Subgroups — C₃₁×#19727 #21476486

Order 7936.

874 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3207	C₂	1	2	yes	maximal, complemented
2	C₃₁×#3205	C₂	1	2	yes	maximal, complemented
3	C₃₁×#3184	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#3151	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#1721	C₂	1	2	yes	maximal, complemented
6	C₃₁×#1721	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#1717	C₂	1	2	yes	maximal, complemented
8	C₃₁×#1715	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#1712	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#1708	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#1453	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₃₁×AGL(1,ℤ/8)	—	2	2	no	—
13	C₃₁×#532	C₂²	1	1	yes	characteristic
14	C₃₁×#532	C₂²	1	2	yes	—
15	C₂×C₃₁×#127	C₂²	1	1	yes	characteristic
16	C₃₁×#498	C₂²	1	1	yes	characteristic, complemented
17	C₃₁×#496	—	2	2	no	—
18	C₃₁×#493	C₂²	1	1	yes	characteristic
19	C₃₁×#493	C₂²	1	1	yes	characteristic
20	C₃₁×#493	C₂²	1	2	yes	—
21	C₃₁×#493	C₂²	1	2	yes	—
22	C₃₁×#493	C₂²	1	1	yes	characteristic, complemented
23	C₃₁×#493	C₂²	1	2	yes	complemented
24	C₃₁×#492	C₂²	1	1	yes	characteristic
25	C₃₁×#492	C₂²	1	1	yes	characteristic
26	C₃₁×#492	C₂²	1	2	yes	complemented
27	C₃₁×#487	C₂²	1	2	yes	complemented
28	C₃₁×#486	C₂²	1	2	yes	—
29	C₃₁×#486	C₂²	1	2	yes	—
30	C₃₁×#486	C₂²	1	2	yes	complemented
31	C₃₁×#486	C₂²	1	2	yes	complemented
32	C₃₁×#469	—	2	2	no	—
33	C₃₁×#463	—	2	4	no	—
34	C₃₁×#459	—	2	4	no	—
35	C₃₁×#449	—	2	4	no	—
36	C₃₁×#447	—	2	4	no	—
37	C₃₁×#442	—	2	2	no	—
38	C₃₁×#431	C₂²	1	2	yes	—
39	C₄×M₁₆×C₃₁	C₂²	1	1	yes	characteristic
40	C₃₁×#322	C₂²	1	1	yes	characteristic, complemented
41	C₃₁×#322	C₂²	1	2	yes	complemented
42	C₈²×C₃₁	C₂²	1	1	yes	characteristic, complemented
43	C₂×#41×C₃₁	—	2	1	no	—
44	C₂×#41×C₃₁	—	2	2	no	—
45	C₂²×D₄×C₃₁	—	2	1	no	—
46	C₂²×D₄×C₃₁	—	2	2	no	—
47	C₃₁×AGL(1,ℤ/8)	—	4	8	no	—
48	C₂×SD₁₆×C₃₁	—	2	2	no	—
49	C₂×SD₁₆×C₃₁	—	2	2	no	—
50	C₂×SD₁₆×C₃₁	—	2	4	no	—
51	C₂×D₈×C₃₁	—	2	2	no	—
52	C₂×D₈×C₃₁	—	2	2	no	—
53	C₂×D₈×C₃₁	—	2	2	no	—
54	C₂×D₈×C₃₁	—	2	4	no	—
55	C₂×D₈×C₃₁	—	2	4	no	—
56	C₂×D₈×C₃₁	—	2	4	no	—
57	C₂×M₁₆×C₃₁	D₄	1	2	yes	—
58	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
59	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
60	C₃₁×#127	—	2	2	no	—
61	C₃₁×#127	—	2	1	no	—
62	C₃₁×#127	C₂³	1	1	yes	characteristic
63	C₃₁×#127	C₂³	1	1	yes	characteristic
64	C₃₁×#127	C₂³	1	2	yes	—
65	C₃₁×#127	C₂³	1	1	yes	characteristic
66	C₃₁×#124	—	2	2	no	—
67	C₃₁×#124	—	2	1	no	—
68	C₃₁×#121	—	2	2	no	—
69	C₃₁×#121	—	2	2	no	—
70	C₃₁×#121	—	2	2	no	—
71	C₄×D₄×C₃₁	—	2	2	no	—
72	C₄×D₄×C₃₁	—	2	2	no	—
73	C₄×D₄×C₃₁	—	2	2	no	—
74	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
75	C₃₁×#106	—	2	2	no	—
76	C₃₁×C₄⋊C₈	D₄	1	4	yes	—
77	C₃₁×#103	—	2	4	no	—
78	C₃₁×#102	—	2	4	no	—
79	C₃₁×#102	—	2	4	no	—
80	C₃₁×#102	—	2	4	no	—
81	C₃₁×#102	—	2	4	no	—
82	C₃₁×C₂²⋊C₈	D₄	1	4	yes	—
83	C₃₁×#97	D₄	1	2	yes	—
84	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
85	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
86	C₄×C₈×C₃₁	C₂³	1	2	yes	—
87	C₄×C₈×C₃₁	C₂³	1	2	yes	—
88	C₂⁴×C₃₁	—	4	1	no	—
89	#41×C₃₁	—	4	4	no	—
90	#41×C₃₁	—	8	4	no	—
91	C₂×Q₈×C₃₁	—	2	2	no	—
92	C₂×Q₈×C₃₁	—	2	1	no	—
93	C₂×D₄×C₃₁	—	2	2	no	—
94	C₂×D₄×C₃₁	—	2	2	no	—
95	C₂×D₄×C₃₁	—	2	2	no	—
96	C₂×D₄×C₃₁	—	2	2	no	—
97	C₂×D₄×C₃₁	—	2	2	no	—
98	C₂×D₄×C₃₁	—	2	2	no	—
99	C₂×D₄×C₃₁	—	2	1	no	—
100	C₂×D₄×C₃₁	—	2	1	no	—
101	C₂×D₄×C₃₁	—	2	1	no	—
102	C₂×D₄×C₃₁	—	4	4	no	—
103	C₂×D₄×C₃₁	—	4	1	no	—
104	C₂×D₄×C₃₁	—	4	2	no	—
105	C₂×D₄×C₃₁	—	4	1	no	—
106	C₂×D₄×C₃₁	—	4	2	no	—
107	C₂×D₄×C₃₁	—	8	4	no	—
108	C₂²×C₄×C₃₁	—	4	1	no	—
109	C₂²×C₄×C₃₁	—	4	2	no	—
110	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
111	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
112	SD₁₆×C₃₁	—	4	4	no	—
113	SD₁₆×C₃₁	—	4	4	no	—
114	SD₁₆×C₃₁	—	8	4	no	—
115	D₈×C₃₁	—	4	4	no	—
116	D₈×C₃₁	—	4	4	no	—
117	D₈×C₃₁	—	4	4	no	—
118	D₈×C₃₁	—	8	4	no	—
119	D₈×C₃₁	—	8	4	no	—
120	D₈×C₃₁	—	8	4	no	—
121	M₁₆×C₃₁	—	2	4	no	—
122	C₂×C₈×C₃₁	C₂×D₄	1	2	yes	—
123	C₂×C₈×C₃₁	C₂×D₄	1	4	yes	—
124	C₂×C₈×C₃₁	C₂×D₄	1	4	yes	—
125	C₂×C₈×C₃₁	C₂×D₄	1	2	yes	—
126	C₄⋊C₄×C₃₁	—	2	2	no	—
127	C₄⋊C₄×C₃₁	—	2	2	no	—
128	C₄⋊C₄×C₃₁	—	2	2	no	—
129	C₂²⋊C₄×C₃₁	—	4	2	no	—
130	C₂²⋊C₄×C₃₁	—	4	2	no	—
131	C₂²⋊C₄×C₃₁	—	4	2	no	—
132	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
133	C₄²×C₃₁	C₂×D₄	1	2	yes	—
134	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
135	#19727	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
136	C₂³×C₃₁	—	4	1	no	—
137	C₂³×C₃₁	—	4	2	no	—
138	C₂³×C₃₁	—	4	1	no	—
139	C₂³×C₃₁	—	4	1	no	—
140	C₂³×C₃₁	—	8	2	no	—
141	C₂³×C₃₁	—	8	4	no	—
142	C₂³×C₃₁	#127	1	1	yes	characteristic
143	Q₈×C₃₁	—	4	2	no	—
144	Q₈×C₃₁	—	4	4	no	—
145	D₄×C₃₁	—	4	2	no	—
146	D₄×C₃₁	—	4	2	no	—
147	D₄×C₃₁	—	4	2	no	—
148	D₄×C₃₁	—	4	4	no	—
149	D₄×C₃₁	—	4	4	no	—
150	D₄×C₃₁	—	4	4	no	—
151	D₄×C₃₁	—	4	4	no	—
152	D₄×C₃₁	—	4	4	no	—
153	D₄×C₃₁	—	4	4	no	—
154	D₄×C₃₁	—	8	2	no	—
155	D₄×C₃₁	—	8	4	no	—
156	D₄×C₃₁	—	8	2	no	—
157	D₄×C₃₁	—	8	4	no	—
158	C₂×C₄×C₃₁	—	2	2	no	—
159	C₂×C₄×C₃₁	—	2	4	no	—
160	C₂×C₄×C₃₁	—	4	1	no	—
161	C₂×C₄×C₃₁	—	4	2	no	—
162	C₂×C₄×C₃₁	—	8	2	no	—
163	C₂×C₄×C₃₁	—	8	4	no	—
164	C₂×C₄×C₃₁	#127	1	1	yes	characteristic
165	C₂×C₄×C₃₁	#127	1	2	yes	—
166	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
167	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
168	C₈×C₃₁	—	2	2	no	—
169	C₈×C₃₁	—	2	4	no	—
170	C₈×C₃₁	—	2	4	no	—
171	C₈×C₃₁	AGL(1,ℤ/8)	1	4	yes	—
172	#3207	C₂×C₃₁	1	2	yes	complemented
173	#3205	C₂×C₃₁	1	2	yes	complemented
174	#3184	C₂×C₃₁	1	1	yes	characteristic, complemented
175	#3151	C₂×C₃₁	1	1	yes	characteristic, complemented
176	#1721	C₂×C₃₁	1	2	yes	complemented
177	#1721	C₂×C₃₁	1	1	yes	characteristic, complemented
178	#1717	C₂×C₃₁	1	2	yes	complemented
179	#1715	C₂×C₃₁	1	1	yes	characteristic, complemented
180	#1712	C₂×C₃₁	1	1	yes	characteristic, complemented
181	#1708	C₂×C₃₁	1	1	yes	characteristic, complemented
182	#1453	C₂×C₃₁	1	1	yes	characteristic, complemented
183	C₂²×C₃₁	—	2	1	no	—
184	C₂²×C₃₁	—	2	2	no	—
185	C₂²×C₃₁	—	8	1	no	—
186	C₂²×C₃₁	—	8	1	no	—
187	C₂²×C₃₁	—	8	1	no	—
188	C₂²×C₃₁	—	8	2	no	—
189	C₂²×C₃₁	—	8	2	no	—
190	C₂²×C₃₁	—	8	2	no	—
191	C₂²×C₃₁	—	8	2	no	—
192	C₂²×C₃₁	—	8	2	no	—
193	C₂²×C₃₁	—	8	2	no	—
194	C₂²×C₃₁	—	16	4	no	—
195	C₂²×C₃₁	C₂×#127	1	1	yes	characteristic
196	C₄×C₃₁	—	2	1	no	—
197	C₄×C₃₁	—	2	2	no	—
198	C₄×C₃₁	—	8	1	no	—
199	C₄×C₃₁	—	8	2	no	—
200	C₄×C₃₁	C₂×AGL(1,ℤ/8)	1	2	yes	—
201	C₄×C₃₁	#576	1	4	yes	—
202	C₂×AGL(1,ℤ/8)	—	2	2	no	—
203	#532	C₂²×C₃₁	1	1	yes	characteristic
204	#532	C₂²×C₃₁	1	2	yes	—
205	C₂×#127	C₂²×C₃₁	1	1	yes	characteristic
206	#498	C₂²×C₃₁	1	1	yes	characteristic, complemented
207	#496	—	2	2	no	—
208	#493	C₂²×C₃₁	1	1	yes	characteristic
209	#493	C₂²×C₃₁	1	1	yes	characteristic
210	#493	C₂²×C₃₁	1	2	yes	—
211	#493	C₂²×C₃₁	1	2	yes	—
212	#493	C₂²×C₃₁	1	1	yes	characteristic, complemented
213	#493	C₂²×C₃₁	1	2	yes	complemented
214	#492	C₂²×C₃₁	1	1	yes	characteristic
215	#492	C₂²×C₃₁	1	1	yes	characteristic
216	#492	C₂²×C₃₁	1	2	yes	complemented
217	#487	C₂²×C₃₁	1	2	yes	complemented
218	#486	C₂²×C₃₁	1	2	yes	—
219	#486	C₂²×C₃₁	1	2	yes	—
220	#486	C₂²×C₃₁	1	2	yes	complemented
221	#486	C₂²×C₃₁	1	2	yes	complemented
222	#469	—	2	2	no	—
223	#463	—	2	4	no	—
224	#459	—	2	4	no	—
225	#449	—	2	4	no	—
226	#447	—	2	4	no	—
227	#442	—	2	2	no	—
228	#431	C₂²×C₃₁	1	2	yes	—
229	C₄×M₁₆	C₂²×C₃₁	1	1	yes	characteristic
230	#322	C₂²×C₃₁	1	1	yes	characteristic, complemented
231	#322	C₂²×C₃₁	1	2	yes	complemented
232	C₈²	C₂²×C₃₁	1	1	yes	characteristic, complemented
233	C₂×C₃₁	—	4	1	no	—
234	C₂×C₃₁	—	16	1	no	—
235	C₂×C₃₁	—	16	2	no	—
236	C₂×C₃₁	—	16	1	no	—
237	C₂×C₃₁	—	16	1	no	—
238	C₂×C₃₁	#3151	1	1	yes	characteristic
239	C₂×C₃₁	#3155	1	2	yes	—
240	C₂×#41	—	2	1	no	—
241	C₂×#41	—	2	2	no	—
242	C₂²×D₄	—	2	1	no	—
243	C₂²×D₄	—	2	2	no	—
244	AGL(1,ℤ/8)	—	4	8	no	—
245	C₂×SD₁₆	—	2	2	no	—
246	C₂×SD₁₆	—	2	2	no	—
247	C₂×SD₁₆	—	2	4	no	—
248	C₂×D₈	—	2	2	no	—
249	C₂×D₈	—	2	2	no	—
250	C₂×D₈	—	2	2	no	—
251	C₂×D₈	—	2	4	no	—
252	C₂×D₈	—	2	4	no	—
253	C₂×D₈	—	2	4	no	—
254	C₂×M₁₆	D₄×C₃₁	1	2	yes	—
255	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
256	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
257	#127	—	2	2	no	—
258	#127	—	2	1	no	—
259	#127	C₂³×C₃₁	1	1	yes	characteristic
260	#127	C₂³×C₃₁	1	1	yes	characteristic
261	#127	C₂³×C₃₁	1	2	yes	—
262	#127	C₂³×C₃₁	1	1	yes	characteristic
263	#124	—	2	2	no	—
264	#124	—	2	1	no	—
265	#121	—	2	2	no	—
266	#121	—	2	2	no	—
267	#121	—	2	2	no	—
268	C₄×D₄	—	2	2	no	—
269	C₄×D₄	—	2	2	no	—
270	C₄×D₄	—	2	2	no	—
271	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
272	#106	—	2	2	no	—
273	C₄⋊C₈	D₄×C₃₁	1	4	yes	—
274	#103	—	2	4	no	—
275	#102	—	2	4	no	—
276	#102	—	2	4	no	—
277	#102	—	2	4	no	—
278	#102	—	2	4	no	—
279	C₂²⋊C₈	D₄×C₃₁	1	4	yes	—
280	#97	D₄×C₃₁	1	2	yes	—
281	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
282	C₄×C₈	C₂³×C₃₁	1	2	yes	—
283	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
284	C₄×C₈	C₂³×C₃₁	1	2	yes	—
285	C₃₁	#19727	1	1	yes	characteristic, direct product factor, Sylow
286	C₂⁴	—	4	1	no	—
287	#41	—	4	4	no	—
288	#41	—	8	4	no	—
289	C₂×Q₈	—	2	2	no	—
290	C₂×Q₈	—	2	1	no	—
291	C₂×D₄	—	2	2	no	—
292	C₂×D₄	—	2	2	no	—
293	C₂×D₄	—	2	2	no	—
294	C₂×D₄	—	2	2	no	—
295	C₂×D₄	—	2	2	no	—
296	C₂×D₄	—	2	2	no	—
297	C₂×D₄	—	2	1	no	—
298	C₂×D₄	—	2	1	no	—
299	C₂×D₄	—	2	1	no	—
300	C₂×D₄	—	4	4	no	—
301	C₂×D₄	—	4	1	no	—
302	C₂×D₄	—	4	2	no	—
303	C₂×D₄	—	4	1	no	—
304	C₂×D₄	—	4	2	no	—
305	C₂×D₄	—	8	4	no	—
306	C₂²×C₄	—	4	1	no	—
307	C₂²×C₄	—	4	2	no	—
308	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
309	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
310	SD₁₆	—	4	4	no	—
311	SD₁₆	—	4	4	no	—
312	SD₁₆	—	8	4	no	—
313	D₈	—	4	4	no	—
314	D₈	—	4	4	no	—
315	D₈	—	4	4	no	—
316	D₈	—	8	4	no	—
317	D₈	—	8	4	no	—
318	D₈	—	8	4	no	—
319	M₁₆	—	2	4	no	—
320	C₂×C₈	C₂×D₄×C₃₁	1	2	yes	—
321	C₂×C₈	C₂×D₄×C₃₁	1	4	yes	—
322	C₂×C₈	C₂×D₄×C₃₁	1	4	yes	—
323	C₂×C₈	C₂×D₄×C₃₁	1	2	yes	—
324	C₄⋊C₄	—	2	2	no	—
325	C₄⋊C₄	—	2	2	no	—
326	C₄⋊C₄	—	2	2	no	—
327	C₂²⋊C₄	—	4	2	no	—
328	C₂²⋊C₄	—	4	2	no	—
329	C₂²⋊C₄	—	4	2	no	—
330	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
331	C₄²	C₂×D₄×C₃₁	1	2	yes	—
332	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
333	C₂³	—	4	1	no	—
334	C₂³	—	4	2	no	—
335	C₂³	—	4	1	no	—
336	C₂³	—	4	1	no	—
337	C₂³	—	8	2	no	—
338	C₂³	—	8	4	no	—
339	C₂³	C₃₁×#127	1	1	yes	characteristic
340	Q₈	—	4	2	no	—
341	Q₈	—	4	4	no	—
342	D₄	—	4	2	no	—
343	D₄	—	4	2	no	—
344	D₄	—	4	2	no	—
345	D₄	—	4	4	no	—
346	D₄	—	4	4	no	—
347	D₄	—	4	4	no	—
348	D₄	—	4	4	no	—
349	D₄	—	4	4	no	—
350	D₄	—	4	4	no	—
351	D₄	—	8	2	no	—
352	D₄	—	8	4	no	—
353	D₄	—	8	2	no	—
354	D₄	—	8	4	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	4	no	—
357	C₂×C₄	—	4	1	no	—
358	C₂×C₄	—	4	2	no	—
359	C₂×C₄	—	8	2	no	—
360	C₂×C₄	—	8	4	no	—
361	C₂×C₄	C₃₁×#127	1	1	yes	characteristic
362	C₂×C₄	C₃₁×#127	1	2	yes	—
363	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
364	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
365	C₈	—	2	2	no	—
366	C₈	—	2	4	no	—
367	C₈	—	2	4	no	—
368	C₈	C₃₁×AGL(1,ℤ/8)	1	4	yes	—
369	C₂²	—	2	1	no	—
370	C₂²	—	2	2	no	—
371	C₂²	—	8	1	no	—
372	C₂²	—	8	1	no	—
373	C₂²	—	8	1	no	—
374	C₂²	—	8	2	no	—
375	C₂²	—	8	2	no	—
376	C₂²	—	8	2	no	—
377	C₂²	—	8	2	no	—
378	C₂²	—	8	2	no	—
379	C₂²	—	8	2	no	—
380	C₂²	—	16	4	no	—
381	C₂²	C₂×C₃₁×#127	1	1	yes	characteristic
382	C₄	—	2	1	no	—
383	C₄	—	2	2	no	—
384	C₄	—	8	1	no	—
385	C₄	—	8	2	no	—
386	C₄	C₂×C₃₁×AGL(1,ℤ/8)	1	2	yes	—
387	C₄	C₃₁×#576	1	4	yes	—
388	C₂	—	4	1	no	—
389	C₂	—	16	1	no	—
390	C₂	—	16	1	no	—
391	C₂	—	16	1	no	—
392	C₂	—	16	2	no	—
393	C₂	C₃₁×#3151	1	1	yes	characteristic
394	C₂	C₃₁×#3155	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂×#127
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×#3207	C₂	semidirect
2. C₃₁×#3205	C₂	semidirect
3. C₃₁×#3184	C₂	semidirect
4. C₃₁×#3151	C₂	semidirect
5. C₃₁×#1721	C₂	semidirect
6. C₃₁×#1721	C₂	semidirect
7. C₃₁×#1717	C₂	semidirect
8. C₃₁×#1715	C₂	semidirect
9. C₃₁×#1712	C₂	semidirect
10. C₃₁×#1708	C₂	semidirect
11. C₃₁×#1453	C₂	semidirect
16. C₃₁×#498	C₂²	semidirect
22. C₃₁×#493	C₂²	semidirect
23. C₃₁×#493	C₂²	semidirect
26. C₃₁×#492	C₂²	semidirect
27. C₃₁×#487	C₂²	semidirect
30. C₃₁×#486	C₂²	semidirect
31. C₃₁×#486	C₂²	semidirect
40. C₃₁×#322	C₂²	semidirect
41. C₃₁×#322	C₂²	semidirect
42. C₈²×C₃₁	C₂²	semidirect
135. #19727	C₃₁	direct (N × H)
172. #3207	C₂×C₃₁	semidirect
173. #3205	C₂×C₃₁	semidirect
174. #3184	C₂×C₃₁	semidirect
175. #3151	C₂×C₃₁	semidirect
176. #1721	C₂×C₃₁	semidirect
177. #1721	C₂×C₃₁	semidirect
178. #1717	C₂×C₃₁	semidirect
179. #1715	C₂×C₃₁	semidirect
180. #1712	C₂×C₃₁	semidirect
181. #1708	C₂×C₃₁	semidirect
182. #1453	C₂×C₃₁	semidirect
206. #498	C₂²×C₃₁	semidirect
212. #493	C₂²×C₃₁	semidirect
213. #493	C₂²×C₃₁	semidirect
216. #492	C₂²×C₃₁	semidirect
217. #487	C₂²×C₃₁	semidirect
220. #486	C₂²×C₃₁	semidirect
221. #486	C₂²×C₃₁	semidirect
230. #322	C₂²×C₃₁	semidirect
231. #322	C₂²×C₃₁	semidirect
232. C₈²	C₂²×C₃₁	semidirect
285. C₃₁	#19727	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃₁×#3207	2
C₃₁×#3205	2
C₃₁×#3184	2
C₃₁×#3151	2
C₃₁×#1721	2
C₃₁×#1717	2
C₃₁×#1715	2
C₃₁×#1712	2
C₃₁×#1708	2
C₃₁×#1453	2
#19727	31

Subgroups — C31×#19727 #21476486

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#19727 #21476486