Subgroups — C₃₁×#10266 #21467025

Order 7936.

710 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#492	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃₁×#474	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃₁×#459	C₂	1	1	yes	maximal, characteristic
4	C₃₁×#1954	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃₁×#332	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₃₁×#331	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#1277	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×SD₁₆×C₃₁	—	2	2	no	—
9	C₂²×D₈×C₃₁	—	2	1	no	—
10	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
11	C₂×C₃₁×#127	C₂²	1	1	yes	characteristic
12	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
13	C₃₁×#492	—	2	2	no	—
14	C₃₁×#492	—	2	2	no	—
15	C₃₁×#474	—	2	2	no	—
16	C₃₁×#474	—	2	2	no	—
17	C₃₁×#459	—	2	2	no	—
18	C₃₁×#459	—	2	2	no	—
19	C₂×C₃₁×#107	—	2	1	no	—
20	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
23	C₂×C₃₁×#102	—	2	1	no	—
24	C₂×C₃₁×#102	—	2	1	no	—
25	C₂×C₃₁×C₂²⋊C₈	—	2	2	no	—
26	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
27	C₃₁×#332	—	2	2	no	—
28	C₃₁×#331	—	2	2	no	—
29	C₂²×Q₈×C₃₁	—	2	1	no	—
30	C₂²×D₄×C₃₁	—	2	1	no	—
31	C₂²×D₄×C₃₁	—	2	1	no	—
32	C₂²×D₄×C₃₁	—	2	1	no	—
33	C₂²×D₄×C₃₁	D₄	1	1	yes	characteristic
34	C₂³×C₄×C₃₁	—	2	1	no	—
35	C₂×SD₁₆×C₃₁	—	2	8	no	—
36	C₂×SD₁₆×C₃₁	—	4	4	no	—
37	C₂×SD₁₆×C₃₁	—	4	4	no	—
38	C₂×D₈×C₃₁	—	2	4	no	—
39	C₂×D₈×C₃₁	—	4	2	no	—
40	C₂×D₈×C₃₁	—	4	2	no	—
41	C₂²×C₈×C₃₁	—	2	1	no	—
42	C₂²×C₈×C₃₁	—	2	1	no	—
43	C₂²×C₈×C₃₁	—	2	1	no	—
44	C₂²×C₈×C₃₁	D₄	1	2	yes	—
45	C₃₁×C₄⋊Q₈	—	2	1	no	—
46	C₃₁×C₄⋊Q₈	—	2	1	no	—
47	C₃₁×C₄⋊Q₈	—	2	1	no	—
48	C₃₁×C₄⋊Q₈	D₄	1	2	yes	—
49	C₃₁×#127	—	2	1	no	—
50	C₃₁×#127	—	2	1	no	—
51	C₃₁×#127	—	2	1	no	—
52	C₃₁×#127	D₄	1	2	yes	—
53	C₄×D₄×C₃₁	—	2	1	no	—
54	C₄×D₄×C₃₁	—	2	1	no	—
55	C₄×D₄×C₃₁	—	2	1	no	—
56	C₄×D₄×C₃₁	—	2	1	no	—
57	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
58	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
59	C₂×C₄⋊C₄×C₃₁	D₄	1	1	yes	characteristic
60	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
61	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
62	C₃₁×#107	—	2	4	no	—
63	C₃₁×C₄⋊C₈	—	2	1	no	—
64	C₃₁×C₄⋊C₈	—	2	1	no	—
65	C₃₁×C₄⋊C₈	—	2	1	no	—
66	C₃₁×C₄⋊C₈	—	2	1	no	—
67	C₃₁×C₄⋊C₈	D₄	1	2	yes	—
68	C₃₁×C₄⋊C₈	D₄	1	2	yes	—
69	C₃₁×#102	—	2	4	no	—
70	C₃₁×#102	—	2	4	no	—
71	C₃₁×C₂²⋊C₈	—	4	4	no	—
72	C₄×C₈×C₃₁	—	2	1	no	—
73	C₄×C₈×C₃₁	—	2	1	no	—
74	C₂⁴×C₃₁	—	2	1	no	—
75	C₂⁴×C₃₁	—	4	1	no	—
76	C₂×Q₈×C₃₁	—	2	2	no	—
77	C₂×Q₈×C₃₁	—	4	1	no	—
78	C₂×Q₈×C₃₁	—	4	2	no	—
79	C₂×Q₈×C₃₁	—	4	2	no	—
80	C₂×D₄×C₃₁	—	2	1	no	—
81	C₂×D₄×C₃₁	—	2	1	no	—
82	C₂×D₄×C₃₁	—	2	2	no	—
83	C₂×D₄×C₃₁	—	2	2	no	—
84	C₂×D₄×C₃₁	—	2	2	no	—
85	C₂×D₄×C₃₁	—	2	1	no	—
86	C₂×D₄×C₃₁	—	2	1	no	—
87	C₂×D₄×C₃₁	—	2	1	no	—
88	C₂×D₄×C₃₁	—	4	1	no	—
89	C₂×D₄×C₃₁	—	4	1	no	—
90	C₂×D₄×C₃₁	—	4	1	no	—
91	C₂×D₄×C₃₁	—	4	2	no	—
92	C₂×D₄×C₃₁	—	4	1	no	—
93	C₂×D₄×C₃₁	—	4	1	no	—
94	C₂×D₄×C₃₁	—	4	1	no	—
95	C₂×D₄×C₃₁	—	4	2	no	—
96	C₂×D₄×C₃₁	—	4	1	no	—
97	C₂×D₄×C₃₁	—	8	2	no	—
98	C₂×D₄×C₃₁	SD₁₆	1	2	yes	complemented
99	C₂²×C₄×C₃₁	—	2	1	no	—
100	C₂²×C₄×C₃₁	—	4	1	no	—
101	C₂²×C₄×C₃₁	—	4	1	no	—
102	C₂²×C₄×C₃₁	—	4	1	no	—
103	C₂²×C₄×C₃₁	—	4	2	no	—
104	C₂²×C₄×C₃₁	—	4	2	no	—
105	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₃₁	#41	1	1	yes	characteristic
108	SD₁₆×C₃₁	—	4	16	no	—
109	D₈×C₃₁	—	4	8	no	—
110	C₂×C₈×C₃₁	—	2	2	no	—
111	C₂×C₈×C₃₁	—	2	2	no	—
112	C₂×C₈×C₃₁	—	2	2	no	—
113	C₂×C₈×C₃₁	—	2	2	no	—
114	C₂×C₈×C₃₁	—	4	1	no	—
115	C₂×C₈×C₃₁	—	4	1	no	—
116	C₂×C₈×C₃₁	—	4	1	no	—
117	C₂×C₈×C₃₁	—	4	1	no	—
118	C₂×C₈×C₃₁	—	4	1	no	—
119	C₂×C₈×C₃₁	—	4	2	no	—
120	C₂×C₈×C₃₁	D₈	1	4	yes	complemented
121	C₄⋊C₄×C₃₁	—	2	1	no	—
122	C₄⋊C₄×C₃₁	—	2	2	no	—
123	C₄⋊C₄×C₃₁	—	2	1	no	—
124	C₄⋊C₄×C₃₁	—	2	2	no	—
125	C₄⋊C₄×C₃₁	—	4	1	no	—
126	C₄⋊C₄×C₃₁	—	4	1	no	—
127	C₂²⋊C₄×C₃₁	—	4	1	no	—
128	C₂²⋊C₄×C₃₁	—	4	1	no	—
129	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
130	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
131	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
132	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
133	#10266	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
134	C₂³×C₃₁	—	2	2	no	—
135	C₂³×C₃₁	—	4	1	no	—
136	C₂³×C₃₁	—	4	2	no	—
137	C₂³×C₃₁	—	4	1	no	—
138	C₂³×C₃₁	—	4	2	no	—
139	C₂³×C₃₁	—	4	2	no	—
140	C₂³×C₃₁	—	8	2	no	—
141	C₂³×C₃₁	—	8	1	no	—
142	C₂³×C₃₁	—	8	1	no	—
143	C₂³×C₃₁	—	8	2	no	—
144	C₂³×C₃₁	#121	1	1	yes	characteristic
145	Q₈×C₃₁	—	4	4	no	—
146	Q₈×C₃₁	—	8	1	no	—
147	Q₈×C₃₁	—	8	1	no	—
148	D₄×C₃₁	—	2	2	no	—
149	D₄×C₃₁	—	2	2	no	—
150	D₄×C₃₁	—	4	4	no	—
151	D₄×C₃₁	—	4	1	no	—
152	D₄×C₃₁	—	4	2	no	—
153	D₄×C₃₁	—	4	1	no	—
154	D₄×C₃₁	—	4	2	no	—
155	D₄×C₃₁	—	8	2	no	—
156	D₄×C₃₁	—	8	2	no	—
157	D₄×C₃₁	—	8	1	no	—
158	D₄×C₃₁	—	8	1	no	—
159	D₄×C₃₁	—	8	1	no	—
160	D₄×C₃₁	—	8	1	no	—
161	C₂×C₄×C₃₁	—	2	2	no	—
162	C₂×C₄×C₃₁	—	4	1	no	—
163	C₂×C₄×C₃₁	—	4	2	no	—
164	C₂×C₄×C₃₁	—	4	2	no	—
165	C₂×C₄×C₃₁	—	8	2	no	—
166	C₂×C₄×C₃₁	—	8	2	no	—
167	C₂×C₄×C₃₁	—	8	1	no	—
168	C₂×C₄×C₃₁	—	8	1	no	—
169	C₂×C₄×C₃₁	#120	1	1	yes	characteristic
170	C₂×C₄×C₃₁	#120	1	1	yes	characteristic
171	C₂×C₄×C₃₁	#120	1	1	yes	characteristic
172	C₂×C₄×C₃₁	#121	1	1	yes	characteristic
173	C₂×C₄×C₃₁	#121	1	1	yes	characteristic
174	C₂×C₄×C₃₁	#127	1	1	yes	characteristic
175	C₂×C₄×C₃₁	C₂×D₈	1	2	yes	—
176	C₂×C₄×C₃₁	C₂×SD₁₆	1	1	yes	characteristic
177	C₂×C₄×C₃₁	#135	1	1	yes	characteristic
178	C₂×C₄×C₃₁	AGL(1,ℤ/8)	1	2	yes	—
179	C₂×C₄×C₃₁	AGL(1,ℤ/8)	1	1	yes	characteristic
180	C₂×C₄×C₃₁	#137	1	1	yes	characteristic
181	C₈×C₃₁	—	2	4	no	—
182	C₈×C₃₁	—	4	2	no	—
183	C₈×C₃₁	—	4	2	no	—
184	C₈×C₃₁	—	8	1	no	—
185	C₂×#492	C₂×C₃₁	1	1	yes	characteristic, complemented
186	C₂×#474	C₂×C₃₁	1	1	yes	characteristic, complemented
187	C₂×#459	C₂×C₃₁	1	1	yes	characteristic
188	#1954	C₂×C₃₁	1	1	yes	characteristic, complemented
189	C₂×#332	C₂×C₃₁	1	1	yes	characteristic, complemented
190	C₂×#331	C₂×C₃₁	1	1	yes	characteristic, complemented
191	#1277	C₂×C₃₁	1	1	yes	characteristic, complemented
192	C₂²×C₃₁	—	4	4	no	—
193	C₂²×C₃₁	—	4	2	no	—
194	C₂²×C₃₁	—	8	2	no	—
195	C₂²×C₃₁	—	8	1	no	—
196	C₂²×C₃₁	—	8	1	no	—
197	C₂²×C₃₁	—	8	2	no	—
198	C₂²×C₃₁	—	8	2	no	—
199	C₂²×C₃₁	—	8	2	no	—
200	C₂²×C₃₁	—	16	2	no	—
201	C₂²×C₃₁	—	16	2	no	—
202	C₂²×C₃₁	#392	1	1	yes	characteristic
203	C₂²×C₃₁	#459	1	2	yes	—
204	C₂²×C₃₁	#465	1	1	yes	characteristic
205	C₂²×C₃₁	#468	1	1	yes	characteristic
206	C₂²×C₃₁	#471	1	2	yes	—
207	C₄×C₃₁	—	2	1	no	—
208	C₄×C₃₁	—	2	1	no	—
209	C₄×C₃₁	—	8	1	no	—
210	C₄×C₃₁	—	8	2	no	—
211	C₄×C₃₁	#447	1	2	yes	—
212	C₄×C₃₁	#448	1	1	yes	characteristic
213	C₄×C₃₁	#449	1	1	yes	characteristic
214	C₄×C₃₁	#450	1	1	yes	characteristic
215	C₄×C₃₁	#452	1	1	yes	characteristic
216	C₄×C₃₁	#493	1	1	yes	characteristic
217	C₄×C₃₁	#496	1	1	yes	characteristic
218	C₂²×SD₁₆	—	2	2	no	—
219	C₂²×D₈	—	2	1	no	—
220	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
221	C₂×#127	C₂²×C₃₁	1	1	yes	characteristic
222	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
223	#492	—	2	2	no	—
224	#492	—	2	2	no	—
225	#474	—	2	2	no	—
226	#474	—	2	2	no	—
227	#459	—	2	2	no	—
228	#459	—	2	2	no	—
229	C₂×#107	—	2	1	no	—
230	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
231	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
232	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
233	C₂×#102	—	2	1	no	—
234	C₂×#102	—	2	1	no	—
235	C₂×C₂²⋊C₈	—	2	2	no	—
236	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
237	#332	—	2	2	no	—
238	#331	—	2	2	no	—
239	C₂×C₃₁	—	8	2	no	—
240	C₂×C₃₁	—	16	2	no	—
241	C₂×C₃₁	#1665	1	2	yes	—
242	C₂×C₃₁	#1685	1	2	yes	—
243	C₂×C₃₁	#2000	1	1	yes	characteristic
244	C₂×C₃₁	#2011	1	1	yes	characteristic
245	C₂×C₃₁	#2019	1	1	yes	characteristic
246	C₂²×Q₈	—	2	1	no	—
247	C₂²×D₄	—	2	1	no	—
248	C₂²×D₄	—	2	1	no	—
249	C₂²×D₄	—	2	1	no	—
250	C₂²×D₄	D₄×C₃₁	1	1	yes	characteristic
251	C₂³×C₄	—	2	1	no	—
252	C₂×SD₁₆	—	2	8	no	—
253	C₂×SD₁₆	—	4	4	no	—
254	C₂×SD₁₆	—	4	4	no	—
255	C₂×D₈	—	2	4	no	—
256	C₂×D₈	—	4	2	no	—
257	C₂×D₈	—	4	2	no	—
258	C₂²×C₈	—	2	1	no	—
259	C₂²×C₈	—	2	1	no	—
260	C₂²×C₈	—	2	1	no	—
261	C₂²×C₈	D₄×C₃₁	1	2	yes	—
262	C₄⋊Q₈	—	2	1	no	—
263	C₄⋊Q₈	—	2	1	no	—
264	C₄⋊Q₈	—	2	1	no	—
265	C₄⋊Q₈	D₄×C₃₁	1	2	yes	—
266	#127	—	2	1	no	—
267	#127	—	2	1	no	—
268	#127	—	2	1	no	—
269	#127	D₄×C₃₁	1	2	yes	—
270	C₄×D₄	—	2	1	no	—
271	C₄×D₄	—	2	1	no	—
272	C₄×D₄	—	2	1	no	—
273	C₄×D₄	—	2	1	no	—
274	C₂×C₄⋊C₄	—	2	1	no	—
275	C₂×C₄⋊C₄	—	2	1	no	—
276	C₂×C₄⋊C₄	D₄×C₃₁	1	1	yes	characteristic
277	C₂×C₂²⋊C₄	—	2	1	no	—
278	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
279	#107	—	2	4	no	—
280	C₄⋊C₈	—	2	1	no	—
281	C₄⋊C₈	—	2	1	no	—
282	C₄⋊C₈	—	2	1	no	—
283	C₄⋊C₈	—	2	1	no	—
284	C₄⋊C₈	D₄×C₃₁	1	2	yes	—
285	C₄⋊C₈	D₄×C₃₁	1	2	yes	—
286	#102	—	2	4	no	—
287	#102	—	2	4	no	—
288	C₂²⋊C₈	—	4	4	no	—
289	C₄×C₈	—	2	1	no	—
290	C₄×C₈	—	2	1	no	—
291	C₃₁	#10266	1	1	yes	characteristic, direct product factor, Sylow
292	C₂⁴	—	2	1	no	—
293	C₂⁴	—	4	1	no	—
294	C₂×Q₈	—	2	2	no	—
295	C₂×Q₈	—	4	1	no	—
296	C₂×Q₈	—	4	2	no	—
297	C₂×Q₈	—	4	2	no	—
298	C₂×D₄	—	2	1	no	—
299	C₂×D₄	—	2	1	no	—
300	C₂×D₄	—	2	2	no	—
301	C₂×D₄	—	2	2	no	—
302	C₂×D₄	—	2	2	no	—
303	C₂×D₄	—	2	1	no	—
304	C₂×D₄	—	2	1	no	—
305	C₂×D₄	—	2	1	no	—
306	C₂×D₄	—	4	1	no	—
307	C₂×D₄	—	4	1	no	—
308	C₂×D₄	—	4	1	no	—
309	C₂×D₄	—	4	2	no	—
310	C₂×D₄	—	4	1	no	—
311	C₂×D₄	—	4	1	no	—
312	C₂×D₄	—	4	1	no	—
313	C₂×D₄	—	4	2	no	—
314	C₂×D₄	—	4	1	no	—
315	C₂×D₄	—	8	2	no	—
316	C₂×D₄	SD₁₆×C₃₁	1	2	yes	complemented
317	C₂²×C₄	—	2	1	no	—
318	C₂²×C₄	—	4	1	no	—
319	C₂²×C₄	—	4	1	no	—
320	C₂²×C₄	—	4	1	no	—
321	C₂²×C₄	—	4	2	no	—
322	C₂²×C₄	—	4	2	no	—
323	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
324	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
325	C₂²×C₄	#41×C₃₁	1	1	yes	characteristic
326	SD₁₆	—	4	16	no	—
327	D₈	—	4	8	no	—
328	C₂×C₈	—	2	2	no	—
329	C₂×C₈	—	2	2	no	—
330	C₂×C₈	—	2	2	no	—
331	C₂×C₈	—	2	2	no	—
332	C₂×C₈	—	4	1	no	—
333	C₂×C₈	—	4	1	no	—
334	C₂×C₈	—	4	1	no	—
335	C₂×C₈	—	4	1	no	—
336	C₂×C₈	—	4	1	no	—
337	C₂×C₈	—	4	2	no	—
338	C₂×C₈	D₈×C₃₁	1	4	yes	complemented
339	C₄⋊C₄	—	2	1	no	—
340	C₄⋊C₄	—	2	2	no	—
341	C₄⋊C₄	—	2	1	no	—
342	C₄⋊C₄	—	2	2	no	—
343	C₄⋊C₄	—	4	1	no	—
344	C₄⋊C₄	—	4	1	no	—
345	C₂²⋊C₄	—	4	1	no	—
346	C₂²⋊C₄	—	4	1	no	—
347	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
348	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
349	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
350	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
351	C₂³	—	2	2	no	—
352	C₂³	—	4	2	no	—
353	C₂³	—	4	1	no	—
354	C₂³	—	4	2	no	—
355	C₂³	—	4	1	no	—
356	C₂³	—	4	2	no	—
357	C₂³	—	8	2	no	—
358	C₂³	—	8	1	no	—
359	C₂³	—	8	1	no	—
360	C₂³	—	8	2	no	—
361	C₂³	C₃₁×#121	1	1	yes	characteristic
362	Q₈	—	4	4	no	—
363	Q₈	—	8	1	no	—
364	Q₈	—	8	1	no	—
365	D₄	—	2	2	no	—
366	D₄	—	2	2	no	—
367	D₄	—	4	4	no	—
368	D₄	—	4	1	no	—
369	D₄	—	4	2	no	—
370	D₄	—	4	1	no	—
371	D₄	—	4	2	no	—
372	D₄	—	8	2	no	—
373	D₄	—	8	2	no	—
374	D₄	—	8	1	no	—
375	D₄	—	8	1	no	—
376	D₄	—	8	1	no	—
377	D₄	—	8	1	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	4	2	no	—
380	C₂×C₄	—	4	1	no	—
381	C₂×C₄	—	4	2	no	—
382	C₂×C₄	—	8	2	no	—
383	C₂×C₄	—	8	2	no	—
384	C₂×C₄	—	8	1	no	—
385	C₂×C₄	—	8	1	no	—
386	C₂×C₄	C₃₁×#120	1	1	yes	characteristic
387	C₂×C₄	C₃₁×#120	1	1	yes	characteristic
388	C₂×C₄	C₃₁×#120	1	1	yes	characteristic
389	C₂×C₄	C₃₁×#121	1	1	yes	characteristic
390	C₂×C₄	C₃₁×#121	1	1	yes	characteristic
391	C₂×C₄	C₃₁×#127	1	1	yes	characteristic
392	C₂×C₄	C₂×D₈×C₃₁	1	2	yes	—
393	C₂×C₄	C₂×SD₁₆×C₃₁	1	1	yes	characteristic
394	C₂×C₄	C₃₁×#135	1	1	yes	characteristic
395	C₂×C₄	C₃₁×AGL(1,ℤ/8)	1	2	yes	—
396	C₂×C₄	C₃₁×AGL(1,ℤ/8)	1	1	yes	characteristic
397	C₂×C₄	C₃₁×#137	1	1	yes	characteristic
398	C₈	—	2	4	no	—
399	C₈	—	4	2	no	—
400	C₈	—	4	2	no	—
401	C₈	—	8	1	no	—
402	C₂²	—	4	4	no	—
403	C₂²	—	4	2	no	—
404	C₂²	—	8	2	no	—
405	C₂²	—	8	1	no	—
406	C₂²	—	8	1	no	—
407	C₂²	—	8	2	no	—
408	C₂²	—	8	2	no	—
409	C₂²	—	8	2	no	—
410	C₂²	—	16	2	no	—
411	C₂²	—	16	2	no	—
412	C₂²	C₃₁×#392	1	1	yes	characteristic
413	C₂²	C₃₁×#459	1	2	yes	—
414	C₂²	C₃₁×#465	1	1	yes	characteristic
415	C₂²	C₃₁×#468	1	1	yes	characteristic
416	C₂²	C₃₁×#471	1	2	yes	—
417	C₄	—	2	1	no	—
418	C₄	—	2	1	no	—
419	C₄	—	8	1	no	—
420	C₄	—	8	2	no	—
421	C₄	C₃₁×#447	1	2	yes	—
422	C₄	C₃₁×#448	1	1	yes	characteristic
423	C₄	C₃₁×#449	1	1	yes	characteristic
424	C₄	C₃₁×#450	1	1	yes	characteristic
425	C₄	C₃₁×#452	1	1	yes	characteristic
426	C₄	C₃₁×#493	1	1	yes	characteristic
427	C₄	C₃₁×#496	1	1	yes	characteristic
428	C₂	—	8	2	no	—
429	C₂	—	16	2	no	—
430	C₂	C₃₁×#1665	1	2	yes	—
431	C₂	C₃₁×#1685	1	2	yes	—
432	C₂	C₃₁×#2000	1	1	yes	characteristic
433	C₂	C₃₁×#2011	1	1	yes	characteristic
434	C₂	C₃₁×#2019	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃₁	#121
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₃₁
prime radical	C₂×C₃₁×#459	C₂
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₃₁ ◁ C₂×C₄²×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃₁×#492	C₂	semidirect
2. C₂×C₃₁×#474	C₂	semidirect
4. C₃₁×#1954	C₂	semidirect
5. C₂×C₃₁×#332	C₂	semidirect
6. C₂×C₃₁×#331	C₂	semidirect
7. C₃₁×#1277	C₂	semidirect
98. C₂×D₄×C₃₁	SD₁₆	semidirect
120. C₂×C₈×C₃₁	D₈	semidirect
133. #10266	C₃₁	direct (N × H)
185. C₂×#492	C₂×C₃₁	semidirect
186. C₂×#474	C₂×C₃₁	semidirect
188. #1954	C₂×C₃₁	semidirect
189. C₂×#332	C₂×C₃₁	semidirect
190. C₂×#331	C₂×C₃₁	semidirect
191. #1277	C₂×C₃₁	semidirect
291. C₃₁	#10266	direct (N × H)
316. C₂×D₄	SD₁₆×C₃₁	semidirect
338. C₂×C₈	D₈×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×#492	2
C₂×C₃₁×#474	2
C₂×C₃₁×#459	2
C₃₁×#1954	2
C₂×C₃₁×#332	2
C₂×C₃₁×#331	2
C₃₁×#1277	2
#10266	31

Subgroups — C31×#10266 #21467025

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#10266 #21467025