₁	—	2	1	no	—
134	C₂×C₄×C₃₁	—	2	1	no	—
135	C₂×C₄×C₃₁	—	2	1	no	—
136	C₂×C₄×C₃₁	—	2	1	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	1	no	—
143	C₂×C₄×C₃₁	—	2	1	no	—
144	C₂×C₄×C₃₁	—	2	1	no	—
145	C₂×C₄×C₃₁	—	2	1	no	—
146	C₂×C₄×C₃₁	—	2	1	no	—
147	C₂×C₄×C₃₁	—	2	1	no	—
148	C₂×C₄×C₃₁	—	2	1	no	—
149	C₂×C₄×C₃₁	—	4	4	no	—
150	C₂×C₄×C₃₁	—	4	4	no	—
151	C₂×C₄×C₃₁	C₂×Q₈	1	2	yes	—
152	C₂×C₄×C₃₁	#41	1	2	yes	—
153	C₂×C₄×C₃₁	#41	1	2	yes	—
154	#2780	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
155	C₂²×C₃₁	—	2	2	no	—
156	C₂²×C₃₁	—	2	2	no	—
157	C₂²×C₃₁	—	2	2	no	—
158	C₂²×C₃₁	—	2	2	no	—
159	C₂²×C₃₁	—	2	2	no	—
160	C₂²×C₃₁	—	2	2	no	—
161	C₂²×C₃₁	—	4	1	no	—
162	C₂²×C₃₁	—	4	1	no	—
163	C₂²×C₃₁	—	4	1	no	—
164	C₂²×C₃₁	—	4	1	no	—
165	C₂²×C₃₁	—	4	1	no	—
166	C₂²×C₃₁	—	4	1	no	—
167	C₂²×C₃₁	—	4	1	no	—
168	C₂²×C₃₁	—	4	1	no	—
169	C₂²×C₃₁	C₂²×Q₈	1	1	yes	characteristic
170	C₂²×C₃₁	C₂×#41	1	1	yes	characteristic
171	C₂²×C₃₁	C₂×#41	1	1	yes	characteristic
172	C₂²×C₃₁	H(5,𝔽₂)	1	1	yes	characteristic
173	C₂²×C₃₁	H(5,𝔽₂)	1	1	yes	characteristic
174	C₂²×C₃₁	H(5,𝔽₂)	1	1	yes	characteristic
175	C₂²×C₃₁	H(5,𝔽₂)	1	1	yes	characteristic
176	C₄×C₃₁	—	2	2	no	—
177	C₄×C₃₁	—	2	2	no	—
178	C₄×C₃₁	—	2	2	no	—
179	C₄×C₃₁	—	4	1	no	—
180	C₄×C₃₁	—	4	1	no	—
181	C₄×C₃₁	—	4	1	no	—
182	C₄×C₃₁	—	4	1	no	—
183	C₄×C₃₁	—	4	1	no	—
184	C₄×C₃₁	—	4	1	no	—
185	C₄×C₃₁	—	4	1	no	—
186	C₄×C₃₁	—	4	1	no	—
187	C₄×C₃₁	—	4	1	no	—
188	C₄×C₃₁	—	4	1	no	—
189	#400	C₂×C₃₁	1	1	yes	characteristic, complemented
190	#399	C₂×C₃₁	1	1	yes	characteristic, complemented
191	#398	C₂×C₃₁	1	1	yes	characteristic, complemented
192	#396	C₂×C₃₁	1	1	yes	characteristic, complemented
193	#396	C₂×C₃₁	1	1	yes	characteristic, complemented
194	#396	C₂×C₃₁	1	1	yes	characteristic, complemented
195	#390	C₂×C₃₁	1	1	yes	characteristic
196	#389	C₂×C₃₁	1	1	yes	characteristic, complemented
197	#387	C₂×C₃₁	1	1	yes	characteristic, complemented
198	#386	C₂×C₃₁	1	1	yes	characteristic
199	#386	C₂×C₃₁	1	1	yes	characteristic
200	#385	C₂×C₃₁	1	1	yes	characteristic, complemented
201	#385	C₂×C₃₁	1	1	yes	characteristic, complemented
202	#385	C₂×C₃₁	1	1	yes	characteristic, complemented
203	#380	C₂×C₃₁	1	1	yes	characteristic, complemented
204	C₂×C₃₁	—	4	2	no	—
205	C₂×C₃₁	—	4	2	no	—
206	C₂×C₃₁	#538	1	1	yes	characteristic
207	C₂×C₃₁	#540	1	1	yes	characteristic
208	C₂×C₃₁	#543	1	1	yes	characteristic
209	C₂×C₃₁	#553	1	1	yes	characteristic
210	C₂×C₃₁	#554	1	1	yes	characteristic
211	C₂×C₃₁	#554	1	1	yes	characteristic
212	C₂×C₃₁	#560	1	1	yes	characteristic
213	C₂²×D₄	C₂²×C₃₁	1	1	yes	characteristic
214	C₂³×C₄	C₂²×C₃₁	1	1	yes	characteristic
215	C₂³×C₄	C₂²×C₃₁	1	1	yes	characteristic
216	C₂×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
217	C₂×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
218	C₂×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
219	C₂×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
220	C₂×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
221	C₂×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
222	C₂×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
223	C₂×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
224	C₂×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
225	C₂×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
226	C₂×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
227	C₂×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
228	C₂×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
229	C₂×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
230	C₂×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
231	C₂×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
232	C₂×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
233	C₂×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
234	C₂×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
235	C₂×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
236	C₂×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
237	C₂×C₄²	C₂²×C₃₁	1	1	yes	characteristic
238	#95	C₂²×C₃₁	1	1	yes	characteristic
239	#95	C₂²×C₃₁	1	1	yes	characteristic
240	#95	C₂²×C₃₁	1	1	yes	characteristic
241	#95	C₂²×C₃₁	1	1	yes	characteristic
242	#95	C₂²×C₃₁	1	1	yes	characteristic
243	#95	C₂²×C₃₁	1	1	yes	characteristic
244	#95	C₂²×C₃₁	1	1	yes	characteristic
245	#95	C₂²×C₃₁	1	1	yes	characteristic
246	#95	C₂²×C₃₁	1	1	yes	characteristic
247	#95	C₂²×C₃₁	1	1	yes	characteristic
248	C₃₁	#2780	1	1	yes	characteristic, direct product factor, Sylow
249	C₂⁴	C₂³×C₃₁	1	1	yes	characteristic
250	C₂⁴	C₂³×C₃₁	1	1	yes	characteristic
251	C₂×D₄	—	4	1	no	—
252	C₂×D₄	—	4	1	no	—
253	C₂×D₄	Q₈×C₃₁	1	4	yes	—
254	C₂²×C₄	—	2	2	no	—
255	C₂²×C₄	—	4	1	no	—
256	C₂²×C₄	—	4	1	no	—
257	C₂²×C₄	—	4	1	no	—
258	C₂²×C₄	—	4	1	no	—
259	C₂²×C₄	—	4	1	no	—
260	C₂²×C₄	C₂³×C₃₁	1	1	yes	characteristic
261	C₂²×C₄	C₂³×C₃₁	1	1	yes	characteristic
262	C₂²×C₄	C₂³×C₃₁	1	1	yes	characteristic
263	C₂²×C₄	C₂³×C₃₁	1	1	yes	characteristic
264	C₂²×C₄	C₂³×C₃₁	1	1	yes	characteristic
265	C₂²×C₄	C₂³×C₃₁	1	1	yes	characteristic
266	C₂²×C₄	C₂³×C₃₁	1	1	yes	characteristic
267	C₂²×C₄	C₂³×C₃₁	1	1	yes	characteristic
268	C₂²×C₄	C₂³×C₃₁	1	1	yes	characteristic
269	C₂²×C₄	C₂³×C₃₁	1	1	yes	characteristic
270	C₂²×C₄	C₂³×C₃₁	1	1	yes	characteristic
271	C₂²×C₄	C₂³×C₃₁	1	1	yes	characteristic
272	C₂²×C₄	C₂³×C₃₁	1	1	yes	characteristic
273	C₄⋊C₄	—	2	2	no	—
274	C₄⋊C₄	—	2	2	no	—
275	C₄⋊C₄	—	4	1	no	—
276	C₄⋊C₄	—	4	1	no	—
277	C₄⋊C₄	—	4	1	no	—
278	C₄⋊C₄	—	4	1	no	—
279	C₄⋊C₄	—	4	1	no	—
280	C₄⋊C₄	—	4	1	no	—
281	C₄⋊C₄	—	4	1	no	—
282	C₄⋊C₄	—	4	1	no	—
283	C₄⋊C₄	—	4	1	no	—
284	C₂²⋊C₄	—	2	2	no	—
285	C₂²⋊C₄	—	2	2	no	—
286	C₂²⋊C₄	—	2	2	no	—
287	C₂²⋊C₄	—	4	1	no	—
288	C₂²⋊C₄	—	4	1	no	—
289	C₂²⋊C₄	—	4	1	no	—
290	C₂²⋊C₄	—	4	1	no	—
291	C₂²⋊C₄	—	4	1	no	—
292	C₂²⋊C₄	—	4	1	no	—
293	C₂²⋊C₄	—	4	1	no	—
294	C₄²	—	4	1	no	—
295	C₂³	—	2	1	no	—
296	C₂³	—	2	1	no	—
297	C₂³	—	2	1	no	—
298	C₂³	—	2	1	no	—
299	C₂³	—	2	1	no	—
300	C₂³	—	2	1	no	—
301	C₂³	—	2	1	no	—
302	C₂³	—	2	1	no	—
303	C₂³	—	2	1	no	—
304	C₂³	—	2	1	no	—
305	C₂³	—	2	1	no	—
306	C₂³	—	2	1	no	—
307	C₂³	C₂×Q₈×C₃₁	1	2	yes	—
308	C₂³	C₂×Q₈×C₃₁	1	2	yes	—
309	C₂³	C₂⁴×C₃₁	1	1	yes	characteristic
310	D₄	—	4	4	no	—
311	C₂×C₄	—	2	1	no	—
312	C₂×C₄	—	2	1	no	—
313	C₂×C₄	—	2	1	no	—
314	C₂×C₄	—	2	1	no	—
315	C₂×C₄	—	2	1	no	—
316	C₂×C₄	—	2	1	no	—
317	C₂×C₄	—	2	1	no	—
318	C₂×C₄	—	2	1	no	—
319	C₂×C₄	—	2	1	no	—
320	C₂×C₄	—	2	1	no	—
321	C₂×C₄	—	2	1	no	—
322	C₂×C₄	—	2	1	no	—
323	C₂×C₄	—	2	1	no	—
324	C₂×C₄	—	2	1	no	—
325	C₂×C₄	—	2	1	no	—
326	C₂×C₄	—	2	1	no	—
327	C₂×C₄	—	2	1	no	—
328	C₂×C₄	—	2	1	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	1	no	—
335	C₂×C₄	—	2	1	no	—
336	C₂×C₄	—	2	1	no	—
337	C₂×C₄	—	2	1	no	—
338	C₂×C₄	—	2	1	no	—
339	C₂×C₄	—	2	1	no	—
340	C₂×C₄	—	2	1	no	—
341	C₂×C₄	—	2	1	no	—
342	C₂×C₄	—	2	1	no	—
343	C₂×C₄	—	2	1	no	—
344	C₂×C₄	—	2	1	no	—
345	C₂×C₄	—	2	1	no	—
346	C₂×C₄	—	2	1	no	—
347	C₂×C₄	—	4	4	no	—
348	C₂×C₄	—	4	4	no	—
349	C₂×C₄	C₂×Q₈×C₃₁	1	2	yes	—
350	C₂×C₄	#41×C₃₁	1	2	yes	—
351	C₂×C₄	#41×C₃₁	1	2	yes	—
352	C₂²	—	2	2	no	—
353	C₂²	—	2	2	no	—
354	C₂²	—	2	2	no	—
355	C₂²	—	2	2	no	—
356	C₂²	—	2	2	no	—
357	C₂²	—	2	2	no	—
358	C₂²	—	4	1	no	—
359	C₂²	—	4	1	no	—
360	C₂²	—	4	1	no	—
361	C₂²	—	4	1	no	—
362	C₂²	—	4	1	no	—
363	C₂²	—	4	1	no	—
364	C₂²	—	4	1	no	—
365	C₂²	—	4	1	no	—
366	C₂²	C₂²×Q₈×C₃₁	1	1	yes	characteristic
367	C₂²	C₂×#41×C₃₁	1	1	yes	characteristic
368	C₂²	C₂×#41×C₃₁	1	1	yes	characteristic
369	C₂²	C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
370	C₂²	C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
371	C₂²	C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
372	C₂²	C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
373	C₄	—	2	2	no	—
374	C₄	—	2	2	no	—
375	C₄	—	2	2	no	—
376	C₄	—	4	1	no	—
377	C₄	—	4	1	no	—
378	C₄	—	4	1	no	—
379	C₄	—	4	1	no	—
380	C₄	—	4	1	no	—
381	C₄	—	4	1	no	—
382	C₄	—	4	1	no	—
383	C₄	—	4	1	no	—
384	C₄	—	4	1	no	—
385	C₄	—	4	1	no	—
386	C₂	—	4	2	no	—
387	C₂	—	4	2	no	—
388	C₂	C₃₁×#538	1	1	yes	characteristic
389	C₂	C₃₁×#540	1	1	yes	characteristic
390	C₂	C₃₁×#543	1	1	yes	characteristic
391	C₂	C₃₁×#553	1	1	yes	characteristic
392	C₂	C₃₁×#554	1	1	yes	characteristic
393	C₂	C₃₁×#554	1	1	yes	characteristic
394	C₂	C₃₁×#560	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃₁	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₃₁
prime radical	C₂²×D₄×C₃₁	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#400	C₂	semidirect
2. C₃₁×#399	C₂	semidirect
3. C₃₁×#398	C₂	semidirect
4. C₃₁×#396	C₂	semidirect
5. C₃₁×#396	C₂	semidirect
6. C₃₁×#396	C₂	semidirect
8. C₃₁×#389	C₂	semidirect
9. C₃₁×#387	C₂	semidirect
12. C₃₁×#385	C₂	semidirect
13. C₃₁×#385	C₂	semidirect
14. C₃₁×#385	C₂	semidirect
15. C₃₁×#380	C₂	semidirect
154. #2780	C₃₁	direct (N × H)
189. #400	C₂×C₃₁	semidirect
190. #399	C₂×C₃₁	semidirect
191. #398	C₂×C₃₁	semidirect
192. #396	C₂×C₃₁	semidirect
193. #396	C₂×C₃₁	semidirect
194. #396	C₂×C₃₁	semidirect
196. #389	C₂×C₃₁	semidirect
197. #387	C₂×C₃₁	semidirect
200. #385	C₂×C₃₁	semidirect
201. #385	C₂×C₃₁	semidirect
202. #385	C₂×C₃₁	semidirect
203. #380	C₂×C₃₁	semidirect
248. C₃₁	#2780	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×#400	2
C₃₁×#399	2
C₃₁×#398	2
C₃₁×#396	2
C₃₁×#390	2
C₃₁×#389	2
C₃₁×#387	2
C₃₁×#386	2
C₃₁×#385	2
C₃₁×#380	2
#2780	31

Subgroups — C31×#2780 #16842713

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#2780 #16842713