Subgroups — C₃₁×#19386 #21476145

Order 7936.

792 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	C₃₁×#3205	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3036	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃₁×#459	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#2972	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#1681	C₂	1	4	yes	maximal, complemented
6	C₃₁×#1667	C₂	1	4	yes	maximal, complemented
7	C₃₁×#1571	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#1545	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#1540	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₃₁×AGL(1,ℤ/8)	—	2	1	no	—
11	C₂²×D₈×C₃₁	—	2	1	no	—
12	C₃₁×#532	C₂²	1	1	yes	characteristic
13	C₂×C₃₁×#127	C₂²	1	1	yes	characteristic
14	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
15	C₃₁×#493	C₂²	1	2	yes	complemented
16	C₃₁×#486	C₂²	1	2	yes	complemented
17	C₃₁×#463	—	2	2	no	—
18	C₃₁×#461	C₂²	1	2	yes	complemented
19	C₃₁×#459	—	2	2	no	—
20	C₃₁×#459	—	2	2	no	—
21	C₃₁×#459	C₂²	1	4	yes	—
22	C₃₁×#459	C₂²	1	2	yes	complemented
23	C₃₁×#447	—	2	2	no	—
24	C₈×D₄×C₃₁	—	2	2	no	—
25	C₈×D₄×C₃₁	C₂²	1	4	yes	complemented
26	C₃₁×#431	C₂²	1	1	yes	characteristic
27	C₃₁×#431	C₂²	1	1	yes	characteristic
28	C₃₁×#423	C₂²	1	1	yes	characteristic
29	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
30	C₃₁×#417	—	2	1	no	—
31	C₂×C₃₁×#102	—	2	1	no	—
32	C₂×C₃₁×C₂²⋊C₈	—	2	2	no	—
33	C₃₁×#335	C₂²	1	4	yes	complemented
34	C₃₁×#332	C₂²	1	2	yes	complemented
35	C₃₁×#331	C₂²	1	2	yes	complemented
36	C₃₁×#331	C₂²	1	4	yes	complemented
37	C₂×#41×C₃₁	—	2	1	no	—
38	C₂²×D₄×C₃₁	—	2	1	no	—
39	C₂²×D₄×C₃₁	—	2	1	no	—
40	C₂²×D₄×C₃₁	—	2	1	no	—
41	C₂²×D₄×C₃₁	D₄	1	1	yes	characteristic
42	C₂³×C₄×C₃₁	—	2	1	no	—
43	C₃₁×AGL(1,ℤ/8)	—	4	4	no	—
44	C₂×SD₁₆×C₃₁	—	2	2	no	—
45	C₂×D₈×C₃₁	—	2	4	no	—
46	C₂×D₈×C₃₁	—	2	2	no	—
47	C₂×D₈×C₃₁	—	2	4	no	—
48	C₂×D₈×C₃₁	—	4	4	no	—
49	C₂×M₁₆×C₃₁	—	2	1	no	—
50	C₂²×C₈×C₃₁	—	2	1	no	—
51	C₂²×C₈×C₃₁	—	2	4	no	—
52	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
53	C₃₁×#127	—	2	1	no	—
54	C₃₁×#127	—	2	1	no	—
55	C₃₁×#127	—	2	1	no	—
56	C₃₁×#127	C₂³	1	2	yes	—
57	C₃₁×#127	C₂³	1	1	yes	characteristic
58	C₃₁×#124	—	2	1	no	—
59	C₃₁×#121	—	2	1	no	—
60	C₃₁×#121	—	2	1	no	—
61	C₄×D₄×C₃₁	—	2	1	no	—
62	C₄×D₄×C₃₁	—	2	1	no	—
63	C₄×D₄×C₃₁	—	2	1	no	—
64	C₄×D₄×C₃₁	—	2	1	no	—
65	C₄×D₄×C₃₁	D₄	1	2	yes	—
66	C₄×D₄×C₃₁	C₂³	1	2	yes	—
67	C₂×C₄⋊C₄×C₃₁	D₄	1	1	yes	characteristic
68	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
69	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
70	C₃₁×C₄⋊C₈	—	2	1	no	—
71	C₃₁×C₄⋊C₈	—	2	1	no	—
72	C₃₁×C₄⋊C₈	D₄	1	2	yes	—
73	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
74	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
75	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
76	C₃₁×#103	—	2	2	no	—
77	C₃₁×#102	—	2	4	no	—
78	C₃₁×#102	—	2	4	no	—
79	C₃₁×#102	—	2	2	no	—
80	C₃₁×C₂²⋊C₈	—	2	1	no	—
81	C₃₁×C₂²⋊C₈	—	2	4	no	—
82	C₃₁×C₂²⋊C₈	D₄	1	2	yes	—
83	C₄×C₈×C₃₁	—	2	1	no	—
84	C₄×C₈×C₃₁	C₂³	1	2	yes	—
85	C₂⁴×C₃₁	—	2	1	no	—
86	C₂⁴×C₃₁	—	4	1	no	—
87	#41×C₃₁	—	4	2	no	—
88	#41×C₃₁	—	4	2	no	—
89	C₂×Q₈×C₃₁	—	2	1	no	—
90	C₂×D₄×C₃₁	—	2	1	no	—
91	C₂×D₄×C₃₁	—	2	2	no	—
92	C₂×D₄×C₃₁	—	2	1	no	—
93	C₂×D₄×C₃₁	—	2	2	no	—
94	C₂×D₄×C₃₁	—	2	2	no	—
95	C₂×D₄×C₃₁	—	2	1	no	—
96	C₂×D₄×C₃₁	—	2	1	no	—
97	C₂×D₄×C₃₁	—	2	2	no	—
98	C₂×D₄×C₃₁	—	4	1	no	—
99	C₂×D₄×C₃₁	—	4	1	no	—
100	C₂×D₄×C₃₁	—	4	1	no	—
101	C₂×D₄×C₃₁	—	4	1	no	—
102	C₂×D₄×C₃₁	—	4	2	no	—
103	C₂×D₄×C₃₁	—	4	2	no	—
104	C₂×D₄×C₃₁	—	8	2	no	—
105	C₂×D₄×C₃₁	—	8	2	no	—
106	C₂×D₄×C₃₁	D₈	1	4	yes	complemented
107	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
108	C₂²×C₄×C₃₁	—	2	1	no	—
109	C₂²×C₄×C₃₁	—	2	2	no	—
110	C₂²×C₄×C₃₁	—	2	2	no	—
111	C₂²×C₄×C₃₁	—	4	1	no	—
112	C₂²×C₄×C₃₁	—	8	2	no	—
113	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₃₁	#41	1	1	yes	characteristic
116	SD₁₆×C₃₁	—	4	4	no	—
117	D₈×C₃₁	—	4	8	no	—
118	D₈×C₃₁	—	4	4	no	—
119	D₈×C₃₁	—	8	4	no	—
120	M₁₆×C₃₁	—	4	2	no	—
121	C₂×C₈×C₃₁	—	2	2	no	—
122	C₂×C₈×C₃₁	—	2	2	no	—
123	C₂×C₈×C₃₁	—	2	2	no	—
124	C₂×C₈×C₃₁	—	4	2	no	—
125	C₂×C₈×C₃₁	—	8	4	no	—
126	C₂×C₈×C₃₁	C₂×D₄	1	4	yes	—
127	C₄⋊C₄×C₃₁	—	2	1	no	—
128	C₄⋊C₄×C₃₁	—	2	1	no	—
129	C₄⋊C₄×C₃₁	—	2	1	no	—
130	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
131	C₂²⋊C₄×C₃₁	—	2	2	no	—
132	C₂²⋊C₄×C₃₁	—	2	2	no	—
133	C₂²⋊C₄×C₃₁	—	4	1	no	—
134	C₂²⋊C₄×C₃₁	—	4	1	no	—
135	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
136	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
137	C₄²×C₃₁	#41	1	1	yes	characteristic
138	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
139	#19386	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
140	C₂³×C₃₁	—	2	2	no	—
141	C₂³×C₃₁	—	2	4	no	—
142	C₂³×C₃₁	—	4	1	no	—
143	C₂³×C₃₁	—	4	2	no	—
144	C₂³×C₃₁	—	8	1	no	—
145	C₂³×C₃₁	—	8	1	no	—
146	C₂³×C₃₁	—	8	2	no	—
147	C₂³×C₃₁	—	8	2	no	—
148	C₂³×C₃₁	—	8	2	no	—
149	C₂³×C₃₁	#121	1	1	yes	characteristic
150	Q₈×C₃₁	—	4	1	no	—
151	Q₈×C₃₁	—	4	1	no	—
152	D₄×C₃₁	—	2	2	no	—
153	D₄×C₃₁	—	2	4	no	—
154	D₄×C₃₁	—	4	2	no	—
155	D₄×C₃₁	—	4	1	no	—
156	D₄×C₃₁	—	4	2	no	—
157	D₄×C₃₁	—	4	1	no	—
158	D₄×C₃₁	—	4	2	no	—
159	D₄×C₃₁	—	4	4	no	—
160	D₄×C₃₁	—	8	1	no	—
161	D₄×C₃₁	—	8	2	no	—
162	D₄×C₃₁	—	8	2	no	—
163	D₄×C₃₁	—	8	2	no	—
164	D₄×C₃₁	—	8	2	no	—
165	D₄×C₃₁	—	8	2	no	—
166	D₄×C₃₁	C₂×D₈	1	4	yes	—
167	C₂×C₄×C₃₁	—	2	2	no	—
168	C₂×C₄×C₃₁	—	2	2	no	—
169	C₂×C₄×C₃₁	—	4	1	no	—
170	C₂×C₄×C₃₁	—	4	4	no	—
171	C₂×C₄×C₃₁	—	4	1	no	—
172	C₂×C₄×C₃₁	—	8	2	no	—
173	C₂×C₄×C₃₁	—	8	1	no	—
174	C₂×C₄×C₃₁	—	8	2	no	—
175	C₂×C₄×C₃₁	#121	1	1	yes	characteristic
176	C₂×C₄×C₃₁	#121	1	1	yes	characteristic
177	C₂×C₄×C₃₁	#121	1	1	yes	characteristic
178	C₂×C₄×C₃₁	C₂×D₈	1	2	yes	—
179	C₂×C₄×C₃₁	#135	1	2	yes	—
180	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
181	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
182	C₂×C₄×C₃₁	C₂×#41	1	1	yes	characteristic
183	C₈×C₃₁	—	2	4	no	—
184	C₈×C₃₁	—	4	2	no	—
185	C₈×C₃₁	—	4	2	no	—
186	C₈×C₃₁	—	4	2	no	—
187	#3205	C₂×C₃₁	1	1	yes	characteristic, complemented
188	#3036	C₂×C₃₁	1	1	yes	characteristic, complemented
189	C₂×#459	C₂×C₃₁	1	1	yes	characteristic, complemented
190	#2972	C₂×C₃₁	1	1	yes	characteristic, complemented
191	#1681	C₂×C₃₁	1	4	yes	complemented
192	#1667	C₂×C₃₁	1	4	yes	complemented
193	#1571	C₂×C₃₁	1	1	yes	characteristic, complemented
194	#1545	C₂×C₃₁	1	1	yes	characteristic, complemented
195	#1540	C₂×C₃₁	1	1	yes	characteristic, complemented
196	C₂²×C₃₁	—	2	1	no	—
197	C₂²×C₃₁	—	2	1	no	—
198	C₂²×C₃₁	—	2	4	no	—
199	C₂²×C₃₁	—	4	2	no	—
200	C₂²×C₃₁	—	4	2	no	—
201	C₂²×C₃₁	—	8	4	no	—
202	C₂²×C₃₁	—	8	2	no	—
203	C₂²×C₃₁	—	8	1	no	—
204	C₂²×C₃₁	—	8	1	no	—
205	C₂²×C₃₁	—	8	2	no	—
206	C₂²×C₃₁	—	8	2	no	—
207	C₂²×C₃₁	—	8	1	no	—
208	C₂²×C₃₁	—	16	4	no	—
209	C₂²×C₃₁	#466	1	2	yes	—
210	C₂²×C₃₁	C₂×#121	1	1	yes	characteristic
211	C₄×C₃₁	—	2	1	no	—
212	C₄×C₃₁	—	2	1	no	—
213	C₄×C₃₁	—	2	1	no	—
214	C₄×C₃₁	—	4	2	no	—
215	C₄×C₃₁	—	8	1	no	—
216	C₄×C₃₁	#466	1	2	yes	—
217	C₄×C₃₁	C₂²×D₈	1	1	yes	characteristic
218	C₄×C₃₁	C₂×#135	1	1	yes	characteristic
219	C₄×C₃₁	#576	1	2	yes	—
220	C₂×AGL(1,ℤ/8)	—	2	1	no	—
221	C₂²×D₈	—	2	1	no	—
222	#532	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	#493	C₂²×C₃₁	1	2	yes	complemented
226	#486	C₂²×C₃₁	1	2	yes	complemented
227	#463	—	2	2	no	—
228	#461	C₂²×C₃₁	1	2	yes	complemented
229	#459	—	2	2	no	—
230	#459	—	2	2	no	—
231	#459	C₂²×C₃₁	1	4	yes	—
232	#459	C₂²×C₃₁	1	2	yes	complemented
233	#447	—	2	2	no	—
234	C₈×D₄	—	2	2	no	—
235	C₈×D₄	C₂²×C₃₁	1	4	yes	complemented
236	#431	C₂²×C₃₁	1	1	yes	characteristic
237	#431	C₂²×C₃₁	1	1	yes	characteristic
238	#423	C₂²×C₃₁	1	1	yes	characteristic
239	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
240	#417	—	2	1	no	—
241	C₂×#102	—	2	1	no	—
242	C₂×C₂²⋊C₈	—	2	2	no	—
243	#335	C₂²×C₃₁	1	4	yes	complemented
244	#332	C₂²×C₃₁	1	2	yes	complemented
245	#331	C₂²×C₃₁	1	2	yes	complemented
246	#331	C₂²×C₃₁	1	4	yes	complemented
247	C₂×C₃₁	—	2	2	no	—
248	C₂×C₃₁	—	4	4	no	—
249	C₂×C₃₁	—	16	1	no	—
250	C₂×C₃₁	—	16	2	no	—
251	C₂×C₃₁	#3041	1	1	yes	characteristic
252	C₂×C₃₁	C₂×#466	1	1	yes	characteristic
253	C₂×C₃₁	#3068	1	1	yes	characteristic
254	C₂×#41	—	2	1	no	—
255	C₂²×D₄	—	2	1	no	—
256	C₂²×D₄	—	2	1	no	—
257	C₂²×D₄	—	2	1	no	—
258	C₂²×D₄	D₄×C₃₁	1	1	yes	characteristic
259	C₂³×C₄	—	2	1	no	—
260	AGL(1,ℤ/8)	—	4	4	no	—
261	C₂×SD₁₆	—	2	2	no	—
262	C₂×D₈	—	2	4	no	—
263	C₂×D₈	—	2	2	no	—
264	C₂×D₈	—	2	4	no	—
265	C₂×D₈	—	4	4	no	—
266	C₂×M₁₆	—	2	1	no	—
267	C₂²×C₈	—	2	1	no	—
268	C₂²×C₈	—	2	4	no	—
269	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
270	#127	—	2	1	no	—
271	#127	—	2	1	no	—
272	#127	—	2	1	no	—
273	#127	C₂³×C₃₁	1	2	yes	—
274	#127	C₂³×C₃₁	1	1	yes	characteristic
275	#124	—	2	1	no	—
276	#121	—	2	1	no	—
277	#121	—	2	1	no	—
278	C₄×D₄	—	2	1	no	—
279	C₄×D₄	—	2	1	no	—
280	C₄×D₄	—	2	1	no	—
281	C₄×D₄	—	2	1	no	—
282	C₄×D₄	D₄×C₃₁	1	2	yes	—
283	C₄×D₄	C₂³×C₃₁	1	2	yes	—
284	C₂×C₄⋊C₄	D₄×C₃₁	1	1	yes	characteristic
285	C₂×C₂²⋊C₄	—	2	1	no	—
286	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
287	C₄⋊C₈	—	2	1	no	—
288	C₄⋊C₈	—	2	1	no	—
289	C₄⋊C₈	D₄×C₃₁	1	2	yes	—
290	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
291	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
292	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
293	#103	—	2	2	no	—
294	#102	—	2	4	no	—
295	#102	—	2	4	no	—
296	#102	—	2	2	no	—
297	C₂²⋊C₈	—	2	1	no	—
298	C₂²⋊C₈	—	2	4	no	—
299	C₂²⋊C₈	D₄×C₃₁	1	2	yes	—
300	C₄×C₈	—	2	1	no	—
301	C₄×C₈	C₂³×C₃₁	1	2	yes	—
302	C₃₁	#19386	1	1	yes	characteristic, direct product factor, Sylow
303	C₂⁴	—	2	1	no	—
304	C₂⁴	—	4	1	no	—
305	#41	—	4	2	no	—
306	#41	—	4	2	no	—
307	C₂×Q₈	—	2	1	no	—
308	C₂×D₄	—	2	1	no	—
309	C₂×D₄	—	2	2	no	—
310	C₂×D₄	—	2	1	no	—
311	C₂×D₄	—	2	2	no	—
312	C₂×D₄	—	2	2	no	—
313	C₂×D₄	—	2	1	no	—
314	C₂×D₄	—	2	1	no	—
315	C₂×D₄	—	2	2	no	—
316	C₂×D₄	—	4	1	no	—
317	C₂×D₄	—	4	1	no	—
318	C₂×D₄	—	4	1	no	—
319	C₂×D₄	—	4	1	no	—
320	C₂×D₄	—	4	2	no	—
321	C₂×D₄	—	4	2	no	—
322	C₂×D₄	—	8	2	no	—
323	C₂×D₄	—	8	2	no	—
324	C₂×D₄	D₈×C₃₁	1	4	yes	complemented
325	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
326	C₂²×C₄	—	2	1	no	—
327	C₂²×C₄	—	2	2	no	—
328	C₂²×C₄	—	2	2	no	—
329	C₂²×C₄	—	4	1	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	#41×C₃₁	1	1	yes	characteristic
334	SD₁₆	—	4	4	no	—
335	D₈	—	4	8	no	—
336	D₈	—	4	4	no	—
337	D₈	—	8	4	no	—
338	M₁₆	—	4	2	no	—
339	C₂×C₈	—	2	2	no	—
340	C₂×C₈	—	2	2	no	—
341	C₂×C₈	—	2	2	no	—
342	C₂×C₈	—	4	2	no	—
343	C₂×C₈	—	8	4	no	—
344	C₂×C₈	C₂×D₄×C₃₁	1	4	yes	—
345	C₄⋊C₄	—	2	1	no	—
346	C₄⋊C₄	—	2	1	no	—
347	C₄⋊C₄	—	2	1	no	—
348	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
349	C₂²⋊C₄	—	2	2	no	—
350	C₂²⋊C₄	—	2	2	no	—
351	C₂²⋊C₄	—	4	1	no	—
352	C₂²⋊C₄	—	4	1	no	—
353	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
354	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
355	C₄²	#41×C₃₁	1	1	yes	characteristic
356	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
357	C₂³	—	2	2	no	—
358	C₂³	—	2	4	no	—
359	C₂³	—	4	1	no	—
360	C₂³	—	4	2	no	—
361	C₂³	—	8	1	no	—
362	C₂³	—	8	1	no	—
363	C₂³	—	8	2	no	—
364	C₂³	—	8	2	no	—
365	C₂³	—	8	2	no	—
366	C₂³	C₃₁×#121	1	1	yes	characteristic
367	Q₈	—	4	1	no	—
368	Q₈	—	4	1	no	—
369	D₄	—	2	4	no	—
370	D₄	—	2	2	no	—
371	D₄	—	4	2	no	—
372	D₄	—	4	1	no	—
373	D₄	—	4	2	no	—
374	D₄	—	4	1	no	—
375	D₄	—	4	2	no	—
376	D₄	—	4	4	no	—
377	D₄	—	8	1	no	—
378	D₄	—	8	2	no	—
379	D₄	—	8	2	no	—
380	D₄	—	8	2	no	—
381	D₄	—	8	2	no	—
382	D₄	—	8	2	no	—
383	D₄	C₂×D₈×C₃₁	1	4	yes	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	4	1	no	—
387	C₂×C₄	—	4	4	no	—
388	C₂×C₄	—	4	1	no	—
389	C₂×C₄	—	8	2	no	—
390	C₂×C₄	—	8	1	no	—
391	C₂×C₄	—	8	2	no	—
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	C₂×D₈×C₃₁	1	2	yes	—
396	C₂×C₄	C₃₁×#135	1	2	yes	—
397	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
398	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
399	C₂×C₄	C₂×#41×C₃₁	1	1	yes	characteristic
400	C₈	—	2	4	no	—
401	C₈	—	4	2	no	—
402	C₈	—	4	2	no	—
403	C₈	—	4	2	no	—
404	C₂²	—	2	1	no	—
405	C₂²	—	2	1	no	—
406	C₂²	—	2	4	no	—
407	C₂²	—	4	2	no	—
408	C₂²	—	4	2	no	—
409	C₂²	—	8	4	no	—
410	C₂²	—	8	2	no	—
411	C₂²	—	8	1	no	—
412	C₂²	—	8	1	no	—
413	C₂²	—	8	2	no	—
414	C₂²	—	8	2	no	—
415	C₂²	—	8	1	no	—
416	C₂²	—	16	4	no	—
417	C₂²	C₃₁×#466	1	2	yes	—
418	C₂²	C₂×C₃₁×#121	1	1	yes	characteristic
419	C₄	—	2	1	no	—
420	C₄	—	2	1	no	—
421	C₄	—	2	1	no	—
422	C₄	—	4	2	no	—
423	C₄	—	8	1	no	—
424	C₄	C₃₁×#466	1	2	yes	—
425	C₄	C₂²×D₈×C₃₁	1	1	yes	characteristic
426	C₄	C₂×C₃₁×#135	1	1	yes	characteristic
427	C₄	C₃₁×#576	1	2	yes	—
428	C₂	—	2	2	no	—
429	C₂	—	4	4	no	—
430	C₂	—	16	2	no	—
431	C₂	—	16	1	no	—
432	C₂	C₃₁×#3041	1	1	yes	characteristic
433	C₂	C₂×C₃₁×#466	1	1	yes	characteristic
434	C₂	C₃₁×#3068	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₃₁
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₂×C₄²×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3205	C₂	semidirect
2. C₃₁×#3036	C₂	semidirect
3. C₂×C₃₁×#459	C₂	semidirect
4. C₃₁×#2972	C₂	semidirect
5. C₃₁×#1681	C₂	semidirect
6. C₃₁×#1667	C₂	semidirect
7. C₃₁×#1571	C₂	semidirect
8. C₃₁×#1545	C₂	semidirect
9. C₃₁×#1540	C₂	semidirect
15. C₃₁×#493	C₂²	semidirect
16. C₃₁×#486	C₂²	semidirect
18. C₃₁×#461	C₂²	semidirect
22. C₃₁×#459	C₂²	semidirect
25. C₈×D₄×C₃₁	C₂²	semidirect
33. C₃₁×#335	C₂²	semidirect
34. C₃₁×#332	C₂²	semidirect
35. C₃₁×#331	C₂²	semidirect
36. C₃₁×#331	C₂²	semidirect
106. C₂×D₄×C₃₁	D₈	semidirect
139. #19386	C₃₁	direct (N × H)
187. #3205	C₂×C₃₁	semidirect
188. #3036	C₂×C₃₁	semidirect
189. C₂×#459	C₂×C₃₁	semidirect
190. #2972	C₂×C₃₁	semidirect
191. #1681	C₂×C₃₁	semidirect
192. #1667	C₂×C₃₁	semidirect
193. #1571	C₂×C₃₁	semidirect
194. #1545	C₂×C₃₁	semidirect
195. #1540	C₂×C₃₁	semidirect
225. #493	C₂²×C₃₁	semidirect
226. #486	C₂²×C₃₁	semidirect
228. #461	C₂²×C₃₁	semidirect
232. #459	C₂²×C₃₁	semidirect
235. C₈×D₄	C₂²×C₃₁	semidirect
243. #335	C₂²×C₃₁	semidirect
244. #332	C₂²×C₃₁	semidirect
245. #331	C₂²×C₃₁	semidirect
246. #331	C₂²×C₃₁	semidirect
302. C₃₁	#19386	direct (N × H)
324. C₂×D₄	D₈×C₃₁	semidirect

Maximal subgroups

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

subgroup	index
C₃₁×#3205	2
C₃₁×#3036	2
C₂×C₃₁×#459	2
C₃₁×#2972	2
C₃₁×#1681	2
C₃₁×#1667	2
C₃₁×#1571	2
C₃₁×#1545	2
C₃₁×#1540	2
#19386	31

Subgroups — C31×#19386 #21476145

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#19386 #21476145