Subgroups — C₃₁×#25279 #21482038

Order 7936.

878 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#486	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃₁×#475	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#2548	C₂	1	1	yes	maximal, characteristic
4	C₃₁×#2365	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#2065	C₂	1	2	yes	maximal, complemented
6	C₃₁×#2042	C₂	1	2	yes	maximal, complemented
7	C₃₁×#1983	C₂	1	2	yes	maximal, complemented
8	C₃₁×#1982	C₂	1	1	yes	maximal, characteristic
9	C₃₁×#1939	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#1926	C₂	1	2	yes	maximal, complemented
11	C₄×C₃₁×#103	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
13	C₂×C₃₁×#127	C₂²	1	1	yes	characteristic
14	C₂×C₃₁×#124	C₂²	1	2	yes	—
15	C₂×C₄×Q₈×C₃₁	—	2	1	no	—
16	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
17	C₃₁×#486	—	2	4	no	—
18	C₃₁×#475	—	2	4	no	—
19	C₂×C₃₁×#106	C₂²	1	2	yes	—
20	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×C₃₁×C₄⋊C₈	C₂²	1	2	yes	—
22	C₂×C₃₁×#103	C₂²	1	1	yes	characteristic
23	C₂×C₃₁×#103	C₂²	1	2	yes	—
24	C₂×C₃₁×#103	C₂²	1	1	yes	characteristic
25	C₂×C₃₁×#102	C₂²	1	2	yes	—
26	C₂×C₃₁×#102	C₂²	1	2	yes	—
27	C₂×C₃₁×#102	C₂²	1	2	yes	—
28	C₂×C₃₁×#102	C₂²	1	2	yes	—
29	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
30	C₃₁×#394	—	2	2	no	—
31	C₃₁×#391	—	2	1	no	—
32	C₃₁×#390	—	2	1	no	—
33	C₃₁×#390	—	2	1	no	—
34	C₃₁×#390	C₂²	1	2	yes	—
35	C₃₁×#389	C₂²	1	2	yes	—
36	C₃₁×#387	—	2	2	no	—
37	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
38	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
39	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
40	C₃₁×#340	C₂²	1	1	yes	characteristic
41	C₃₁×#340	C₂²	1	1	yes	characteristic
42	C₃₁×#336	C₂²	1	2	yes	—
43	C₂²×Q₈×C₃₁	—	2	1	no	—
44	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
45	C₂²×D₄×C₃₁	—	2	1	no	—
46	C₂²×D₄×C₃₁	—	2	1	no	—
47	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
48	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
49	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
50	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
51	C₃₁×C₄⋊Q₈	—	2	2	no	—
52	C₃₁×C₄⋊Q₈	D₄	1	4	yes	—
53	C₃₁×#127	—	2	2	no	—
54	C₃₁×#127	—	2	2	no	—
55	C₃₁×#124	—	2	4	no	—
56	C₃₁×#124	—	4	2	no	—
57	C₄×Q₈×C₃₁	—	2	2	no	—
58	C₄×Q₈×C₃₁	—	2	2	no	—
59	C₄×Q₈×C₃₁	—	4	4	no	—
60	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
61	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
62	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
63	C₂×C₄⋊C₄×C₃₁	D₄	1	1	yes	characteristic
64	C₂×C₄⋊C₄×C₃₁	D₄	1	1	yes	characteristic
65	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
66	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
67	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
68	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
69	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
70	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
71	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
72	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
73	C₂×C₄²×C₃₁	—	2	2	no	—
74	C₂×C₄²×C₃₁	—	2	1	no	—
75	C₂×C₄²×C₃₁	—	2	1	no	—
76	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
77	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
78	C₃₁×#106	—	2	4	no	—
79	C₃₁×C₄⋊C₈	—	2	2	no	—
80	C₃₁×C₄⋊C₈	—	4	2	no	—
81	C₃₁×#103	—	2	2	no	—
82	C₃₁×#103	—	2	4	no	—
83	C₃₁×#103	—	2	2	no	—
84	C₃₁×#102	—	2	4	no	—
85	C₃₁×#102	—	2	4	no	—
86	C₃₁×#102	—	2	4	no	—
87	C₃₁×#102	—	4	2	no	—
88	C₄×C₈×C₃₁	—	2	2	no	—
89	C₃₁×#95	—	2	1	no	—
90	C₃₁×#95	—	2	2	no	—
91	C₃₁×#95	—	2	2	no	—
92	C₃₁×#95	D₄	1	2	yes	—
93	C₂⁴×C₃₁	—	2	2	no	—
94	C₂×Q₈×C₃₁	—	2	4	no	—
95	C₂×Q₈×C₃₁	—	2	1	no	—
96	C₂×Q₈×C₃₁	—	2	1	no	—
97	C₂×Q₈×C₃₁	—	2	1	no	—
98	C₂×Q₈×C₃₁	—	2	1	no	—
99	C₂×Q₈×C₃₁	—	2	1	no	—
100	C₂×Q₈×C₃₁	—	4	2	no	—
101	C₂×Q₈×C₃₁	—	4	2	no	—
102	C₂×Q₈×C₃₁	#41	1	2	yes	—
103	C₂×D₄×C₃₁	—	2	2	no	—
104	C₂×D₄×C₃₁	—	2	2	no	—
105	C₂×D₄×C₃₁	—	2	2	no	—
106	C₂×D₄×C₃₁	—	2	2	no	—
107	C₂×D₄×C₃₁	—	2	2	no	—
108	C₂×D₄×C₃₁	—	2	2	no	—
109	C₂×D₄×C₃₁	—	4	2	no	—
110	C₂×D₄×C₃₁	—	4	2	no	—
111	C₂×D₄×C₃₁	—	4	2	no	—
112	C₂×D₄×C₃₁	—	4	2	no	—
113	C₂×D₄×C₃₁	—	8	1	no	—
114	C₂×D₄×C₃₁	—	8	1	no	—
115	C₂²×C₄×C₃₁	—	2	1	no	—
116	C₂²×C₄×C₃₁	—	2	2	no	—
117	C₂²×C₄×C₃₁	—	2	1	no	—
118	C₂²×C₄×C₃₁	—	2	1	no	—
119	C₂²×C₄×C₃₁	—	2	1	no	—
120	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
121	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
122	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
125	C₂×C₈×C₃₁	—	2	1	no	—
126	C₂×C₈×C₃₁	—	2	1	no	—
127	C₂×C₈×C₃₁	—	2	2	no	—
128	C₂×C₈×C₃₁	—	2	2	no	—
129	C₂×C₈×C₃₁	—	2	1	no	—
130	C₂×C₈×C₃₁	—	2	1	no	—
131	C₂×C₈×C₃₁	—	2	2	no	—
132	C₂×C₈×C₃₁	—	2	1	no	—
133	C₂×C₈×C₃₁	—	2	1	no	—
134	C₄⋊C₄×C₃₁	—	2	4	no	—
135	C₄⋊C₄×C₃₁	—	2	2	no	—
136	C₄⋊C₄×C₃₁	—	2	2	no	—
137	C₄⋊C₄×C₃₁	—	2	2	no	—
138	C₄⋊C₄×C₃₁	—	2	1	no	—
139	C₄⋊C₄×C₃₁	—	2	1	no	—
140	C₄⋊C₄×C₃₁	—	2	1	no	—
141	C₄⋊C₄×C₃₁	—	2	1	no	—
142	C₄⋊C₄×C₃₁	—	2	1	no	—
143	C₄⋊C₄×C₃₁	—	4	4	no	—
144	C₄⋊C₄×C₃₁	—	4	2	no	—
145	C₄⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
146	C₄⋊C₄×C₃₁	#41	1	2	yes	—
147	C₂²⋊C₄×C₃₁	—	4	4	no	—
148	C₂²⋊C₄×C₃₁	—	4	4	no	—
149	C₂²⋊C₄×C₃₁	—	8	2	no	—
150	C₂²⋊C₄×C₃₁	—	8	2	no	—
151	C₄²×C₃₁	—	2	2	no	—
152	C₄²×C₃₁	—	2	2	no	—
153	C₄²×C₃₁	—	4	4	no	—
154	C₄²×C₃₁	—	4	2	no	—
155	C₄²×C₃₁	—	4	2	no	—
156	C₄²×C₃₁	C₂×D₄	1	2	yes	—
157	C₄²×C₃₁	#41	1	2	yes	—
158	#25279	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
159	C₂³×C₃₁	—	4	2	no	—
160	C₂³×C₃₁	—	4	2	no	—
161	C₂³×C₃₁	—	4	2	no	—
162	C₂³×C₃₁	—	4	2	no	—
163	C₂³×C₃₁	—	4	2	no	—
164	C₂³×C₃₁	—	4	2	no	—
165	C₂³×C₃₁	—	4	2	no	—
166	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
167	Q₈×C₃₁	—	2	2	no	—
168	Q₈×C₃₁	—	2	2	no	—
169	Q₈×C₃₁	—	4	1	no	—
170	Q₈×C₃₁	—	4	1	no	—
171	Q₈×C₃₁	—	4	8	no	—
172	D₄×C₃₁	—	4	2	no	—
173	D₄×C₃₁	—	4	2	no	—
174	D₄×C₃₁	—	4	2	no	—
175	D₄×C₃₁	—	4	2	no	—
176	D₄×C₃₁	—	8	4	no	—
177	D₄×C₃₁	—	8	4	no	—
178	C₂×C₄×C₃₁	—	2	1	no	—
179	C₂×C₄×C₃₁	—	2	1	no	—
180	C₂×C₄×C₃₁	—	2	4	no	—
181	C₂×C₄×C₃₁	—	2	2	no	—
182	C₂×C₄×C₃₁	—	2	2	no	—
183	C₂×C₄×C₃₁	—	2	2	no	—
184	C₂×C₄×C₃₁	—	2	2	no	—
185	C₂×C₄×C₃₁	—	2	2	no	—
186	C₂×C₄×C₃₁	—	2	2	no	—
187	C₂×C₄×C₃₁	—	2	2	no	—
188	C₂×C₄×C₃₁	—	2	2	no	—
189	C₂×C₄×C₃₁	—	4	1	no	—
190	C₂×C₄×C₃₁	—	4	1	no	—
191	C₂×C₄×C₃₁	—	4	2	no	—
192	C₂×C₄×C₃₁	—	4	1	no	—
193	C₂×C₄×C₃₁	—	4	2	no	—
194	C₂×C₄×C₃₁	—	4	1	no	—
195	C₂×C₄×C₃₁	—	4	1	no	—
196	C₂×C₄×C₃₁	—	4	1	no	—
197	C₂×C₄×C₃₁	—	4	1	no	—
198	C₂×C₄×C₃₁	—	4	1	no	—
199	C₂×C₄×C₃₁	—	4	1	no	—
200	C₂×C₄×C₃₁	—	4	1	no	—
201	C₂×C₄×C₃₁	#121	1	2	yes	—
202	C₂×C₄×C₃₁	#121	1	2	yes	—
203	C₂×C₄×C₃₁	#135	1	2	yes	—
204	C₂×C₄×C₃₁	AGL(1,ℤ/8)	1	2	yes	—
205	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
206	C₂×C₄×C₃₁	C₂×#41	1	1	yes	characteristic
207	C₂×C₄×C₃₁	C₂×#41	1	1	yes	characteristic
208	C₂×C₄×C₃₁	C₂×#41	1	1	yes	characteristic
209	C₂×C₄×C₃₁	H(5,𝔽₂)	1	1	yes	characteristic
210	C₂×C₄×C₃₁	2₋¹⁺⁴	1	1	yes	characteristic
211	C₈×C₃₁	—	4	1	no	—
212	C₈×C₃₁	—	4	1	no	—
213	C₈×C₃₁	—	4	2	no	—
214	C₂×#486	C₂×C₃₁	1	1	yes	characteristic
215	C₂×#475	C₂×C₃₁	1	1	yes	characteristic, complemented
216	#2548	C₂×C₃₁	1	1	yes	characteristic
217	#2365	C₂×C₃₁	1	1	yes	characteristic, complemented
218	#2065	C₂×C₃₁	1	2	yes	complemented
219	#2042	C₂×C₃₁	1	2	yes	complemented
220	#1983	C₂×C₃₁	1	2	yes	complemented
221	#1982	C₂×C₃₁	1	1	yes	characteristic
222	#1939	C₂×C₃₁	1	1	yes	characteristic, complemented
223	#1926	C₂×C₃₁	1	2	yes	complemented
224	C₄×#103	C₂×C₃₁	1	1	yes	characteristic, complemented
225	C₂²×C₃₁	—	8	2	no	—
226	C₂²×C₃₁	—	8	2	no	—
227	C₂²×C₃₁	—	8	2	no	—
228	C₂²×C₃₁	—	8	2	no	—
229	C₂²×C₃₁	—	8	2	no	—
230	C₂²×C₃₁	—	8	2	no	—
231	C₂²×C₃₁	—	8	2	no	—
232	C₂²×C₃₁	C₂×#121	1	1	yes	characteristic
233	C₂²×C₃₁	#546	1	1	yes	characteristic
234	C₂²×C₃₁	#548	1	1	yes	characteristic
235	C₂²×C₃₁	C₂×#135	1	1	yes	characteristic
236	C₂²×C₃₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
237	C₂²×C₃₁	#577	1	1	yes	characteristic
238	C₂²×C₃₁	#577	1	1	yes	characteristic
239	C₄×C₃₁	—	2	2	no	—
240	C₄×C₃₁	—	4	2	no	—
241	C₄×C₃₁	—	4	2	no	—
242	C₄×C₃₁	—	4	2	no	—
243	C₄×C₃₁	—	4	4	no	—
244	C₄×C₃₁	—	4	2	no	—
245	C₄×C₃₁	—	8	1	no	—
246	C₄×C₃₁	—	8	1	no	—
247	C₄×C₃₁	#463	1	4	yes	—
248	C₄×C₃₁	#529	1	1	yes	characteristic
249	C₄×C₃₁	#542	1	1	yes	characteristic
250	C₄×C₃₁	#548	1	1	yes	characteristic
251	C₄×C₃₁	#550	1	1	yes	characteristic
252	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
253	C₂×#127	C₂²×C₃₁	1	1	yes	characteristic
254	C₂×#124	C₂²×C₃₁	1	2	yes	—
255	C₂×C₄×Q₈	—	2	1	no	—
256	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
257	#486	—	2	4	no	—
258	#475	—	2	4	no	—
259	C₂×#106	C₂²×C₃₁	1	2	yes	—
260	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
261	C₂×C₄⋊C₈	C₂²×C₃₁	1	2	yes	—
262	C₂×#103	C₂²×C₃₁	1	2	yes	—
263	C₂×#103	C₂²×C₃₁	1	1	yes	characteristic
264	C₂×#103	C₂²×C₃₁	1	1	yes	characteristic
265	C₂×#102	C₂²×C₃₁	1	2	yes	—
266	C₂×#102	C₂²×C₃₁	1	2	yes	—
267	C₂×#102	C₂²×C₃₁	1	2	yes	—
268	C₂×#102	C₂²×C₃₁	1	2	yes	—
269	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
270	#394	—	2	2	no	—
271	#391	—	2	1	no	—
272	#390	—	2	1	no	—
273	#390	—	2	1	no	—
274	#390	C₂²×C₃₁	1	2	yes	—
275	#389	C₂²×C₃₁	1	2	yes	—
276	#387	—	2	2	no	—
277	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
278	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
279	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
280	#340	C₂²×C₃₁	1	1	yes	characteristic
281	#340	C₂²×C₃₁	1	1	yes	characteristic
282	#336	C₂²×C₃₁	1	2	yes	—
283	C₂×C₃₁	—	16	2	no	—
284	C₂×C₃₁	#2426	1	1	yes	characteristic
285	C₂×C₃₁	C₂×#463	1	1	yes	characteristic
286	C₂×C₃₁	#3043	1	1	yes	characteristic
287	C₂×C₃₁	#3304	1	1	yes	characteristic
288	C₂×C₃₁	#3332	1	1	yes	characteristic
289	C₂×C₃₁	#3365	1	1	yes	characteristic
290	C₂×C₃₁	#3373	1	1	yes	characteristic
291	C₂²×Q₈	—	2	1	no	—
292	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
293	C₂²×D₄	—	2	1	no	—
294	C₂²×D₄	—	2	1	no	—
295	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
296	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
297	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
298	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
299	C₄⋊Q₈	—	2	2	no	—
300	C₄⋊Q₈	D₄×C₃₁	1	4	yes	—
301	#127	—	2	2	no	—
302	#127	—	2	2	no	—
303	#124	—	2	4	no	—
304	#124	—	4	2	no	—
305	C₄×Q₈	—	2	2	no	—
306	C₄×Q₈	—	2	2	no	—
307	C₄×Q₈	—	4	4	no	—
308	C₂×C₄⋊C₄	—	2	1	no	—
309	C₂×C₄⋊C₄	—	2	2	no	—
310	C₂×C₄⋊C₄	—	2	1	no	—
311	C₂×C₄⋊C₄	D₄×C₃₁	1	1	yes	characteristic
312	C₂×C₄⋊C₄	D₄×C₃₁	1	1	yes	characteristic
313	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
314	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
315	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
316	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
317	C₂×C₂²⋊C₄	—	2	2	no	—
318	C₂×C₂²⋊C₄	—	2	2	no	—
319	C₂×C₂²⋊C₄	—	2	2	no	—
320	C₂×C₂²⋊C₄	—	2	2	no	—
321	C₂×C₄²	—	2	2	no	—
322	C₂×C₄²	—	2	1	no	—
323	C₂×C₄²	—	2	1	no	—
324	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
325	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
326	#106	—	2	4	no	—
327	C₄⋊C₈	—	2	2	no	—
328	C₄⋊C₈	—	4	2	no	—
329	#103	—	2	2	no	—
330	#103	—	2	4	no	—
331	#103	—	2	2	no	—
332	#102	—	2	4	no	—
333	#102	—	2	4	no	—
334	#102	—	2	4	no	—
335	#102	—	4	2	no	—
336	C₄×C₈	—	2	2	no	—
337	#95	—	2	1	no	—
338	#95	—	2	2	no	—
339	#95	—	2	2	no	—
340	#95	D₄×C₃₁	1	2	yes	—
341	C₃₁	#25279	1	1	yes	characteristic, direct product factor, Sylow
342	C₂⁴	—	2	2	no	—
343	C₂×Q₈	—	2	4	no	—
344	C₂×Q₈	—	2	1	no	—
345	C₂×Q₈	—	2	1	no	—
346	C₂×Q₈	—	2	1	no	—
347	C₂×Q₈	—	2	1	no	—
348	C₂×Q₈	—	2	1	no	—
349	C₂×Q₈	—	4	2	no	—
350	C₂×Q₈	—	4	2	no	—
351	C₂×Q₈	#41×C₃₁	1	2	yes	—
352	C₂×D₄	—	2	2	no	—
353	C₂×D₄	—	2	2	no	—
354	C₂×D₄	—	2	2	no	—
355	C₂×D₄	—	2	2	no	—
356	C₂×D₄	—	2	2	no	—
357	C₂×D₄	—	2	2	no	—
358	C₂×D₄	—	4	2	no	—
359	C₂×D₄	—	4	2	no	—
360	C₂×D₄	—	4	2	no	—
361	C₂×D₄	—	4	2	no	—
362	C₂×D₄	—	8	1	no	—
363	C₂×D₄	—	8	1	no	—
364	C₂²×C₄	—	2	1	no	—
365	C₂²×C₄	—	2	2	no	—
366	C₂²×C₄	—	2	1	no	—
367	C₂²×C₄	—	2	1	no	—
368	C₂²×C₄	—	2	1	no	—
369	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
370	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
371	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
372	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
373	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
374	C₂×C₈	—	2	1	no	—
375	C₂×C₈	—	2	1	no	—
376	C₂×C₈	—	2	2	no	—
377	C₂×C₈	—	2	2	no	—
378	C₂×C₈	—	2	1	no	—
379	C₂×C₈	—	2	1	no	—
380	C₂×C₈	—	2	2	no	—
381	C₂×C₈	—	2	1	no	—
382	C₂×C₈	—	2	1	no	—
383	C₄⋊C₄	—	2	4	no	—
384	C₄⋊C₄	—	2	2	no	—
385	C₄⋊C₄	—	2	2	no	—
386	C₄⋊C₄	—	2	2	no	—
387	C₄⋊C₄	—	2	1	no	—
388	C₄⋊C₄	—	2	1	no	—
389	C₄⋊C₄	—	2	1	no	—
390	C₄⋊C₄	—	2	1	no	—
391	C₄⋊C₄	—	2	1	no	—
392	C₄⋊C₄	—	4	4	no	—
393	C₄⋊C₄	—	4	2	no	—
394	C₄⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
395	C₄⋊C₄	#41×C₃₁	1	2	yes	—
396	C₂²⋊C₄	—	4	4	no	—
397	C₂²⋊C₄	—	4	4	no	—
398	C₂²⋊C₄	—	8	2	no	—
399	C₂²⋊C₄	—	8	2	no	—
400	C₄²	—	2	2	no	—
401	C₄²	—	2	2	no	—
402	C₄²	—	4	4	no	—
403	C₄²	—	4	2	no	—
404	C₄²	—	4	2	no	—
405	C₄²	C₂×D₄×C₃₁	1	2	yes	—
406	C₄²	#41×C₃₁	1	2	yes	—
407	C₂³	—	4	2	no	—
408	C₂³	—	4	2	no	—
409	C₂³	—	4	2	no	—
410	C₂³	—	4	2	no	—
411	C₂³	—	4	2	no	—
412	C₂³	—	4	2	no	—
413	C₂³	—	4	2	no	—
414	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
415	Q₈	—	2	2	no	—
416	Q₈	—	2	2	no	—
417	Q₈	—	4	8	no	—
418	Q₈	—	4	1	no	—
419	Q₈	—	4	1	no	—
420	D₄	—	4	2	no	—
421	D₄	—	4	2	no	—
422	D₄	—	4	2	no	—
423	D₄	—	4	2	no	—
424	D₄	—	8	4	no	—
425	D₄	—	8	4	no	—
426	C₂×C₄	—	2	1	no	—
427	C₂×C₄	—	2	1	no	—
428	C₂×C₄	—	2	4	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	2	2	no	—
432	C₂×C₄	—	2	2	no	—
433	C₂×C₄	—	2	2	no	—
434	C₂×C₄	—	2	2	no	—
435	C₂×C₄	—	2	2	no	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	4	1	no	—
438	C₂×C₄	—	4	1	no	—
439	C₂×C₄	—	4	2	no	—
440	C₂×C₄	—	4	1	no	—
441	C₂×C₄	—	4	2	no	—
442	C₂×C₄	—	4	1	no	—
443	C₂×C₄	—	4	1	no	—
444	C₂×C₄	—	4	1	no	—
445	C₂×C₄	—	4	1	no	—
446	C₂×C₄	—	4	1	no	—
447	C₂×C₄	—	4	1	no	—
448	C₂×C₄	—	4	1	no	—
449	C₂×C₄	C₃₁×#121	1	2	yes	—
450	C₂×C₄	C₃₁×#121	1	2	yes	—
451	C₂×C₄	C₃₁×#135	1	2	yes	—
452	C₂×C₄	C₃₁×AGL(1,ℤ/8)	1	2	yes	—
453	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
454	C₂×C₄	C₂×#41×C₃₁	1	1	yes	characteristic
455	C₂×C₄	C₂×#41×C₃₁	1	1	yes	characteristic
456	C₂×C₄	C₂×#41×C₃₁	1	1	yes	characteristic
457	C₂×C₄	C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
458	C₂×C₄	C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
459	C₈	—	4	1	no	—
460	C₈	—	4	1	no	—
461	C₈	—	4	2	no	—
462	C₂²	—	8	2	no	—
463	C₂²	—	8	2	no	—
464	C₂²	—	8	2	no	—
465	C₂²	—	8	2	no	—
466	C₂²	—	8	2	no	—
467	C₂²	—	8	2	no	—
468	C₂²	—	8	2	no	—
469	C₂²	C₂×C₃₁×#121	1	1	yes	characteristic
470	C₂²	C₃₁×#546	1	1	yes	characteristic
471	C₂²	C₃₁×#548	1	1	yes	characteristic
472	C₂²	C₂×C₃₁×#135	1	1	yes	characteristic
473	C₂²	C₂×C₃₁×AGL(1,ℤ/8)	1	1	yes	characteristic
474	C₂²	C₃₁×#577	1	1	yes	characteristic
475	C₂²	C₃₁×#577	1	1	yes	characteristic
476	C₄	—	2	2	no	—
477	C₄	—	4	2	no	—
478	C₄	—	4	2	no	—
479	C₄	—	4	2	no	—
480	C₄	—	4	4	no	—
481	C₄	—	4	2	no	—
482	C₄	—	8	1	no	—
483	C₄	—	8	1	no	—
484	C₄	C₃₁×#463	1	4	yes	—
485	C₄	C₃₁×#529	1	1	yes	characteristic
486	C₄	C₃₁×#542	1	1	yes	characteristic
487	C₄	C₃₁×#548	1	1	yes	characteristic
488	C₄	C₃₁×#550	1	1	yes	characteristic
489	C₂	—	16	2	no	—
490	C₂	C₃₁×#2426	1	1	yes	characteristic
491	C₂	C₂×C₃₁×#463	1	1	yes	characteristic
492	C₂	C₃₁×#3043	1	1	yes	characteristic
493	C₂	C₃₁×#3304	1	1	yes	characteristic
494	C₂	C₃₁×#3332	1	1	yes	characteristic
495	C₂	C₃₁×#3365	1	1	yes	characteristic
496	C₂	C₃₁×#3373	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₃₁
prime radical	C₂×C₃₁×#127	C₂²
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
2. C₂×C₃₁×#475	C₂	semidirect
4. C₃₁×#2365	C₂	semidirect
5. C₃₁×#2065	C₂	semidirect
6. C₃₁×#2042	C₂	semidirect
7. C₃₁×#1983	C₂	semidirect
9. C₃₁×#1939	C₂	semidirect
10. C₃₁×#1926	C₂	semidirect
11. C₄×C₃₁×#103	C₂	semidirect
158. #25279	C₃₁	direct (N × H)
215. C₂×#475	C₂×C₃₁	semidirect
217. #2365	C₂×C₃₁	semidirect
218. #2065	C₂×C₃₁	semidirect
219. #2042	C₂×C₃₁	semidirect
220. #1983	C₂×C₃₁	semidirect
222. #1939	C₂×C₃₁	semidirect
223. #1926	C₂×C₃₁	semidirect
224. C₄×#103	C₂×C₃₁	semidirect
341. C₃₁	#25279	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×#486	2
C₂×C₃₁×#475	2
C₃₁×#2548	2
C₃₁×#2365	2
C₃₁×#2065	2
C₃₁×#2042	2
C₃₁×#1983	2
C₃₁×#1982	2
C₃₁×#1939	2
C₃₁×#1926	2
C₄×C₃₁×#103	2
#25279	31

Subgroups — C31×#25279 #21482038

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#25279 #21482038