Subgroups — C₃₁×#24629 #21481388

Order 7936.

862 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#462	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄×SD₁₆×C₃₁	C₂	1	1	yes	maximal, characteristic
3	C₃₁×#2547	C₂	1	1	yes	maximal, characteristic
4	C₃₁×#2355	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#2056	C₂	1	2	yes	maximal, complemented
6	C₃₁×#2015	C₂	1	2	yes	maximal
7	C₃₁×#1983	C₂	1	2	yes	maximal
8	C₃₁×#1956	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#1939	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#1927	C₂	1	2	yes	maximal, complemented
11	C₃₁×#1802	C₂	1	1	yes	maximal, characteristic
12	C₂²×Q₁₆×C₃₁	C₂²	1	2	yes	—
13	C₂²×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
14	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
15	C₂×C₃₁×#124	C₂²	1	2	yes	—
16	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
17	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
18	C₃₁×#462	—	2	4	no	—
19	C₄×SD₁₆×C₃₁	—	2	4	no	—
20	C₂×C₃₁×#106	C₂²	1	1	yes	characteristic
21	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×C₃₁×C₄⋊C₈	C₂²	1	2	yes	—
23	C₂×C₃₁×#103	C₂²	1	1	yes	characteristic
24	C₂×C₃₁×#103	C₂²	1	2	yes	—
25	C₂×C₃₁×#103	C₂²	1	2	yes	—
26	C₂×C₃₁×#103	C₂²	1	2	yes	—
27	C₂×C₃₁×#102	C₂²	1	1	yes	characteristic
28	C₂×C₃₁×#102	C₂²	1	2	yes	—
29	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
30	C₃₁×#397	—	2	2	no	—
31	C₃₁×#391	C₂²	1	2	yes	—
32	C₃₁×#391	C₂²	1	2	yes	—
33	C₃₁×#387	—	2	2	no	—
34	C₃₁×#384	C₂²	1	1	yes	characteristic
35	C₃₁×#382	—	2	1	no	—
36	C₃₁×#380	—	2	1	no	—
37	C₃₁×#380	—	2	1	no	—
38	C₄×C₄⋊C₄×C₃₁	—	2	1	no	—
39	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
40	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
41	C₃₁×#340	C₂²	1	2	yes	—
42	C₃₁×#336	C₂²	1	2	yes	—
43	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
44	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
45	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
46	C₂³×C₄×C₃₁	—	2	1	no	—
47	C₂×Q₁₆×C₃₁	—	2	4	no	—
48	C₂×Q₁₆×C₃₁	—	4	2	no	—
49	C₂×Q₁₆×C₃₁	—	4	2	no	—
50	C₂×SD₁₆×C₃₁	—	2	2	no	—
51	C₂×SD₁₆×C₃₁	—	2	2	no	—
52	C₂×SD₁₆×C₃₁	—	2	2	no	—
53	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
54	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
55	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
56	C₃₁×C₄⋊Q₈	—	2	2	no	—
57	C₃₁×C₄⋊Q₈	—	2	2	no	—
58	C₃₁×#124	—	2	4	no	—
59	C₃₁×#124	—	4	2	no	—
60	C₄×Q₈×C₃₁	—	2	2	no	—
61	C₄×Q₈×C₃₁	D₄	1	4	yes	—
62	C₄×D₄×C₃₁	—	2	2	no	—
63	C₄×D₄×C₃₁	—	2	2	no	—
64	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
65	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
66	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
67	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
68	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
69	C₂×C₄⋊C₄×C₃₁	D₄	1	1	yes	characteristic
70	C₂×C₄⋊C₄×C₃₁	D₄	1	1	yes	characteristic
71	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
72	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
73	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
74	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
75	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
76	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
77	C₂×C₄²×C₃₁	—	2	1	no	—
78	C₂×C₄²×C₃₁	—	2	2	no	—
79	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
80	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
81	C₃₁×#106	—	2	2	no	—
82	C₃₁×C₄⋊C₈	—	2	2	no	—
83	C₃₁×C₄⋊C₈	—	4	2	no	—
84	C₃₁×#103	—	2	2	no	—
85	C₃₁×#103	—	2	4	no	—
86	C₃₁×#103	—	2	4	no	—
87	C₃₁×#103	—	4	2	no	—
88	C₃₁×#102	—	2	2	no	—
89	C₃₁×#102	—	4	2	no	—
90	C₄×C₈×C₃₁	—	2	2	no	—
91	C₃₁×#95	—	2	2	no	—
92	C₃₁×#95	—	2	2	no	—
93	C₃₁×#95	—	2	2	no	—
94	C₃₁×#95	—	2	2	no	—
95	C₃₁×#95	—	2	2	no	—
96	C₃₁×#95	D₄	1	2	yes	—
97	C₂⁴×C₃₁	—	2	1	no	—
98	C₂×Q₈×C₃₁	—	2	1	no	—
99	C₂×Q₈×C₃₁	—	2	2	no	—
100	C₂×Q₈×C₃₁	—	2	1	no	—
101	C₂×Q₈×C₃₁	—	2	1	no	—
102	C₂×Q₈×C₃₁	—	2	2	no	—
103	C₂×Q₈×C₃₁	—	2	2	no	—
104	C₂×Q₈×C₃₁	—	2	2	no	—
105	C₂×Q₈×C₃₁	—	2	1	no	—
106	C₂×Q₈×C₃₁	—	2	1	no	—
107	C₂×Q₈×C₃₁	—	2	2	no	—
108	C₂×Q₈×C₃₁	—	2	2	no	—
109	C₂×Q₈×C₃₁	C₂×D₄	1	2	yes	—
110	C₂×D₄×C₃₁	—	2	1	no	—
111	C₂×D₄×C₃₁	—	2	1	no	—
112	C₂×D₄×C₃₁	—	2	1	no	—
113	C₂×D₄×C₃₁	—	2	1	no	—
114	C₂×D₄×C₃₁	—	2	1	no	—
115	C₂×D₄×C₃₁	#41	1	2	yes	—
116	C₂²×C₄×C₃₁	—	2	1	no	—
117	C₂²×C₄×C₃₁	—	2	1	no	—
118	C₂²×C₄×C₃₁	—	2	1	no	—
119	C₂²×C₄×C₃₁	—	2	2	no	—
120	C₂²×C₄×C₃₁	—	2	2	no	—
121	C₂²×C₄×C₃₁	—	4	2	no	—
122	C₂²×C₄×C₃₁	—	4	2	no	—
123	C₂²×C₄×C₃₁	—	4	2	no	—
124	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
125	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
126	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
129	Q₁₆×C₃₁	—	4	8	no	—
130	SD₁₆×C₃₁	—	2	8	no	—
131	C₂×C₈×C₃₁	—	2	1	no	—
132	C₂×C₈×C₃₁	—	2	1	no	—
133	C₂×C₈×C₃₁	—	2	1	no	—
134	C₂×C₈×C₃₁	—	2	2	no	—
135	C₂×C₈×C₃₁	—	2	2	no	—
136	C₂×C₈×C₃₁	—	2	1	no	—
137	C₂×C₈×C₃₁	—	2	1	no	—
138	C₂×C₈×C₃₁	—	2	2	no	—
139	C₂×C₈×C₃₁	#41	1	2	yes	—
140	C₄⋊C₄×C₃₁	—	2	4	no	—
141	C₄⋊C₄×C₃₁	—	2	2	no	—
142	C₄⋊C₄×C₃₁	—	2	2	no	—
143	C₄⋊C₄×C₃₁	—	2	1	no	—
144	C₄⋊C₄×C₃₁	—	2	1	no	—
145	C₄⋊C₄×C₃₁	—	2	2	no	—
146	C₄⋊C₄×C₃₁	—	2	1	no	—
147	C₄⋊C₄×C₃₁	—	2	2	no	—
148	C₄⋊C₄×C₃₁	—	4	2	no	—
149	C₄⋊C₄×C₃₁	—	4	2	no	—
150	C₄⋊C₄×C₃₁	—	4	2	no	—
151	C₄⋊C₄×C₃₁	—	8	1	no	—
152	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
153	C₂²⋊C₄×C₃₁	—	4	4	no	—
154	C₂²⋊C₄×C₃₁	—	4	4	no	—
155	C₂²⋊C₄×C₃₁	—	4	2	no	—
156	C₄²×C₃₁	—	2	4	no	—
157	C₄²×C₃₁	—	2	2	no	—
158	C₄²×C₃₁	—	2	2	no	—
159	C₄²×C₃₁	—	8	2	no	—
160	C₄²×C₃₁	C₂×D₄	1	2	yes	—
161	C₄²×C₃₁	#41	1	2	yes	—
162	#24629	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
163	C₂³×C₃₁	—	2	2	no	—
164	C₂³×C₃₁	—	4	1	no	—
165	C₂³×C₃₁	—	4	1	no	—
166	C₂³×C₃₁	—	4	1	no	—
167	C₂³×C₃₁	—	4	1	no	—
168	C₂³×C₃₁	—	4	1	no	—
169	C₂³×C₃₁	—	4	1	no	—
170	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
171	Q₈×C₃₁	—	2	2	no	—
172	Q₈×C₃₁	—	2	2	no	—
173	Q₈×C₃₁	—	4	1	no	—
174	Q₈×C₃₁	—	4	1	no	—
175	Q₈×C₃₁	—	4	2	no	—
176	Q₈×C₃₁	—	4	2	no	—
177	Q₈×C₃₁	—	4	2	no	—
178	Q₈×C₃₁	—	4	2	no	—
179	D₄×C₃₁	—	2	2	no	—
180	D₄×C₃₁	—	2	2	no	—
181	D₄×C₃₁	—	4	1	no	—
182	D₄×C₃₁	—	4	1	no	—
183	C₂×C₄×C₃₁	—	2	1	no	—
184	C₂×C₄×C₃₁	—	2	1	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	—	2	2	no	—
190	C₂×C₄×C₃₁	—	2	2	no	—
191	C₂×C₄×C₃₁	—	2	2	no	—
192	C₂×C₄×C₃₁	—	2	2	no	—
193	C₂×C₄×C₃₁	—	4	1	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	2	no	—
199	C₂×C₄×C₃₁	—	4	2	no	—
200	C₂×C₄×C₃₁	—	4	2	no	—
201	C₂×C₄×C₃₁	—	4	2	no	—
202	C₂×C₄×C₃₁	—	4	2	no	—
203	C₂×C₄×C₃₁	—	4	1	no	—
204	C₂×C₄×C₃₁	—	4	1	no	—
205	C₂×C₄×C₃₁	—	4	2	no	—
206	C₂×C₄×C₃₁	—	8	4	no	—
207	C₂×C₄×C₃₁	#121	1	2	yes	—
208	C₂×C₄×C₃₁	#121	1	2	yes	—
209	C₂×C₄×C₃₁	#135	1	2	yes	—
210	C₂×C₄×C₃₁	#137	1	2	yes	—
211	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
212	C₂×C₄×C₃₁	C₂×#41	1	1	yes	characteristic
213	C₂×C₄×C₃₁	C₂×#41	1	1	yes	characteristic
214	C₂×C₄×C₃₁	C₂×#41	1	1	yes	characteristic
215	C₂×C₄×C₃₁	H(5,𝔽₂)	1	1	yes	characteristic
216	C₂×C₄×C₃₁	H(5,𝔽₂)	1	1	yes	characteristic
217	C₈×C₃₁	—	2	2	no	—
218	C₈×C₃₁	—	4	1	no	—
219	C₈×C₃₁	—	4	2	no	—
220	C₂×#462	C₂×C₃₁	1	1	yes	characteristic, complemented
221	C₂×C₄×SD₁₆	C₂×C₃₁	1	1	yes	characteristic
222	#2547	C₂×C₃₁	1	1	yes	characteristic
223	#2355	C₂×C₃₁	1	1	yes	characteristic, complemented
224	#2056	C₂×C₃₁	1	2	yes	complemented
225	#2015	C₂×C₃₁	1	2	yes	—
226	#1983	C₂×C₃₁	1	2	yes	—
227	#1956	C₂×C₃₁	1	1	yes	characteristic, complemented
228	#1939	C₂×C₃₁	1	1	yes	characteristic, complemented
229	#1927	C₂×C₃₁	1	2	yes	complemented
230	#1802	C₂×C₃₁	1	1	yes	characteristic
231	C₂²×C₃₁	—	4	2	no	—
232	C₂²×C₃₁	—	4	2	no	—
233	C₂²×C₃₁	—	4	2	no	—
234	C₂²×C₃₁	—	8	1	no	—
235	C₂²×C₃₁	—	8	1	no	—
236	C₂²×C₃₁	—	8	1	no	—
237	C₂²×C₃₁	—	8	1	no	—
238	C₂²×C₃₁	C₂×#121	1	1	yes	characteristic
239	C₂²×C₃₁	#546	1	1	yes	characteristic
240	C₂²×C₃₁	#550	1	1	yes	characteristic
241	C₂²×C₃₁	C₂×#135	1	1	yes	characteristic
242	C₂²×C₃₁	C₂×#137	1	1	yes	characteristic
243	C₂²×C₃₁	#577	1	1	yes	characteristic
244	C₂²×C₃₁	#578	1	1	yes	characteristic
245	C₄×C₃₁	—	2	2	no	—
246	C₄×C₃₁	—	4	2	no	—
247	C₄×C₃₁	—	4	2	no	—
248	C₄×C₃₁	—	4	2	no	—
249	C₄×C₃₁	—	4	2	no	—
250	C₄×C₃₁	—	8	2	no	—
251	C₄×C₃₁	—	8	2	no	—
252	C₄×C₃₁	—	8	1	no	—
253	C₄×C₃₁	#464	1	4	yes	—
254	C₄×C₃₁	#525	1	1	yes	characteristic
255	C₄×C₃₁	#535	1	1	yes	characteristic
256	C₄×C₃₁	#553	1	1	yes	characteristic
257	C₄×C₃₁	#555	1	1	yes	characteristic
258	C₂²×Q₁₆	C₂²×C₃₁	1	2	yes	—
259	C₂²×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
260	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
261	C₂×#124	C₂²×C₃₁	1	2	yes	—
262	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
263	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
264	#462	—	2	4	no	—
265	C₄×SD₁₆	—	2	4	no	—
266	C₂×#106	C₂²×C₃₁	1	1	yes	characteristic
267	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
268	C₂×C₄⋊C₈	C₂²×C₃₁	1	2	yes	—
269	C₂×#103	C₂²×C₃₁	1	1	yes	characteristic
270	C₂×#103	C₂²×C₃₁	1	2	yes	—
271	C₂×#103	C₂²×C₃₁	1	2	yes	—
272	C₂×#103	C₂²×C₃₁	1	2	yes	—
273	C₂×#102	C₂²×C₃₁	1	1	yes	characteristic
274	C₂×#102	C₂²×C₃₁	1	2	yes	—
275	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
276	#397	—	2	2	no	—
277	#391	C₂²×C₃₁	1	2	yes	—
278	#391	C₂²×C₃₁	1	2	yes	—
279	#387	—	2	2	no	—
280	#384	C₂²×C₃₁	1	1	yes	characteristic
281	#382	—	2	1	no	—
282	#380	—	2	1	no	—
283	#380	—	2	1	no	—
284	C₄×C₄⋊C₄	—	2	1	no	—
285	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
286	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
287	#340	C₂²×C₃₁	1	2	yes	—
288	#336	C₂²×C₃₁	1	2	yes	—
289	C₂×C₃₁	—	8	2	no	—
290	C₂×C₃₁	#2414	1	1	yes	characteristic
291	C₂×C₃₁	C₂×#464	1	1	yes	characteristic
292	C₂×C₃₁	#3046	1	1	yes	characteristic
293	C₂×C₃₁	#3302	1	1	yes	characteristic
294	C₂×C₃₁	#3331	1	1	yes	characteristic
295	C₂×C₃₁	#3394	1	1	yes	characteristic
296	C₂×C₃₁	#3398	1	1	yes	characteristic
297	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
298	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
299	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
300	C₂³×C₄	—	2	1	no	—
301	C₂×Q₁₆	—	2	4	no	—
302	C₂×Q₁₆	—	4	2	no	—
303	C₂×Q₁₆	—	4	2	no	—
304	C₂×SD₁₆	—	2	2	no	—
305	C₂×SD₁₆	—	2	2	no	—
306	C₂×SD₁₆	—	2	2	no	—
307	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
308	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
309	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
310	C₄⋊Q₈	—	2	2	no	—
311	C₄⋊Q₈	—	2	2	no	—
312	#124	—	2	4	no	—
313	#124	—	4	2	no	—
314	C₄×Q₈	—	2	2	no	—
315	C₄×Q₈	D₄×C₃₁	1	4	yes	—
316	C₄×D₄	—	2	2	no	—
317	C₄×D₄	—	2	2	no	—
318	C₂×C₄⋊C₄	—	2	1	no	—
319	C₂×C₄⋊C₄	—	2	1	no	—
320	C₂×C₄⋊C₄	—	2	1	no	—
321	C₂×C₄⋊C₄	—	2	1	no	—
322	C₂×C₄⋊C₄	—	2	1	no	—
323	C₂×C₄⋊C₄	D₄×C₃₁	1	1	yes	characteristic
324	C₂×C₄⋊C₄	D₄×C₃₁	1	1	yes	characteristic
325	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
326	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
327	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
328	C₂×C₂²⋊C₄	—	2	1	no	—
329	C₂×C₂²⋊C₄	—	2	2	no	—
330	C₂×C₂²⋊C₄	—	2	2	no	—
331	C₂×C₄²	—	2	1	no	—
332	C₂×C₄²	—	2	2	no	—
333	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
334	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
335	#106	—	2	2	no	—
336	C₄⋊C₈	—	2	2	no	—
337	C₄⋊C₈	—	4	2	no	—
338	#103	—	2	2	no	—
339	#103	—	2	4	no	—
340	#103	—	2	4	no	—
341	#103	—	4	2	no	—
342	#102	—	2	2	no	—
343	#102	—	4	2	no	—
344	C₄×C₈	—	2	2	no	—
345	#95	—	2	2	no	—
346	#95	—	2	2	no	—
347	#95	—	2	2	no	—
348	#95	—	2	2	no	—
349	#95	—	2	2	no	—
350	#95	D₄×C₃₁	1	2	yes	—
351	C₃₁	#24629	1	1	yes	characteristic, direct product factor, Sylow
352	C₂⁴	—	2	1	no	—
353	C₂×Q₈	—	2	1	no	—
354	C₂×Q₈	—	2	2	no	—
355	C₂×Q₈	—	2	1	no	—
356	C₂×Q₈	—	2	1	no	—
357	C₂×Q₈	—	2	2	no	—
358	C₂×Q₈	—	2	2	no	—
359	C₂×Q₈	—	2	2	no	—
360	C₂×Q₈	—	2	1	no	—
361	C₂×Q₈	—	2	1	no	—
362	C₂×Q₈	—	2	2	no	—
363	C₂×Q₈	—	2	2	no	—
364	C₂×Q₈	C₂×D₄×C₃₁	1	2	yes	—
365	C₂×D₄	—	2	1	no	—
366	C₂×D₄	—	2	1	no	—
367	C₂×D₄	—	2	1	no	—
368	C₂×D₄	—	2	1	no	—
369	C₂×D₄	—	2	1	no	—
370	C₂×D₄	#41×C₃₁	1	2	yes	—
371	C₂²×C₄	—	2	1	no	—
372	C₂²×C₄	—	2	1	no	—
373	C₂²×C₄	—	2	1	no	—
374	C₂²×C₄	—	2	2	no	—
375	C₂²×C₄	—	2	2	no	—
376	C₂²×C₄	—	4	2	no	—
377	C₂²×C₄	—	4	2	no	—
378	C₂²×C₄	—	4	2	no	—
379	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
380	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
381	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
382	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
383	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
384	Q₁₆	—	4	8	no	—
385	SD₁₆	—	2	8	no	—
386	C₂×C₈	—	2	1	no	—
387	C₂×C₈	—	2	1	no	—
388	C₂×C₈	—	2	1	no	—
389	C₂×C₈	—	2	2	no	—
390	C₂×C₈	—	2	2	no	—
391	C₂×C₈	—	2	1	no	—
392	C₂×C₈	—	2	1	no	—
393	C₂×C₈	—	2	2	no	—
394	C₂×C₈	#41×C₃₁	1	2	yes	—
395	C₄⋊C₄	—	2	4	no	—
396	C₄⋊C₄	—	2	2	no	—
397	C₄⋊C₄	—	2	2	no	—
398	C₄⋊C₄	—	2	1	no	—
399	C₄⋊C₄	—	2	1	no	—
400	C₄⋊C₄	—	2	2	no	—
401	C₄⋊C₄	—	2	1	no	—
402	C₄⋊C₄	—	2	2	no	—
403	C₄⋊C₄	—	4	2	no	—
404	C₄⋊C₄	—	4	2	no	—
405	C₄⋊C₄	—	4	2	no	—
406	C₄⋊C₄	—	8	1	no	—
407	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
408	C₂²⋊C₄	—	4	4	no	—
409	C₂²⋊C₄	—	4	4	no	—
410	C₂²⋊C₄	—	4	2	no	—
411	C₄²	—	2	4	no	—
412	C₄²	—	2	2	no	—
413	C₄²	—	2	2	no	—
414	C₄²	—	8	2	no	—
415	C₄²	C₂×D₄×C₃₁	1	2	yes	—
416	C₄²	#41×C₃₁	1	2	yes	—
417	C₂³	—	2	2	no	—
418	C₂³	—	4	1	no	—
419	C₂³	—	4	1	no	—
420	C₂³	—	4	1	no	—
421	C₂³	—	4	1	no	—
422	C₂³	—	4	1	no	—
423	C₂³	—	4	1	no	—
424	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
425	Q₈	—	2	2	no	—
426	Q₈	—	2	2	no	—
427	Q₈	—	4	1	no	—
428	Q₈	—	4	1	no	—
429	Q₈	—	4	2	no	—
430	Q₈	—	4	2	no	—
431	Q₈	—	4	2	no	—
432	Q₈	—	4	2	no	—
433	D₄	—	2	2	no	—
434	D₄	—	2	2	no	—
435	D₄	—	4	1	no	—
436	D₄	—	4	1	no	—
437	C₂×C₄	—	2	1	no	—
438	C₂×C₄	—	2	1	no	—
439	C₂×C₄	—	2	2	no	—
440	C₂×C₄	—	2	2	no	—
441	C₂×C₄	—	2	2	no	—
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	2	2	no	—
444	C₂×C₄	—	2	2	no	—
445	C₂×C₄	—	2	2	no	—
446	C₂×C₄	—	2	2	no	—
447	C₂×C₄	—	4	1	no	—
448	C₂×C₄	—	4	1	no	—
449	C₂×C₄	—	4	1	no	—
450	C₂×C₄	—	4	1	no	—
451	C₂×C₄	—	4	1	no	—
452	C₂×C₄	—	4	2	no	—
453	C₂×C₄	—	4	2	no	—
454	C₂×C₄	—	4	2	no	—
455	C₂×C₄	—	4	2	no	—
456	C₂×C₄	—	4	2	no	—
457	C₂×C₄	—	4	1	no	—
458	C₂×C₄	—	4	1	no	—
459	C₂×C₄	—	4	2	no	—
460	C₂×C₄	—	8	4	no	—
461	C₂×C₄	C₃₁×#121	1	2	yes	—
462	C₂×C₄	C₃₁×#121	1	2	yes	—
463	C₂×C₄	C₃₁×#135	1	2	yes	—
464	C₂×C₄	C₃₁×#137	1	2	yes	—
465	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
466	C₂×C₄	C₂×#41×C₃₁	1	1	yes	characteristic
467	C₂×C₄	C₂×#41×C₃₁	1	1	yes	characteristic
468	C₂×C₄	C₂×#41×C₃₁	1	1	yes	characteristic
469	C₂×C₄	C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
470	C₂×C₄	C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
471	C₈	—	2	2	no	—
472	C₈	—	4	1	no	—
473	C₈	—	4	2	no	—
474	C₂²	—	4	2	no	—
475	C₂²	—	4	2	no	—
476	C₂²	—	4	2	no	—
477	C₂²	—	8	1	no	—
478	C₂²	—	8	1	no	—
479	C₂²	—	8	1	no	—
480	C₂²	—	8	1	no	—
481	C₂²	C₂×C₃₁×#121	1	1	yes	characteristic
482	C₂²	C₃₁×#546	1	1	yes	characteristic
483	C₂²	C₃₁×#550	1	1	yes	characteristic
484	C₂²	C₂×C₃₁×#135	1	1	yes	characteristic
485	C₂²	C₂×C₃₁×#137	1	1	yes	characteristic
486	C₂²	C₃₁×#577	1	1	yes	characteristic
487	C₂²	C₃₁×#578	1	1	yes	characteristic
488	C₄	—	2	2	no	—
489	C₄	—	4	2	no	—
490	C₄	—	4	2	no	—
491	C₄	—	4	2	no	—
492	C₄	—	4	2	no	—
493	C₄	—	8	2	no	—
494	C₄	—	8	2	no	—
495	C₄	—	8	1	no	—
496	C₄	C₃₁×#464	1	4	yes	—
497	C₄	C₃₁×#525	1	1	yes	characteristic
498	C₄	C₃₁×#535	1	1	yes	characteristic
499	C₄	C₃₁×#553	1	1	yes	characteristic
500	C₄	C₃₁×#555	1	1	yes	characteristic
501	C₂	—	8	2	no	—
502	C₂	C₃₁×#2414	1	1	yes	characteristic
503	C₂	C₂×C₃₁×#464	1	1	yes	characteristic
504	C₂	C₃₁×#3046	1	1	yes	characteristic
505	C₂	C₃₁×#3302	1	1	yes	characteristic
506	C₂	C₃₁×#3331	1	1	yes	characteristic
507	C₂	C₃₁×#3394	1	1	yes	characteristic
508	C₂	C₃₁×#3398	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₃₁
prime radical	C₂²×D₄×C₃₁	C₂³
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
1. C₂×C₃₁×#462	C₂	semidirect
4. C₃₁×#2355	C₂	semidirect
5. C₃₁×#2056	C₂	semidirect
8. C₃₁×#1956	C₂	semidirect
9. C₃₁×#1939	C₂	semidirect
10. C₃₁×#1927	C₂	semidirect
162. #24629	C₃₁	direct (N × H)
220. C₂×#462	C₂×C₃₁	semidirect
223. #2355	C₂×C₃₁	semidirect
224. #2056	C₂×C₃₁	semidirect
227. #1956	C₂×C₃₁	semidirect
228. #1939	C₂×C₃₁	semidirect
229. #1927	C₂×C₃₁	semidirect
351. C₃₁	#24629	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×#462	2
C₂×C₄×SD₁₆×C₃₁	2
C₃₁×#2547	2
C₃₁×#2355	2
C₃₁×#2056	2
C₃₁×#2015	2
C₃₁×#1983	2
C₃₁×#1956	2
C₃₁×#1939	2
C₃₁×#1927	2
C₃₁×#1802	2
#24629	31

Subgroups — C31×#24629 #21481388

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#24629 #21481388