Subgroups — C₃₁×#26255 #21483014

Order 7936.

814 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#494	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×Q₁₆×C₃₁	C₂	1	1	yes	maximal, characteristic
3	C₃₁×#2446	C₂	1	2	yes	maximal
4	C₃₁×#2056	C₂	1	2	yes	maximal
5	C₃₁×#2043	C₂	1	2	yes	maximal
6	C₃₁×#1969	C₂	1	1	yes	maximal, characteristic
7	C₃₁×#1969	C₂	1	1	yes	maximal, characteristic
8	C₃₁×#1969	C₂	1	1	yes	maximal, characteristic
9	C₃₁×#1942	C₂	1	1	yes	maximal, characteristic
10	C₃₁×#1878	C₂	1	2	yes	maximal
11	C₈×C₄⋊C₄×C₃₁	C₂	1	1	yes	maximal, characteristic
12	C₂²×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
13	C₂²×Q₁₆×C₃₁	C₂²	1	2	yes	—
14	C₂²×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
15	C₂×C₃₁×C₄⋊Q₈	C₂²	1	2	yes	—
16	C₂×C₄×Q₈×C₃₁	C₂²	1	2	yes	—
17	C₃₁×#494	—	2	4	no	—
18	C₄×Q₁₆×C₃₁	—	2	4	no	—
19	C₂×C₃₁×#107	C₂²	1	1	yes	characteristic
20	C₂×C₃₁×#107	C₂²	1	1	yes	characteristic
21	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×C₃₁×#103	C₂²	1	2	yes	—
23	C₂×C₃₁×#103	C₂²	1	2	yes	—
24	C₂×C₃₁×#103	C₂²	1	2	yes	—
25	C₂×C₃₁×#103	C₂²	1	2	yes	—
26	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
29	C₃₁×#400	—	2	2	no	—
30	C₃₁×#398	—	2	2	no	—
31	C₃₁×#391	C₂²	1	2	yes	—
32	C₃₁×#391	C₂²	1	2	yes	—
33	C₃₁×#391	C₂²	1	2	yes	—
34	C₃₁×#389	C₂²	1	2	yes	—
35	C₃₁×#387	—	2	2	no	—
36	C₃₁×#387	—	2	2	no	—
37	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
38	C₃₁×#340	C₂²	1	2	yes	—
39	C₃₁×#336	C₂²	1	1	yes	characteristic
40	C₃₁×#336	C₂²	1	1	yes	characteristic
41	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
42	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
43	C₂×Q₁₆×C₃₁	—	2	4	no	—
44	C₂×Q₁₆×C₃₁	—	2	2	no	—
45	C₂×Q₁₆×C₃₁	—	2	2	no	—
46	C₂×Q₁₆×C₃₁	—	2	2	no	—
47	C₂×Q₁₆×C₃₁	—	2	4	no	—
48	C₂×Q₁₆×C₃₁	—	2	2	no	—
49	C₂×Q₁₆×C₃₁	—	2	2	no	—
50	C₂×Q₁₆×C₃₁	—	4	2	no	—
51	C₂×Q₁₆×C₃₁	D₄	1	4	yes	—
52	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
53	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
54	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
55	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
56	C₃₁×C₄⋊Q₈	—	2	4	no	—
57	C₃₁×C₄⋊Q₈	—	4	2	no	—
58	C₄×Q₈×C₃₁	—	2	4	no	—
59	C₄×Q₈×C₃₁	—	4	2	no	—
60	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
61	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
62	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
63	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
64	C₂×C₄⋊C₄×C₃₁	D₄	1	1	yes	characteristic
65	C₂×C₄⋊C₄×C₃₁	D₄	1	1	yes	characteristic
66	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
67	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
68	C₂×C₄²×C₃₁	—	2	2	no	—
69	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
70	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
71	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
72	C₃₁×#107	—	2	2	no	—
73	C₃₁×#107	—	2	2	no	—
74	C₃₁×C₄⋊C₈	—	2	2	no	—
75	C₃₁×#103	—	2	4	no	—
76	C₃₁×#103	—	4	2	no	—
77	C₃₁×#103	—	4	2	no	—
78	C₃₁×#103	—	4	2	no	—
79	C₄×C₈×C₃₁	—	2	2	no	—
80	C₄×C₈×C₃₁	—	2	2	no	—
81	C₄×C₈×C₃₁	—	2	2	no	—
82	C₃₁×#95	—	2	2	no	—
83	C₃₁×#95	—	2	2	no	—
84	C₃₁×#95	—	2	2	no	—
85	C₃₁×#95	—	2	2	no	—
86	C₃₁×#95	—	2	2	no	—
87	C₃₁×#95	—	2	2	no	—
88	C₃₁×#95	—	2	2	no	—
89	C₃₁×#95	D₄	1	1	yes	characteristic
90	C₃₁×#95	D₄	1	1	yes	characteristic
91	C₂×Q₈×C₃₁	—	2	2	no	—
92	C₂×Q₈×C₃₁	—	2	2	no	—
93	C₂×Q₈×C₃₁	—	2	2	no	—
94	C₂×Q₈×C₃₁	—	2	2	no	—
95	C₂×Q₈×C₃₁	—	2	2	no	—
96	C₂×Q₈×C₃₁	—	2	2	no	—
97	C₂×Q₈×C₃₁	—	2	2	no	—
98	C₂×Q₈×C₃₁	—	2	2	no	—
99	C₂×Q₈×C₃₁	—	2	2	no	—
100	C₂×Q₈×C₃₁	—	2	2	no	—
101	C₂×Q₈×C₃₁	—	2	2	no	—
102	C₂×Q₈×C₃₁	C₂×D₄	1	4	yes	—
103	C₂²×C₄×C₃₁	—	2	2	no	—
104	C₂²×C₄×C₃₁	—	2	2	no	—
105	C₂²×C₄×C₃₁	—	2	2	no	—
106	C₂²×C₄×C₃₁	—	2	2	no	—
107	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
114	Q₁₆×C₃₁	—	2	8	no	—
115	Q₁₆×C₃₁	—	4	8	no	—
116	Q₁₆×C₃₁	—	4	4	no	—
117	C₂×C₈×C₃₁	—	2	1	no	—
118	C₂×C₈×C₃₁	—	2	1	no	—
119	C₂×C₈×C₃₁	—	2	1	no	—
120	C₂×C₈×C₃₁	—	2	1	no	—
121	C₂×C₈×C₃₁	—	2	1	no	—
122	C₂×C₈×C₃₁	—	2	1	no	—
123	C₂×C₈×C₃₁	—	2	1	no	—
124	C₂×C₈×C₃₁	—	2	1	no	—
125	C₂×C₈×C₃₁	C₂×D₄	1	2	yes	—
126	C₂×C₈×C₃₁	#41	1	2	yes	—
127	C₂×C₈×C₃₁	#41	1	2	yes	—
128	C₂×C₈×C₃₁	#41	1	2	yes	—
129	C₄⋊C₄×C₃₁	—	2	2	no	—
130	C₄⋊C₄×C₃₁	—	2	2	no	—
131	C₄⋊C₄×C₃₁	—	2	2	no	—
132	C₄⋊C₄×C₃₁	—	2	2	no	—
133	C₄⋊C₄×C₃₁	—	2	2	no	—
134	C₄⋊C₄×C₃₁	—	4	4	no	—
135	C₄⋊C₄×C₃₁	—	4	4	no	—
136	C₄⋊C₄×C₃₁	—	4	4	no	—
137	C₄⋊C₄×C₃₁	—	4	4	no	—
138	C₄⋊C₄×C₃₁	Q₁₆	1	4	yes	complemented
139	C₄²×C₃₁	—	2	1	no	—
140	C₄²×C₃₁	—	2	1	no	—
141	C₄²×C₃₁	—	2	1	no	—
142	C₄²×C₃₁	—	2	1	no	—
143	C₄²×C₃₁	—	2	1	no	—
144	C₄²×C₃₁	—	2	1	no	—
145	C₄²×C₃₁	—	4	4	no	—
146	#26255	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
147	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
148	Q₈×C₃₁	—	2	4	no	—
149	Q₈×C₃₁	—	2	4	no	—
150	Q₈×C₃₁	—	4	2	no	—
151	Q₈×C₃₁	—	4	2	no	—
152	Q₈×C₃₁	—	4	2	no	—
153	Q₈×C₃₁	—	4	2	no	—
154	Q₈×C₃₁	—	4	2	no	—
155	Q₈×C₃₁	—	4	2	no	—
156	C₂×C₄×C₃₁	—	2	1	no	—
157	C₂×C₄×C₃₁	—	2	1	no	—
158	C₂×C₄×C₃₁	—	2	1	no	—
159	C₂×C₄×C₃₁	—	2	1	no	—
160	C₂×C₄×C₃₁	—	2	1	no	—
161	C₂×C₄×C₃₁	—	2	1	no	—
162	C₂×C₄×C₃₁	—	2	1	no	—
163	C₂×C₄×C₃₁	—	2	1	no	—
164	C₂×C₄×C₃₁	—	2	1	no	—
165	C₂×C₄×C₃₁	—	2	1	no	—
166	C₂×C₄×C₃₁	—	2	4	no	—
167	C₂×C₄×C₃₁	—	2	1	no	—
168	C₂×C₄×C₃₁	—	2	1	no	—
169	C₂×C₄×C₃₁	—	2	1	no	—
170	C₂×C₄×C₃₁	—	2	1	no	—
171	C₂×C₄×C₃₁	—	4	2	no	—
172	C₂×C₄×C₃₁	—	4	2	no	—
173	C₂×C₄×C₃₁	—	4	2	no	—
174	C₂×C₄×C₃₁	—	4	2	no	—
175	C₂×C₄×C₃₁	—	4	2	no	—
176	C₂×C₄×C₃₁	—	4	2	no	—
177	C₂×C₄×C₃₁	—	4	2	no	—
178	C₂×C₄×C₃₁	—	4	2	no	—
179	C₂×C₄×C₃₁	—	4	2	no	—
180	C₂×C₄×C₃₁	—	4	2	no	—
181	C₂×C₄×C₃₁	—	4	2	no	—
182	C₂×C₄×C₃₁	C₂×Q₁₆	1	2	yes	—
183	C₂×C₄×C₃₁	C₂×Q₁₆	1	2	yes	—
184	C₂×C₄×C₃₁	C₂×Q₁₆	1	2	yes	—
185	C₂×C₄×C₃₁	#135	1	2	yes	—
186	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
187	C₂×C₄×C₃₁	C₂×#41	1	1	yes	characteristic
188	C₂×C₄×C₃₁	C₂×#41	1	1	yes	characteristic
189	C₂×C₄×C₃₁	C₂×#41	1	1	yes	characteristic
190	C₂×C₄×C₃₁	H(5,𝔽₂)	1	1	yes	characteristic
191	C₂×C₄×C₃₁	H(5,𝔽₂)	1	1	yes	characteristic
192	C₈×C₃₁	—	2	2	no	—
193	C₈×C₃₁	—	4	1	no	—
194	C₈×C₃₁	—	4	1	no	—
195	C₈×C₃₁	#123	1	4	yes	—
196	C₂×#494	C₂×C₃₁	1	1	yes	characteristic
197	C₂×C₄×Q₁₆	C₂×C₃₁	1	1	yes	characteristic
198	#2446	C₂×C₃₁	1	2	yes	—
199	#2056	C₂×C₃₁	1	2	yes	—
200	#2043	C₂×C₃₁	1	2	yes	—
201	#1969	C₂×C₃₁	1	1	yes	characteristic
202	#1969	C₂×C₃₁	1	1	yes	characteristic
203	#1969	C₂×C₃₁	1	1	yes	characteristic
204	#1942	C₂×C₃₁	1	1	yes	characteristic
205	#1878	C₂×C₃₁	1	2	yes	—
206	C₈×C₄⋊C₄	C₂×C₃₁	1	1	yes	characteristic
207	C₂²×C₃₁	#532	1	1	yes	characteristic
208	C₂²×C₃₁	D₄²	1	1	yes	characteristic
209	C₂²×C₃₁	#550	1	1	yes	characteristic
210	C₂²×C₃₁	C₂²×Q₁₆	1	1	yes	characteristic
211	C₂²×C₃₁	C₂×#135	1	1	yes	characteristic
212	C₂²×C₃₁	#578	1	1	yes	characteristic
213	C₂²×C₃₁	#578	1	1	yes	characteristic
214	C₄×C₃₁	—	2	2	no	—
215	C₄×C₃₁	—	2	2	no	—
216	C₄×C₃₁	—	2	2	no	—
217	C₄×C₃₁	—	2	2	no	—
218	C₄×C₃₁	—	4	1	no	—
219	C₄×C₃₁	—	4	4	no	—
220	C₄×C₃₁	—	4	1	no	—
221	C₄×C₃₁	—	8	2	no	—
222	C₄×C₃₁	—	8	2	no	—
223	C₄×C₃₁	—	8	2	no	—
224	C₄×C₃₁	C₂×#123	1	1	yes	characteristic
225	C₄×C₃₁	#540	1	1	yes	characteristic
226	C₄×C₃₁	#546	1	1	yes	characteristic
227	C₄×C₃₁	#559	1	1	yes	characteristic
228	C₂²×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
229	C₂²×Q₁₆	C₂²×C₃₁	1	2	yes	—
230	C₂²×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
231	C₂×C₄⋊Q₈	C₂²×C₃₁	1	2	yes	—
232	C₂×C₄×Q₈	C₂²×C₃₁	1	2	yes	—
233	#494	—	2	4	no	—
234	C₄×Q₁₆	—	2	4	no	—
235	C₂×#107	C₂²×C₃₁	1	1	yes	characteristic
236	C₂×#107	C₂²×C₃₁	1	1	yes	characteristic
237	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
238	C₂×#103	C₂²×C₃₁	1	2	yes	—
239	C₂×#103	C₂²×C₃₁	1	2	yes	—
240	C₂×#103	C₂²×C₃₁	1	2	yes	—
241	C₂×#103	C₂²×C₃₁	1	2	yes	—
242	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
243	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
244	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
245	#400	—	2	2	no	—
246	#398	—	2	2	no	—
247	#391	C₂²×C₃₁	1	2	yes	—
248	#391	C₂²×C₃₁	1	2	yes	—
249	#391	C₂²×C₃₁	1	2	yes	—
250	#389	C₂²×C₃₁	1	2	yes	—
251	#387	—	2	2	no	—
252	#387	—	2	2	no	—
253	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
254	#340	C₂²×C₃₁	1	2	yes	—
255	#336	C₂²×C₃₁	1	1	yes	characteristic
256	#336	C₂²×C₃₁	1	1	yes	characteristic
257	C₂×C₃₁	#2445	1	1	yes	characteristic
258	C₂×C₃₁	#3170	1	1	yes	characteristic
259	C₂×C₃₁	#3177	1	1	yes	characteristic
260	C₂×C₃₁	#3285	1	1	yes	characteristic
261	C₂×C₃₁	D₄×Q₁₆	1	1	yes	characteristic
262	C₂×C₃₁	#3393	1	1	yes	characteristic
263	C₂×C₃₁	#3395	1	1	yes	characteristic
264	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
265	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
266	C₂×Q₁₆	—	2	4	no	—
267	C₂×Q₁₆	—	2	2	no	—
268	C₂×Q₁₆	—	2	2	no	—
269	C₂×Q₁₆	—	2	2	no	—
270	C₂×Q₁₆	—	2	4	no	—
271	C₂×Q₁₆	—	2	2	no	—
272	C₂×Q₁₆	—	2	2	no	—
273	C₂×Q₁₆	—	4	2	no	—
274	C₂×Q₁₆	D₄×C₃₁	1	4	yes	—
275	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
276	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
277	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
278	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
279	C₄⋊Q₈	—	2	4	no	—
280	C₄⋊Q₈	—	4	2	no	—
281	C₄×Q₈	—	2	4	no	—
282	C₄×Q₈	—	4	2	no	—
283	C₂×C₄⋊C₄	—	2	2	no	—
284	C₂×C₄⋊C₄	—	2	2	no	—
285	C₂×C₄⋊C₄	—	2	2	no	—
286	C₂×C₄⋊C₄	—	2	2	no	—
287	C₂×C₄⋊C₄	D₄×C₃₁	1	1	yes	characteristic
288	C₂×C₄⋊C₄	D₄×C₃₁	1	1	yes	characteristic
289	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
290	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
291	C₂×C₄²	—	2	2	no	—
292	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
293	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
294	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
295	#107	—	2	2	no	—
296	#107	—	2	2	no	—
297	C₄⋊C₈	—	2	2	no	—
298	#103	—	2	4	no	—
299	#103	—	4	2	no	—
300	#103	—	4	2	no	—
301	#103	—	4	2	no	—
302	C₄×C₈	—	2	2	no	—
303	C₄×C₈	—	2	2	no	—
304	C₄×C₈	—	2	2	no	—
305	#95	—	2	2	no	—
306	#95	—	2	2	no	—
307	#95	—	2	2	no	—
308	#95	—	2	2	no	—
309	#95	—	2	2	no	—
310	#95	—	2	2	no	—
311	#95	—	2	2	no	—
312	#95	D₄×C₃₁	1	1	yes	characteristic
313	#95	D₄×C₃₁	1	1	yes	characteristic
314	C₃₁	#26255	1	1	yes	characteristic, direct product factor, Sylow
315	C₂×Q₈	—	2	2	no	—
316	C₂×Q₈	—	2	2	no	—
317	C₂×Q₈	—	2	2	no	—
318	C₂×Q₈	—	2	2	no	—
319	C₂×Q₈	—	2	2	no	—
320	C₂×Q₈	—	2	2	no	—
321	C₂×Q₈	—	2	2	no	—
322	C₂×Q₈	—	2	2	no	—
323	C₂×Q₈	—	2	2	no	—
324	C₂×Q₈	—	2	2	no	—
325	C₂×Q₈	—	2	2	no	—
326	C₂×Q₈	C₂×D₄×C₃₁	1	4	yes	—
327	C₂²×C₄	—	2	2	no	—
328	C₂²×C₄	—	2	2	no	—
329	C₂²×C₄	—	2	2	no	—
330	C₂²×C₄	—	2	2	no	—
331	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
332	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
333	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
334	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
335	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
336	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
337	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
338	Q₁₆	—	2	8	no	—
339	Q₁₆	—	4	8	no	—
340	Q₁₆	—	4	4	no	—
341	C₂×C₈	—	2	1	no	—
342	C₂×C₈	—	2	1	no	—
343	C₂×C₈	—	2	1	no	—
344	C₂×C₈	—	2	1	no	—
345	C₂×C₈	—	2	1	no	—
346	C₂×C₈	—	2	1	no	—
347	C₂×C₈	—	2	1	no	—
348	C₂×C₈	—	2	1	no	—
349	C₂×C₈	C₂×D₄×C₃₁	1	2	yes	—
350	C₂×C₈	#41×C₃₁	1	2	yes	—
351	C₂×C₈	#41×C₃₁	1	2	yes	—
352	C₂×C₈	#41×C₃₁	1	2	yes	—
353	C₄⋊C₄	—	2	2	no	—
354	C₄⋊C₄	—	2	2	no	—
355	C₄⋊C₄	—	2	2	no	—
356	C₄⋊C₄	—	2	2	no	—
357	C₄⋊C₄	—	2	2	no	—
358	C₄⋊C₄	—	4	4	no	—
359	C₄⋊C₄	—	4	4	no	—
360	C₄⋊C₄	—	4	4	no	—
361	C₄⋊C₄	—	4	4	no	—
362	C₄⋊C₄	Q₁₆×C₃₁	1	4	yes	complemented
363	C₄²	—	2	1	no	—
364	C₄²	—	2	1	no	—
365	C₄²	—	2	1	no	—
366	C₄²	—	2	1	no	—
367	C₄²	—	2	1	no	—
368	C₄²	—	2	1	no	—
369	C₄²	—	4	4	no	—
370	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
371	Q₈	—	2	4	no	—
372	Q₈	—	2	4	no	—
373	Q₈	—	4	2	no	—
374	Q₈	—	4	2	no	—
375	Q₈	—	4	2	no	—
376	Q₈	—	4	2	no	—
377	Q₈	—	4	2	no	—
378	Q₈	—	4	2	no	—
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	2	1	no	—
381	C₂×C₄	—	2	1	no	—
382	C₂×C₄	—	2	1	no	—
383	C₂×C₄	—	2	1	no	—
384	C₂×C₄	—	2	1	no	—
385	C₂×C₄	—	2	1	no	—
386	C₂×C₄	—	2	1	no	—
387	C₂×C₄	—	2	1	no	—
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	2	4	no	—
390	C₂×C₄	—	2	1	no	—
391	C₂×C₄	—	2	1	no	—
392	C₂×C₄	—	2	1	no	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	4	2	no	—
395	C₂×C₄	—	4	2	no	—
396	C₂×C₄	—	4	2	no	—
397	C₂×C₄	—	4	2	no	—
398	C₂×C₄	—	4	2	no	—
399	C₂×C₄	—	4	2	no	—
400	C₂×C₄	—	4	2	no	—
401	C₂×C₄	—	4	2	no	—
402	C₂×C₄	—	4	2	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	C₂×Q₁₆×C₃₁	1	2	yes	—
406	C₂×C₄	C₂×Q₁₆×C₃₁	1	2	yes	—
407	C₂×C₄	C₂×Q₁₆×C₃₁	1	2	yes	—
408	C₂×C₄	C₃₁×#135	1	2	yes	—
409	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
410	C₂×C₄	C₂×#41×C₃₁	1	1	yes	characteristic
411	C₂×C₄	C₂×#41×C₃₁	1	1	yes	characteristic
412	C₂×C₄	C₂×#41×C₃₁	1	1	yes	characteristic
413	C₂×C₄	C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
414	C₂×C₄	C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
415	C₈	—	2	2	no	—
416	C₈	—	4	1	no	—
417	C₈	—	4	1	no	—
418	C₈	C₃₁×#123	1	4	yes	—
419	C₂²	C₃₁×#532	1	1	yes	characteristic
420	C₂²	D₄²×C₃₁	1	1	yes	characteristic
421	C₂²	C₃₁×#550	1	1	yes	characteristic
422	C₂²	C₂²×Q₁₆×C₃₁	1	1	yes	characteristic
423	C₂²	C₂×C₃₁×#135	1	1	yes	characteristic
424	C₂²	C₃₁×#578	1	1	yes	characteristic
425	C₂²	C₃₁×#578	1	1	yes	characteristic
426	C₄	—	2	2	no	—
427	C₄	—	2	2	no	—
428	C₄	—	2	2	no	—
429	C₄	—	2	2	no	—
430	C₄	—	4	1	no	—
431	C₄	—	4	4	no	—
432	C₄	—	4	1	no	—
433	C₄	—	8	2	no	—
434	C₄	—	8	2	no	—
435	C₄	—	8	2	no	—
436	C₄	C₂×C₃₁×#123	1	1	yes	characteristic
437	C₄	C₃₁×#540	1	1	yes	characteristic
438	C₄	C₃₁×#546	1	1	yes	characteristic
439	C₄	C₃₁×#559	1	1	yes	characteristic
440	C₂	C₃₁×#2445	1	1	yes	characteristic
441	C₂	C₃₁×#3170	1	1	yes	characteristic
442	C₂	C₃₁×#3177	1	1	yes	characteristic
443	C₂	C₃₁×#3285	1	1	yes	characteristic
444	C₂	D₄×Q₁₆×C₃₁	1	1	yes	characteristic
445	C₂	C₃₁×#3393	1	1	yes	characteristic
446	C₂	C₃₁×#3395	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
138. C₄⋊C₄×C₃₁	Q₁₆	semidirect
146. #26255	C₃₁	direct (N × H)
314. C₃₁	#26255	direct (N × H)
362. C₄⋊C₄	Q₁₆×C₃₁	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₃₁×#494	2
C₂×C₄×Q₁₆×C₃₁	2
C₃₁×#2446	2
C₃₁×#2056	2
C₃₁×#2043	2
C₃₁×#1969	2
C₃₁×#1942	2
C₃₁×#1878	2
C₈×C₄⋊C₄×C₃₁	2
#26255	31

Subgroups — C31×#26255 #21483014

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#26255 #21483014