Subgroups — C₃₁×#26065 #21482824

Order 7936.

894 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#500	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃₁×#107	C₂	1	1	yes	maximal, characteristic
3	C₃₁×#2440	C₂	1	2	yes	maximal
4	C₃₁×#2083	C₂	1	2	yes	maximal, complemented
5	C₃₁×#2057	C₂	1	2	yes	maximal, complemented
6	C₃₁×#1942	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#1942	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#1852	C₂	1	2	yes	maximal
9	C₃₁×#1845	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#1808	C₂	1	1	yes	maximal, characteristic
11	C₈×C₂²⋊C₄×C₃₁	C₂	1	1	yes	maximal, characteristic
12	C₂³×C₈×C₃₁	C₂²	1	1	yes	characteristic
13	C₂×C₃₁×C₄⋊Q₈	C₂²	1	2	yes	—
14	C₂×C₃₁×C₂²⋊Q₈	—	2	2	no	—
15	C₂²×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
16	C₃₁×#500	—	2	4	no	—
17	C₂×C₃₁×#107	—	2	4	no	—
18	C₂×C₃₁×#107	C₂²	1	2	yes	—
19	C₂×C₃₁×#107	C₂²	1	1	yes	characteristic
20	C₂×C₃₁×#107	C₂²	1	1	yes	characteristic
21	C₂×C₃₁×#107	C₂²	1	2	yes	—
22	C₂×C₃₁×#107	C₂²	1	1	yes	characteristic
23	C₂×C₃₁×#107	C₂²	1	2	yes	—
24	C₂×C₃₁×#107	C₂²	1	1	yes	characteristic
25	C₂×C₃₁×C₂²⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
28	C₃₁×#398	—	2	2	no	—
29	C₃₁×#395	—	2	2	no	—
30	C₃₁×#389	C₂²	1	2	yes	—
31	C₃₁×#389	C₂²	1	2	yes	—
32	C₃₁×#385	—	2	2	no	—
33	C₃₁×#384	C₂²	1	2	yes	—
34	C₃₁×#380	C₂²	1	2	yes	—
35	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
36	C₃₁×#340	C₂²	1	2	yes	—
37	C₃₁×#340	C₂²	1	2	yes	—
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	—	2	2	no	—
42	C₂³×C₄×C₃₁	—	2	2	no	—
43	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
44	C₂²×C₈×C₃₁	—	2	2	no	—
45	C₂²×C₈×C₃₁	—	2	2	no	—
46	C₂²×C₈×C₃₁	Q₈	1	4	yes	complemented
47	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
48	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
49	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
50	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
51	C₃₁×C₄⋊Q₈	—	2	4	no	—
52	C₃₁×C₄⋊Q₈	—	4	2	no	—
53	C₃₁×C₂²⋊Q₈	—	4	8	no	—
54	C₂×C₄⋊C₄×C₃₁	—	2	4	no	—
55	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
56	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
57	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
58	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
59	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
60	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
61	C₂×C₄⋊C₄×C₃₁	—	4	2	no	—
62	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
63	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
64	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
65	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
66	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
67	C₂×C₂²⋊C₄×C₃₁	D₄	1	1	yes	characteristic
68	C₂×C₂²⋊C₄×C₃₁	D₄	1	1	yes	characteristic
69	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
70	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
71	C₃₁×#107	—	2	2	no	—
72	C₃₁×#107	—	2	2	no	—
73	C₃₁×#107	—	2	2	no	—
74	C₃₁×#107	—	2	4	no	—
75	C₃₁×#107	—	2	4	no	—
76	C₃₁×#107	—	4	2	no	—
77	C₃₁×#107	D₄	1	4	yes	—
78	C₃₁×C₂²⋊C₈	Q₈	1	4	yes	complemented
79	C₄×C₈×C₃₁	—	2	2	no	—
80	C₄×C₈×C₃₁	—	2	2	no	—
81	C₃₁×#95	—	2	2	no	—
82	C₃₁×#95	—	2	2	no	—
83	C₃₁×#95	—	2	2	no	—
84	C₃₁×#95	D₄	1	1	yes	characteristic
85	C₃₁×#95	D₄	1	1	yes	characteristic
86	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
87	C₂×Q₈×C₃₁	—	4	4	no	—
88	C₂×Q₈×C₃₁	—	4	4	no	—
89	C₂×Q₈×C₃₁	—	8	2	no	—
90	C₂²×C₄×C₃₁	—	2	1	no	—
91	C₂²×C₄×C₃₁	—	2	1	no	—
92	C₂²×C₄×C₃₁	—	2	1	no	—
93	C₂²×C₄×C₃₁	—	2	1	no	—
94	C₂²×C₄×C₃₁	—	2	2	no	—
95	C₂²×C₄×C₃₁	—	2	2	no	—
96	C₂²×C₄×C₃₁	—	2	2	no	—
97	C₂²×C₄×C₃₁	—	2	2	no	—
98	C₂²×C₄×C₃₁	—	4	4	no	—
99	C₂²×C₄×C₃₁	—	4	4	no	—
100	C₂²×C₄×C₃₁	—	8	2	no	—
101	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₃₁	C₂×Q₈	1	2	yes	—
107	C₂²×C₄×C₃₁	C₂×Q₈	1	2	yes	—
108	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
109	C₂×C₈×C₃₁	—	2	1	no	—
110	C₂×C₈×C₃₁	—	2	1	no	—
111	C₂×C₈×C₃₁	—	2	1	no	—
112	C₂×C₈×C₃₁	—	2	1	no	—
113	C₂×C₈×C₃₁	—	2	1	no	—
114	C₂×C₈×C₃₁	—	2	1	no	—
115	C₂×C₈×C₃₁	—	2	8	no	—
116	C₂×C₈×C₃₁	C₂×D₄	1	2	yes	—
117	C₂×C₈×C₃₁	C₂×Q₈	1	2	yes	—
118	C₂×C₈×C₃₁	C₂×Q₈	1	2	yes	—
119	C₂×C₈×C₃₁	C₂×Q₈	1	2	yes	—
120	C₂×C₈×C₃₁	C₂×Q₈	1	2	yes	—
121	C₂×C₈×C₃₁	#41	1	2	yes	—
122	C₄⋊C₄×C₃₁	—	2	2	no	—
123	C₄⋊C₄×C₃₁	—	2	2	no	—
124	C₄⋊C₄×C₃₁	—	2	2	no	—
125	C₄⋊C₄×C₃₁	—	2	2	no	—
126	C₄⋊C₄×C₃₁	—	2	2	no	—
127	C₄⋊C₄×C₃₁	—	2	2	no	—
128	C₄⋊C₄×C₃₁	—	2	2	no	—
129	C₄⋊C₄×C₃₁	—	4	4	no	—
130	C₄⋊C₄×C₃₁	—	4	4	no	—
131	C₄⋊C₄×C₃₁	—	4	4	no	—
132	C₄⋊C₄×C₃₁	—	4	4	no	—
133	C₄⋊C₄×C₃₁	—	4	4	no	—
134	C₄⋊C₄×C₃₁	—	8	2	no	—
135	C₄⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
136	C₂²⋊C₄×C₃₁	—	4	4	no	—
137	C₂²⋊C₄×C₃₁	D₈	1	4	yes	—
138	C₂²⋊C₄×C₃₁	Q₁₆	1	4	yes	—
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	#26065	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
144	C₂³×C₃₁	—	2	1	no	—
145	C₂³×C₃₁	—	2	1	no	—
146	C₂³×C₃₁	—	2	1	no	—
147	C₂³×C₃₁	—	2	1	no	—
148	C₂³×C₃₁	C₄⋊Q₈	1	2	yes	—
149	C₂³×C₃₁	C₂×D₈	1	2	yes	—
150	C₂³×C₃₁	C₂×Q₁₆	1	2	yes	—
151	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
152	Q₈×C₃₁	—	8	8	no	—
153	C₂×C₄×C₃₁	—	2	1	no	—
154	C₂×C₄×C₃₁	—	2	1	no	—
155	C₂×C₄×C₃₁	—	2	1	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	2	no	—
164	C₂×C₄×C₃₁	—	2	2	no	—
165	C₂×C₄×C₃₁	—	2	2	no	—
166	C₂×C₄×C₃₁	—	2	2	no	—
167	C₂×C₄×C₃₁	—	2	4	no	—
168	C₂×C₄×C₃₁	—	4	2	no	—
169	C₂×C₄×C₃₁	—	4	2	no	—
170	C₂×C₄×C₃₁	—	4	2	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	—	8	8	no	—
180	C₂×C₄×C₃₁	C₄⋊Q₈	1	2	yes	—
181	C₂×C₄×C₃₁	C₂×D₈	1	2	yes	—
182	C₂×C₄×C₃₁	C₂×D₈	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	C₂²×D₄	1	1	yes	characteristic
186	C₂×C₄×C₃₁	C₂²×Q₈	1	1	yes	characteristic
187	C₂×C₄×C₃₁	C₂²×Q₈	1	1	yes	characteristic
188	C₂×C₄×C₃₁	C₂×#41	1	1	yes	characteristic
189	C₂×C₄×C₃₁	H(5,𝔽₂)	1	1	yes	characteristic
190	C₂×C₄×C₃₁	2₋¹⁺⁴	1	1	yes	characteristic
191	C₈×C₃₁	—	2	2	no	—
192	C₈×C₃₁	—	2	2	no	—
193	C₈×C₃₁	—	2	2	no	—
194	C₈×C₃₁	C₂²⋊Q₈	1	4	yes	complemented
195	C₂×#500	C₂×C₃₁	1	1	yes	characteristic, complemented
196	C₂²×#107	C₂×C₃₁	1	1	yes	characteristic
197	#2440	C₂×C₃₁	1	2	yes	—
198	#2083	C₂×C₃₁	1	2	yes	complemented
199	#2057	C₂×C₃₁	1	2	yes	complemented
200	#1942	C₂×C₃₁	1	1	yes	characteristic, complemented
201	#1942	C₂×C₃₁	1	1	yes	characteristic, complemented
202	#1852	C₂×C₃₁	1	2	yes	—
203	#1845	C₂×C₃₁	1	1	yes	characteristic, complemented
204	#1808	C₂×C₃₁	1	1	yes	characteristic
205	C₈×C₂²⋊C₄	C₂×C₃₁	1	1	yes	characteristic
206	C₂²×C₃₁	—	2	2	no	—
207	C₂²×C₃₁	—	2	2	no	—
208	C₂²×C₃₁	—	2	2	no	—
209	C₂²×C₃₁	—	2	2	no	—
210	C₂²×C₃₁	—	2	2	no	—
211	C₂²×C₃₁	—	2	2	no	—
212	C₂²×C₃₁	#500	1	4	yes	complemented
213	C₂²×C₃₁	C₂×C₄⋊Q₈	1	1	yes	characteristic
214	C₂²×C₃₁	D₄²	1	1	yes	characteristic
215	C₂²×C₃₁	#547	1	1	yes	characteristic
216	C₂²×C₃₁	C₂²×D₈	1	1	yes	characteristic
217	C₂²×C₃₁	C₂²×Q₁₆	1	1	yes	characteristic
218	C₂²×C₃₁	#576	1	1	yes	characteristic
219	C₂²×C₃₁	#578	1	1	yes	characteristic
220	C₄×C₃₁	—	2	2	no	—
221	C₄×C₃₁	—	2	2	no	—
222	C₄×C₃₁	—	2	2	no	—
223	C₄×C₃₁	—	2	2	no	—
224	C₄×C₃₁	—	2	2	no	—
225	C₄×C₃₁	—	4	4	no	—
226	C₄×C₃₁	—	8	2	no	—
227	C₄×C₃₁	—	8	2	no	—
228	C₄×C₃₁	—	8	2	no	—
229	C₄×C₃₁	C₂×C₂²⋊Q₈	1	1	yes	characteristic
230	C₄×C₃₁	#544	1	1	yes	characteristic
231	C₄×C₃₁	D₄×Q₈	1	1	yes	characteristic
232	C₄×C₃₁	#554	1	1	yes	characteristic
233	C₂³×C₈	C₂²×C₃₁	1	1	yes	characteristic
234	C₂×C₄⋊Q₈	C₂²×C₃₁	1	2	yes	—
235	C₂×C₂²⋊Q₈	—	2	2	no	—
236	C₂²×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
237	#500	—	2	4	no	—
238	C₂×#107	—	2	4	no	—
239	C₂×#107	C₂²×C₃₁	1	2	yes	—
240	C₂×#107	C₂²×C₃₁	1	1	yes	characteristic
241	C₂×#107	C₂²×C₃₁	1	1	yes	characteristic
242	C₂×#107	C₂²×C₃₁	1	2	yes	—
243	C₂×#107	C₂²×C₃₁	1	1	yes	characteristic
244	C₂×#107	C₂²×C₃₁	1	2	yes	—
245	C₂×#107	C₂²×C₃₁	1	1	yes	characteristic
246	C₂×C₂²⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
247	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
248	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
249	#398	—	2	2	no	—
250	#395	—	2	2	no	—
251	#389	C₂²×C₃₁	1	2	yes	—
252	#389	C₂²×C₃₁	1	2	yes	—
253	#385	—	2	2	no	—
254	#384	C₂²×C₃₁	1	2	yes	—
255	#380	C₂²×C₃₁	1	2	yes	—
256	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
257	#340	C₂²×C₃₁	1	2	yes	—
258	#340	C₂²×C₃₁	1	2	yes	—
259	#340	C₂²×C₃₁	1	2	yes	—
260	#336	C₂²×C₃₁	1	1	yes	characteristic
261	#336	C₂²×C₃₁	1	1	yes	characteristic
262	C₂×C₃₁	—	2	4	no	—
263	C₂×C₃₁	#2440	1	1	yes	characteristic
264	C₂×C₃₁	C₂×#500	1	1	yes	characteristic
265	C₂×C₃₁	#3164	1	1	yes	characteristic
266	C₂×C₃₁	D₄×D₈	1	1	yes	characteristic
267	C₂×C₃₁	D₄×Q₁₆	1	1	yes	characteristic
268	C₂×C₃₁	#3334	1	1	yes	characteristic
269	C₂×C₃₁	#3338	1	1	yes	characteristic
270	C₂²×Q₈	—	2	2	no	—
271	C₂³×C₄	—	2	2	no	—
272	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
273	C₂²×C₈	—	2	2	no	—
274	C₂²×C₈	—	2	2	no	—
275	C₂²×C₈	Q₈×C₃₁	1	4	yes	complemented
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	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
280	C₄⋊Q₈	—	2	4	no	—
281	C₄⋊Q₈	—	4	2	no	—
282	C₂²⋊Q₈	—	4	8	no	—
283	C₂×C₄⋊C₄	—	2	4	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	—	2	2	no	—
288	C₂×C₄⋊C₄	—	2	2	no	—
289	C₂×C₄⋊C₄	—	2	2	no	—
290	C₂×C₄⋊C₄	—	4	2	no	—
291	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
292	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
293	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
294	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
295	C₂×C₂²⋊C₄	—	2	2	no	—
296	C₂×C₂²⋊C₄	D₄×C₃₁	1	1	yes	characteristic
297	C₂×C₂²⋊C₄	D₄×C₃₁	1	1	yes	characteristic
298	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
299	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
300	#107	—	2	2	no	—
301	#107	—	2	2	no	—
302	#107	—	2	2	no	—
303	#107	—	2	4	no	—
304	#107	—	2	4	no	—
305	#107	—	4	2	no	—
306	#107	D₄×C₃₁	1	4	yes	—
307	C₂²⋊C₈	Q₈×C₃₁	1	4	yes	complemented
308	C₄×C₈	—	2	2	no	—
309	C₄×C₈	—	2	2	no	—
310	#95	—	2	2	no	—
311	#95	—	2	2	no	—
312	#95	—	2	2	no	—
313	#95	D₄×C₃₁	1	1	yes	characteristic
314	#95	D₄×C₃₁	1	1	yes	characteristic
315	C₃₁	#26065	1	1	yes	characteristic, direct product factor, Sylow
316	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
317	C₂×Q₈	—	4	4	no	—
318	C₂×Q₈	—	4	4	no	—
319	C₂×Q₈	—	8	2	no	—
320	C₂²×C₄	—	2	1	no	—
321	C₂²×C₄	—	2	1	no	—
322	C₂²×C₄	—	2	1	no	—
323	C₂²×C₄	—	2	1	no	—
324	C₂²×C₄	—	2	2	no	—
325	C₂²×C₄	—	2	2	no	—
326	C₂²×C₄	—	2	2	no	—
327	C₂²×C₄	—	2	2	no	—
328	C₂²×C₄	—	4	4	no	—
329	C₂²×C₄	—	4	4	no	—
330	C₂²×C₄	—	8	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×Q₈×C₃₁	1	2	yes	—
337	C₂²×C₄	C₂×Q₈×C₃₁	1	2	yes	—
338	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
339	C₂×C₈	—	2	1	no	—
340	C₂×C₈	—	2	1	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	8	no	—
346	C₂×C₈	C₂×D₄×C₃₁	1	2	yes	—
347	C₂×C₈	C₂×Q₈×C₃₁	1	2	yes	—
348	C₂×C₈	C₂×Q₈×C₃₁	1	2	yes	—
349	C₂×C₈	C₂×Q₈×C₃₁	1	2	yes	—
350	C₂×C₈	C₂×Q₈×C₃₁	1	2	yes	—
351	C₂×C₈	#41×C₃₁	1	2	yes	—
352	C₄⋊C₄	—	2	2	no	—
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	—	2	2	no	—
359	C₄⋊C₄	—	4	4	no	—
360	C₄⋊C₄	—	4	4	no	—
361	C₄⋊C₄	—	4	4	no	—
362	C₄⋊C₄	—	4	4	no	—
363	C₄⋊C₄	—	4	4	no	—
364	C₄⋊C₄	—	8	2	no	—
365	C₄⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
366	C₂²⋊C₄	—	4	4	no	—
367	C₂²⋊C₄	D₈×C₃₁	1	4	yes	—
368	C₂²⋊C₄	Q₁₆×C₃₁	1	4	yes	—
369	C₄²	—	2	1	no	—
370	C₄²	—	2	1	no	—
371	C₄²	—	2	1	no	—
372	C₄²	—	2	1	no	—
373	C₂³	—	2	1	no	—
374	C₂³	—	2	1	no	—
375	C₂³	—	2	1	no	—
376	C₂³	—	2	1	no	—
377	C₂³	C₃₁×C₄⋊Q₈	1	2	yes	—
378	C₂³	C₂×D₈×C₃₁	1	2	yes	—
379	C₂³	C₂×Q₁₆×C₃₁	1	2	yes	—
380	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
381	Q₈	—	8	8	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	1	no	—
390	C₂×C₄	—	2	1	no	—
391	C₂×C₄	—	2	1	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	4	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	—	4	2	no	—
406	C₂×C₄	—	4	2	no	—
407	C₂×C₄	—	4	2	no	—
408	C₂×C₄	—	8	8	no	—
409	C₂×C₄	C₃₁×C₄⋊Q₈	1	2	yes	—
410	C₂×C₄	C₂×D₈×C₃₁	1	2	yes	—
411	C₂×C₄	C₂×D₈×C₃₁	1	2	yes	—
412	C₂×C₄	C₂×Q₁₆×C₃₁	1	2	yes	—
413	C₂×C₄	C₂×Q₁₆×C₃₁	1	2	yes	—
414	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
415	C₂×C₄	C₂²×Q₈×C₃₁	1	1	yes	characteristic
416	C₂×C₄	C₂²×Q₈×C₃₁	1	1	yes	characteristic
417	C₂×C₄	C₂×#41×C₃₁	1	1	yes	characteristic
418	C₂×C₄	C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
419	C₂×C₄	C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
420	C₈	—	2	2	no	—
421	C₈	—	2	2	no	—
422	C₈	—	2	2	no	—
423	C₈	C₃₁×C₂²⋊Q₈	1	4	yes	complemented
424	C₂²	—	2	2	no	—
425	C₂²	—	2	2	no	—
426	C₂²	—	2	2	no	—
427	C₂²	—	2	2	no	—
428	C₂²	—	2	2	no	—
429	C₂²	—	2	2	no	—
430	C₂²	C₃₁×#500	1	4	yes	complemented
431	C₂²	C₂×C₃₁×C₄⋊Q₈	1	1	yes	characteristic
432	C₂²	D₄²×C₃₁	1	1	yes	characteristic
433	C₂²	C₃₁×#547	1	1	yes	characteristic
434	C₂²	C₂²×D₈×C₃₁	1	1	yes	characteristic
435	C₂²	C₂²×Q₁₆×C₃₁	1	1	yes	characteristic
436	C₂²	C₃₁×#576	1	1	yes	characteristic
437	C₂²	C₃₁×#578	1	1	yes	characteristic
438	C₄	—	2	2	no	—
439	C₄	—	2	2	no	—
440	C₄	—	2	2	no	—
441	C₄	—	2	2	no	—
442	C₄	—	2	2	no	—
443	C₄	—	4	4	no	—
444	C₄	—	8	2	no	—
445	C₄	—	8	2	no	—
446	C₄	—	8	2	no	—
447	C₄	C₂×C₃₁×C₂²⋊Q₈	1	1	yes	characteristic
448	C₄	C₃₁×#544	1	1	yes	characteristic
449	C₄	D₄×Q₈×C₃₁	1	1	yes	characteristic
450	C₄	C₃₁×#554	1	1	yes	characteristic
451	C₂	—	2	4	no	—
452	C₂	C₃₁×#2440	1	1	yes	characteristic
453	C₂	C₂×C₃₁×#500	1	1	yes	characteristic
454	C₂	C₃₁×#3164	1	1	yes	characteristic
455	C₂	D₄×D₈×C₃₁	1	1	yes	characteristic
456	C₂	D₄×Q₁₆×C₃₁	1	1	yes	characteristic
457	C₂	C₃₁×#3334	1	1	yes	characteristic
458	C₂	C₃₁×#3338	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂×C₃₁×#500	C₂	semidirect
4. C₃₁×#2083	C₂	semidirect
5. C₃₁×#2057	C₂	semidirect
6. C₃₁×#1942	C₂	semidirect
7. C₃₁×#1942	C₂	semidirect
9. C₃₁×#1845	C₂	semidirect
46. C₂²×C₈×C₃₁	Q₈	semidirect
78. C₃₁×C₂²⋊C₈	Q₈	semidirect
143. #26065	C₃₁	direct (N × H)
194. C₈×C₃₁	C₂²⋊Q₈	semidirect
195. C₂×#500	C₂×C₃₁	semidirect
198. #2083	C₂×C₃₁	semidirect
199. #2057	C₂×C₃₁	semidirect
200. #1942	C₂×C₃₁	semidirect
201. #1942	C₂×C₃₁	semidirect
203. #1845	C₂×C₃₁	semidirect
212. C₂²×C₃₁	#500	semidirect
275. C₂²×C₈	Q₈×C₃₁	semidirect
307. C₂²⋊C₈	Q₈×C₃₁	semidirect
315. C₃₁	#26065	direct (N × H)
423. C₈	C₃₁×C₂²⋊Q₈	semidirect
430. C₂²	C₃₁×#500	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃₁×#500	2
C₂²×C₃₁×#107	2
C₃₁×#2440	2
C₃₁×#2083	2
C₃₁×#2057	2
C₃₁×#1942	2
C₃₁×#1852	2
C₃₁×#1845	2
C₃₁×#1808	2
C₈×C₂²⋊C₄×C₃₁	2
#26065	31

Subgroups — C31×#26065 #21482824

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#26065 #21482824