Subgroups — C₃₁×#10048 #21466807

Order 7936.

746 conjugacy classes of subgroups.

The subgroup lattice has 440 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×#459	C₂	1	1	yes	maximal, characteristic
3	C₃₁×#2563	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#1982	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃₁×#333	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₃₁×D₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#1279	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×#459	—	2	2	no	—
16	C₃₁×#459	—	2	2	no	—
17	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
18	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
19	C₂×C₃₁×#102	—	2	1	no	—
20	C₂×C₃₁×#102	—	2	2	no	—
21	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
22	C₃₁×#393	—	2	2	no	—
23	C₃₁×#390	—	2	1	no	—
24	C₃₁×#382	—	2	1	no	—
25	C₃₁×#380	—	2	2	no	—
26	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
27	C₃₁×#333	—	2	2	no	—
28	C₃₁×D₄⋊C₈	—	2	2	no	—
29	C₂²×Q₈×C₃₁	D₄	1	2	yes	—
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	8	no	—
37	C₂×D₈×C₃₁	—	2	4	no	—
38	C₂×D₈×C₃₁	—	4	2	no	—
39	C₂×D₈×C₃₁	—	4	2	no	—
40	C₂²×C₈×C₃₁	—	2	1	no	—
41	C₂²×C₈×C₃₁	—	2	1	no	—
42	C₂²×C₈×C₃₁	—	2	1	no	—
43	C₃₁×C₄⋊Q₈	—	2	1	no	—
44	C₃₁×C₄⋊Q₈	—	2	1	no	—
45	C₃₁×C₄⋊Q₈	—	2	1	no	—
46	C₃₁×C₄⋊Q₈	—	2	1	no	—
47	C₃₁×#127	—	2	1	no	—
48	C₃₁×#127	—	2	1	no	—
49	C₃₁×#127	—	2	1	no	—
50	C₃₁×#127	D₄	1	2	yes	—
51	C₄×D₄×C₃₁	—	2	1	no	—
52	C₄×D₄×C₃₁	—	2	1	no	—
53	C₄×D₄×C₃₁	—	2	1	no	—
54	C₄×D₄×C₃₁	—	2	1	no	—
55	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
56	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
57	C₂×C₄⋊C₄×C₃₁	D₄	1	1	yes	characteristic
58	C₂×C₄⋊C₄×C₃₁	D₄	1	2	yes	—
59	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
60	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
61	C₂×C₄²×C₃₁	—	2	1	no	—
62	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
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	D₄	1	2	yes	—
67	C₃₁×#102	—	2	4	no	—
68	C₃₁×#102	—	4	4	no	—
69	C₄×C₈×C₃₁	—	2	1	no	—
70	C₄×C₈×C₃₁	D₄	1	2	yes	—
71	C₃₁×#95	—	2	4	no	—
72	C₃₁×#95	—	2	1	no	—
73	C₂⁴×C₃₁	—	2	1	no	—
74	C₂⁴×C₃₁	—	4	1	no	—
75	C₂×Q₈×C₃₁	—	2	2	no	—
76	C₂×Q₈×C₃₁	—	2	2	no	—
77	C₂×Q₈×C₃₁	—	4	4	no	—
78	C₂×D₄×C₃₁	—	2	1	no	—
79	C₂×D₄×C₃₁	—	2	2	no	—
80	C₂×D₄×C₃₁	—	2	2	no	—
81	C₂×D₄×C₃₁	—	2	1	no	—
82	C₂×D₄×C₃₁	—	2	2	no	—
83	C₂×D₄×C₃₁	—	2	1	no	—
84	C₂×D₄×C₃₁	—	2	1	no	—
85	C₂×D₄×C₃₁	—	2	1	no	—
86	C₂×D₄×C₃₁	—	4	4	no	—
87	C₂×D₄×C₃₁	—	4	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	1	no	—
92	C₂×D₄×C₃₁	—	4	2	no	—
93	C₂×D₄×C₃₁	—	4	2	no	—
94	C₂×D₄×C₃₁	—	4	1	no	—
95	C₂×D₄×C₃₁	—	4	1	no	—
96	C₂×D₄×C₃₁	SD₁₆	1	2	yes	complemented
97	C₂²×C₄×C₃₁	—	2	1	no	—
98	C₂²×C₄×C₃₁	—	2	2	no	—
99	C₂²×C₄×C₃₁	—	2	2	no	—
100	C₂²×C₄×C₃₁	—	4	1	no	—
101	C₂²×C₄×C₃₁	—	4	1	no	—
102	C₂²×C₄×C₃₁	—	4	2	no	—
103	C₂²×C₄×C₃₁	—	4	2	no	—
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×D₄	1	1	yes	characteristic
107	SD₁₆×C₃₁	—	4	16	no	—
108	D₈×C₃₁	—	4	8	no	—
109	C₂×C₈×C₃₁	—	2	4	no	—
110	C₂×C₈×C₃₁	—	2	2	no	—
111	C₂×C₈×C₃₁	—	2	2	no	—
112	C₂×C₈×C₃₁	—	4	1	no	—
113	C₂×C₈×C₃₁	—	4	1	no	—
114	C₂×C₈×C₃₁	—	4	1	no	—
115	C₂×C₈×C₃₁	—	4	2	no	—
116	C₄⋊C₄×C₃₁	—	2	1	no	—
117	C₄⋊C₄×C₃₁	—	2	1	no	—
118	C₄⋊C₄×C₃₁	—	2	2	no	—
119	C₄⋊C₄×C₃₁	—	2	2	no	—
120	C₄⋊C₄×C₃₁	—	4	1	no	—
121	C₄⋊C₄×C₃₁	—	4	1	no	—
122	C₄⋊C₄×C₃₁	—	4	1	no	—
123	C₄⋊C₄×C₃₁	—	4	1	no	—
124	C₂²⋊C₄×C₃₁	—	4	1	no	—
125	C₂²⋊C₄×C₃₁	—	4	1	no	—
126	C₂²⋊C₄×C₃₁	—	8	4	no	—
127	C₄²×C₃₁	—	4	1	no	—
128	C₄²×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	#41	1	1	yes	characteristic
133	#10048	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	1	no	—
141	C₂³×C₃₁	—	8	1	no	—
142	C₂³×C₃₁	—	8	2	no	—
143	C₂³×C₃₁	—	8	2	no	—
144	C₂³×C₃₁	#120	1	1	yes	characteristic
145	Q₈×C₃₁	—	4	4	no	—
146	Q₈×C₃₁	—	8	2	no	—
147	D₄×C₃₁	—	2	2	no	—
148	D₄×C₃₁	—	2	2	no	—
149	D₄×C₃₁	—	4	4	no	—
150	D₄×C₃₁	—	4	2	no	—
151	D₄×C₃₁	—	4	1	no	—
152	D₄×C₃₁	—	4	2	no	—
153	D₄×C₃₁	—	4	4	no	—
154	D₄×C₃₁	—	4	1	no	—
155	D₄×C₃₁	—	8	2	no	—
156	D₄×C₃₁	—	8	1	no	—
157	D₄×C₃₁	—	8	1	no	—
158	D₄×C₃₁	—	8	1	no	—
159	D₄×C₃₁	—	8	1	no	—
160	C₂×C₄×C₃₁	—	2	2	no	—
161	C₂×C₄×C₃₁	—	4	1	no	—
162	C₂×C₄×C₃₁	—	4	2	no	—
163	C₂×C₄×C₃₁	—	4	2	no	—
164	C₂×C₄×C₃₁	—	4	2	no	—
165	C₂×C₄×C₃₁	—	4	2	no	—
166	C₂×C₄×C₃₁	—	4	2	no	—
167	C₂×C₄×C₃₁	—	4	4	no	—
168	C₂×C₄×C₃₁	—	8	2	no	—
169	C₂×C₄×C₃₁	—	8	1	no	—
170	C₂×C₄×C₃₁	—	8	1	no	—
171	C₂×C₄×C₃₁	#120	1	1	yes	characteristic
172	C₂×C₄×C₃₁	#120	1	1	yes	characteristic
173	C₂×C₄×C₃₁	#121	1	1	yes	characteristic
174	C₂×C₄×C₃₁	#121	1	1	yes	characteristic
175	C₂×C₄×C₃₁	#121	1	1	yes	characteristic
176	C₂×C₄×C₃₁	#127	1	1	yes	characteristic
177	C₂×C₄×C₃₁	C₂×SD₁₆	1	1	yes	characteristic
178	C₂×C₄×C₃₁	#135	1	1	yes	characteristic
179	C₂×C₄×C₃₁	#135	1	2	yes	—
180	C₂×C₄×C₃₁	AGL(1,ℤ/8)	1	1	yes	characteristic
181	C₂×C₄×C₃₁	AGL(1,ℤ/8)	1	2	yes	—
182	C₂×C₄×C₃₁	#137	1	1	yes	characteristic
183	C₈×C₃₁	—	2	4	no	—
184	C₈×C₃₁	—	4	2	no	—
185	C₈×C₃₁	—	8	1	no	—
186	C₂×#492	C₂×C₃₁	1	1	yes	characteristic, complemented
187	C₂×#459	C₂×C₃₁	1	1	yes	characteristic
188	#2563	C₂×C₃₁	1	1	yes	characteristic, complemented
189	#1982	C₂×C₃₁	1	1	yes	characteristic, complemented
190	C₂×#333	C₂×C₃₁	1	1	yes	characteristic, complemented
191	C₂×D₄⋊C₈	C₂×C₃₁	1	1	yes	characteristic, complemented
192	#1279	C₂×C₃₁	1	1	yes	characteristic, complemented
193	C₂²×C₃₁	—	4	4	no	—
194	C₂²×C₃₁	—	4	2	no	—
195	C₂²×C₃₁	—	8	2	no	—
196	C₂²×C₃₁	—	8	1	no	—
197	C₂²×C₃₁	—	8	1	no	—
198	C₂²×C₃₁	—	8	2	no	—
199	C₂²×C₃₁	—	8	2	no	—
200	C₂²×C₃₁	—	8	2	no	—
201	C₂²×C₃₁	—	16	2	no	—
202	C₂²×C₃₁	—	16	2	no	—
203	C₂²×C₃₁	#392	1	1	yes	characteristic
204	C₂²×C₃₁	#448	1	1	yes	characteristic
205	C₂²×C₃₁	#449	1	2	yes	—
206	C₂²×C₃₁	#449	1	1	yes	characteristic
207	C₂²×C₃₁	#453	1	2	yes	—
208	C₄×C₃₁	—	2	1	no	—
209	C₄×C₃₁	—	2	1	no	—
210	C₄×C₃₁	—	8	2	no	—
211	C₄×C₃₁	—	8	2	no	—
212	C₄×C₃₁	—	8	1	no	—
213	C₄×C₃₁	#450	1	1	yes	characteristic
214	C₄×C₃₁	#452	1	1	yes	characteristic
215	C₄×C₃₁	#463	1	2	yes	—
216	C₄×C₃₁	#465	1	1	yes	characteristic
217	C₄×C₃₁	#468	1	1	yes	characteristic
218	C₄×C₃₁	#495	1	1	yes	characteristic
219	C₄×C₃₁	#496	1	1	yes	characteristic
220	C₂²×SD₁₆	—	2	2	no	—
221	C₂²×D₈	—	2	1	no	—
222	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
223	C₂×#127	C₂²×C₃₁	1	1	yes	characteristic
224	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
225	#492	—	2	2	no	—
226	#492	—	2	2	no	—
227	#459	—	2	2	no	—
228	#459	—	2	2	no	—
229	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
230	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
231	C₂×#102	—	2	1	no	—
232	C₂×#102	—	2	2	no	—
233	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
234	#393	—	2	2	no	—
235	#390	—	2	1	no	—
236	#382	—	2	1	no	—
237	#380	—	2	2	no	—
238	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
239	#333	—	2	2	no	—
240	D₄⋊C₈	—	2	2	no	—
241	C₂×C₃₁	—	8	2	no	—
242	C₂×C₃₁	—	16	2	no	—
243	C₂×C₃₁	#1622	1	2	yes	—
244	C₂×C₃₁	#1624	1	2	yes	—
245	C₂×C₃₁	#2000	1	1	yes	characteristic
246	C₂×C₃₁	#2002	1	1	yes	characteristic
247	C₂×C₃₁	#2012	1	1	yes	characteristic
248	C₂²×Q₈	D₄×C₃₁	1	2	yes	—
249	C₂²×D₄	—	2	1	no	—
250	C₂²×D₄	—	2	1	no	—
251	C₂²×D₄	—	2	1	no	—
252	C₂²×D₄	D₄×C₃₁	1	1	yes	characteristic
253	C₂³×C₄	—	2	1	no	—
254	C₂×SD₁₆	—	2	8	no	—
255	C₂×SD₁₆	—	4	8	no	—
256	C₂×D₈	—	2	4	no	—
257	C₂×D₈	—	4	2	no	—
258	C₂×D₈	—	4	2	no	—
259	C₂²×C₈	—	2	1	no	—
260	C₂²×C₈	—	2	1	no	—
261	C₂²×C₈	—	2	1	no	—
262	C₄⋊Q₈	—	2	1	no	—
263	C₄⋊Q₈	—	2	1	no	—
264	C₄⋊Q₈	—	2	1	no	—
265	C₄⋊Q₈	—	2	1	no	—
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×C₄⋊C₄	D₄×C₃₁	1	2	yes	—
278	C₂×C₂²⋊C₄	—	2	1	no	—
279	C₂×C₂²⋊C₄	—	2	4	no	—
280	C₂×C₄²	—	2	1	no	—
281	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
282	C₄⋊C₈	—	2	1	no	—
283	C₄⋊C₈	—	2	1	no	—
284	C₄⋊C₈	—	2	1	no	—
285	C₄⋊C₈	D₄×C₃₁	1	2	yes	—
286	#102	—	2	4	no	—
287	#102	—	4	4	no	—
288	C₄×C₈	—	2	1	no	—
289	C₄×C₈	D₄×C₃₁	1	2	yes	—
290	#95	—	2	4	no	—
291	#95	—	2	1	no	—
292	C₃₁	#10048	1	1	yes	characteristic, direct product factor, Sylow
293	C₂⁴	—	2	1	no	—
294	C₂⁴	—	4	1	no	—
295	C₂×Q₈	—	2	2	no	—
296	C₂×Q₈	—	2	2	no	—
297	C₂×Q₈	—	4	4	no	—
298	C₂×D₄	—	2	1	no	—
299	C₂×D₄	—	2	2	no	—
300	C₂×D₄	—	2	2	no	—
301	C₂×D₄	—	2	1	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	4	no	—
307	C₂×D₄	—	4	1	no	—
308	C₂×D₄	—	4	1	no	—
309	C₂×D₄	—	4	1	no	—
310	C₂×D₄	—	4	1	no	—
311	C₂×D₄	—	4	1	no	—
312	C₂×D₄	—	4	2	no	—
313	C₂×D₄	—	4	2	no	—
314	C₂×D₄	—	4	1	no	—
315	C₂×D₄	—	4	1	no	—
316	C₂×D₄	SD₁₆×C₃₁	1	2	yes	complemented
317	C₂²×C₄	—	2	1	no	—
318	C₂²×C₄	—	2	2	no	—
319	C₂²×C₄	—	2	2	no	—
320	C₂²×C₄	—	4	1	no	—
321	C₂²×C₄	—	4	1	no	—
322	C₂²×C₄	—	4	2	no	—
323	C₂²×C₄	—	4	2	no	—
324	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
325	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
326	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
327	SD₁₆	—	4	16	no	—
328	D₈	—	4	8	no	—
329	C₂×C₈	—	2	4	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	2	no	—
336	C₄⋊C₄	—	2	1	no	—
337	C₄⋊C₄	—	2	1	no	—
338	C₄⋊C₄	—	2	2	no	—
339	C₄⋊C₄	—	2	2	no	—
340	C₄⋊C₄	—	4	1	no	—
341	C₄⋊C₄	—	4	1	no	—
342	C₄⋊C₄	—	4	1	no	—
343	C₄⋊C₄	—	4	1	no	—
344	C₂²⋊C₄	—	4	1	no	—
345	C₂²⋊C₄	—	4	1	no	—
346	C₂²⋊C₄	—	8	4	no	—
347	C₄²	—	4	1	no	—
348	C₄²	—	4	1	no	—
349	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
350	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
351	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
352	C₄²	#41×C₃₁	1	1	yes	characteristic
353	C₂³	—	2	2	no	—
354	C₂³	—	4	2	no	—
355	C₂³	—	4	1	no	—
356	C₂³	—	4	2	no	—
357	C₂³	—	4	1	no	—
358	C₂³	—	4	2	no	—
359	C₂³	—	8	1	no	—
360	C₂³	—	8	1	no	—
361	C₂³	—	8	2	no	—
362	C₂³	—	8	2	no	—
363	C₂³	C₃₁×#120	1	1	yes	characteristic
364	Q₈	—	4	4	no	—
365	Q₈	—	8	2	no	—
366	D₄	—	2	2	no	—
367	D₄	—	2	2	no	—
368	D₄	—	4	4	no	—
369	D₄	—	4	2	no	—
370	D₄	—	4	1	no	—
371	D₄	—	4	2	no	—
372	D₄	—	4	4	no	—
373	D₄	—	4	1	no	—
374	D₄	—	8	2	no	—
375	D₄	—	8	1	no	—
376	D₄	—	8	1	no	—
377	D₄	—	8	1	no	—
378	D₄	—	8	1	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	4	2	no	—
381	C₂×C₄	—	4	2	no	—
382	C₂×C₄	—	4	2	no	—
383	C₂×C₄	—	4	2	no	—
384	C₂×C₄	—	4	4	no	—
385	C₂×C₄	—	4	1	no	—
386	C₂×C₄	—	4	2	no	—
387	C₂×C₄	—	8	2	no	—
388	C₂×C₄	—	8	1	no	—
389	C₂×C₄	—	8	1	no	—
390	C₂×C₄	C₃₁×#120	1	1	yes	characteristic
391	C₂×C₄	C₃₁×#120	1	1	yes	characteristic
392	C₂×C₄	C₃₁×#121	1	1	yes	characteristic
393	C₂×C₄	C₃₁×#121	1	1	yes	characteristic
394	C₂×C₄	C₃₁×#121	1	1	yes	characteristic
395	C₂×C₄	C₃₁×#127	1	1	yes	characteristic
396	C₂×C₄	C₂×SD₁₆×C₃₁	1	1	yes	characteristic
397	C₂×C₄	C₃₁×#135	1	1	yes	characteristic
398	C₂×C₄	C₃₁×#135	1	2	yes	—
399	C₂×C₄	C₃₁×AGL(1,ℤ/8)	1	1	yes	characteristic
400	C₂×C₄	C₃₁×AGL(1,ℤ/8)	1	2	yes	—
401	C₂×C₄	C₃₁×#137	1	1	yes	characteristic
402	C₈	—	2	4	no	—
403	C₈	—	4	2	no	—
404	C₈	—	8	1	no	—
405	C₂²	—	4	4	no	—
406	C₂²	—	4	2	no	—
407	C₂²	—	8	2	no	—
408	C₂²	—	8	1	no	—
409	C₂²	—	8	1	no	—
410	C₂²	—	8	2	no	—
411	C₂²	—	8	2	no	—
412	C₂²	—	8	2	no	—
413	C₂²	—	16	2	no	—
414	C₂²	—	16	2	no	—
415	C₂²	C₃₁×#392	1	1	yes	characteristic
416	C₂²	C₃₁×#448	1	1	yes	characteristic
417	C₂²	C₃₁×#449	1	2	yes	—
418	C₂²	C₃₁×#449	1	1	yes	characteristic
419	C₂²	C₃₁×#453	1	2	yes	—
420	C₄	—	2	1	no	—
421	C₄	—	2	1	no	—
422	C₄	—	8	2	no	—
423	C₄	—	8	2	no	—
424	C₄	—	8	1	no	—
425	C₄	C₃₁×#450	1	1	yes	characteristic
426	C₄	C₃₁×#452	1	1	yes	characteristic
427	C₄	C₃₁×#463	1	2	yes	—
428	C₄	C₃₁×#465	1	1	yes	characteristic
429	C₄	C₃₁×#468	1	1	yes	characteristic
430	C₄	C₃₁×#495	1	1	yes	characteristic
431	C₄	C₃₁×#496	1	1	yes	characteristic
432	C₂	—	8	2	no	—
433	C₂	—	16	2	no	—
434	C₂	C₃₁×#1622	1	2	yes	—
435	C₂	C₃₁×#1624	1	2	yes	—
436	C₂	C₃₁×#2000	1	1	yes	characteristic
437	C₂	C₃₁×#2002	1	1	yes	characteristic
438	C₂	C₃₁×#2012	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃₁	#120
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
3. C₃₁×#2563	C₂	semidirect
4. C₃₁×#1982	C₂	semidirect
5. C₂×C₃₁×#333	C₂	semidirect
6. C₂×C₃₁×D₄⋊C₈	C₂	semidirect
7. C₃₁×#1279	C₂	semidirect
96. C₂×D₄×C₃₁	SD₁₆	semidirect
133. #10048	C₃₁	direct (N × H)
186. C₂×#492	C₂×C₃₁	semidirect
188. #2563	C₂×C₃₁	semidirect
189. #1982	C₂×C₃₁	semidirect
190. C₂×#333	C₂×C₃₁	semidirect
191. C₂×D₄⋊C₈	C₂×C₃₁	semidirect
192. #1279	C₂×C₃₁	semidirect
292. C₃₁	#10048	direct (N × H)
316. C₂×D₄	SD₁₆×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×#459	2
C₃₁×#2563	2
C₃₁×#1982	2
C₂×C₃₁×#333	2
C₂×C₃₁×D₄⋊C₈	2
C₃₁×#1279	2
#10048	31

Subgroups — C31×#10048 #21466807

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#10048 #21466807