Subgroups — C₃₁×#17925 #21474684

Order 7936.

586 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3104	C₂	1	1	yes	maximal, characteristic
2	C₃₁×#2985	C₂	1	1	yes	maximal, characteristic
3	C₃₁×#2982	C₂	1	1	yes	maximal, characteristic
4	C₃₁×#1587	C₂	1	2	yes	maximal, complemented
5	C₃₁×#1584	C₂	1	2	yes	maximal, complemented
6	C₃₁×#1579	C₂	1	2	yes	maximal, complemented
7	C₈×Q₁₆×C₃₁	C₂	1	2	yes	maximal, complemented
8	C₃₁×#1572	C₂	1	1	yes	maximal, characteristic
9	C₃₁×#1491	C₂	1	1	yes	maximal, characteristic
10	C₃₁×#1485	C₂	1	1	yes	maximal, characteristic
11	C₃₁×#1453	C₂	1	1	yes	maximal, characteristic
12	C₃₁×#533	C₂²	1	1	yes	characteristic
13	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
14	C₃₁×#484	C₄	1	2	yes	—
15	C₃₁×#477	C₄	1	2	yes	—
16	C₃₁×#462	C₄	1	2	yes	—
17	C₃₁×#451	C₄	1	2	yes	—
18	C₃₁×#446	—	2	2	no	—
19	C₃₁×#446	C₂²	1	2	yes	—
20	C₈×Q₈×C₃₁	—	2	2	no	—
21	C₈×Q₈×C₃₁	C₂²	1	2	yes	—
22	C₈×Q₈×C₃₁	C₂²	1	2	yes	—
23	C₈×Q₈×C₃₁	C₂²	1	2	yes	—
24	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	—
25	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	—
26	C₃₁×#433	—	2	2	no	—
27	C₃₁×#432	C₂²	1	1	yes	characteristic
28	C₃₁×#431	—	2	2	no	—
29	C₃₁×#431	C₂²	1	1	yes	characteristic
30	C₃₁×#431	C₂²	1	1	yes	characteristic
31	C₃₁×#431	C₂²	1	1	yes	characteristic
32	C₄×M₁₆×C₃₁	C₂²	1	1	yes	characteristic
33	C₃₁×#335	C₂²	1	2	yes	—
34	C₃₁×#334	C₂²	1	2	yes	—
35	C₃₁×Q₈⋊C₈	C₂²	1	2	yes	—
36	C₃₁×Q₈⋊C₈	C₂²	1	2	yes	—
37	C₃₁×Q₈⋊C₈	C₂²	1	2	yes	—
38	C₃₁×Q₈⋊C₈	C₂²	1	2	yes	—
39	C₃₁×#322	C₂²	1	1	yes	characteristic
40	C₃₁×#322	C₂²	1	1	yes	characteristic
41	C₃₁×#322	C₂²	1	1	yes	characteristic
42	C₈²×C₃₁	C₂²	1	1	yes	characteristic
43	C₂²×Q₈×C₃₁	C₂×C₄	1	1	yes	characteristic
44	C₂×Q₁₆×C₃₁	C₂×C₄	1	2	yes	—
45	C₂×Q₁₆×C₃₁	C₂×C₄	1	2	yes	—
46	C₂×M₁₆×C₃₁	—	2	1	no	—
47	C₃₁×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
48	C₃₁×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
49	C₃₁×#125	—	2	1	no	—
50	C₃₁×C₂²⋊Q₈	—	2	1	no	—
51	C₃₁×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
52	C₄×Q₈×C₃₁	—	2	1	no	—
53	C₄×Q₈×C₃₁	—	2	1	no	—
54	C₄×Q₈×C₃₁	—	2	1	no	—
55	C₄×Q₈×C₃₁	C₂×C₄	1	2	yes	—
56	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
57	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
58	C₃₁×#117	—	2	1	no	—
59	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
60	C₂×C₄⋊C₄×C₃₁	C₂×C₄	1	1	yes	characteristic
61	C₂×C₄²×C₃₁	—	2	1	no	—
62	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
63	C₃₁×#107	C₂×C₄	1	2	yes	—
64	C₃₁×#107	C₂×C₄	1	2	yes	—
65	C₃₁×C₄⋊C₈	—	2	2	no	—
66	C₃₁×C₄⋊C₈	—	2	2	no	—
67	C₃₁×C₄⋊C₈	—	2	2	no	—
68	C₃₁×C₄⋊C₈	—	2	2	no	—
69	C₃₁×C₄⋊C₈	C₂×C₄	1	2	yes	—
70	C₃₁×C₄⋊C₈	D₄	1	2	yes	—
71	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
72	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
73	C₃₁×#103	C₂×C₄	1	2	yes	—
74	C₃₁×#103	C₂×C₄	1	2	yes	—
75	C₃₁×#103	C₂×C₄	1	2	yes	—
76	C₃₁×#103	C₂×C₄	1	2	yes	—
77	C₃₁×C₂²⋊C₈	—	2	1	no	—
78	C₃₁×C₂²⋊C₈	—	2	1	no	—
79	C₃₁×C₂²⋊C₈	C₂×C₄	1	2	yes	—
80	C₃₁×C₂²⋊C₈	D₄	1	2	yes	—
81	C₃₁×#97	—	2	2	no	—
82	C₃₁×#97	—	2	1	no	—
83	C₃₁×#97	—	2	1	no	—
84	C₄×C₈×C₃₁	—	2	2	no	—
85	C₄×C₈×C₃₁	—	2	2	no	—
86	C₄×C₈×C₃₁	—	2	2	no	—
87	C₄×C₈×C₃₁	—	2	1	no	—
88	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
89	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
90	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
91	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
92	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
93	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
94	C₂×Q₈×C₃₁	—	2	4	no	—
95	C₂×Q₈×C₃₁	—	2	1	no	—
96	C₂×Q₈×C₃₁	—	2	1	no	—
97	C₂×Q₈×C₃₁	C₂²×C₄	1	2	yes	—
98	C₂×Q₈×C₃₁	C₂²×C₄	1	2	yes	—
99	C₂²×C₄×C₃₁	—	2	1	no	—
100	C₂²×C₄×C₃₁	—	2	1	no	—
101	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
102	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₃₁	#41	1	1	yes	characteristic
104	Q₁₆×C₃₁	—	2	4	no	—
105	Q₁₆×C₃₁	—	2	4	no	—
106	M₁₆×C₃₁	—	4	2	no	—
107	C₂×C₈×C₃₁	—	2	1	no	—
108	C₂×C₈×C₃₁	—	2	2	no	—
109	C₂×C₈×C₃₁	—	2	2	no	—
110	C₂×C₈×C₃₁	—	2	1	no	—
111	C₂×C₈×C₃₁	C₂²×C₄	1	2	yes	—
112	C₂×C₈×C₃₁	C₂²×C₄	1	2	yes	—
113	C₂×C₈×C₃₁	C₂×D₄	1	2	yes	—
114	C₂×C₈×C₃₁	C₂×D₄	1	2	yes	—
115	C₄⋊C₄×C₃₁	—	2	2	no	—
116	C₄⋊C₄×C₃₁	—	2	1	no	—
117	C₄⋊C₄×C₃₁	—	2	1	no	—
118	C₄⋊C₄×C₃₁	—	2	1	no	—
119	C₄⋊C₄×C₃₁	—	2	1	no	—
120	C₄⋊C₄×C₃₁	—	2	2	no	—
121	C₄⋊C₄×C₃₁	—	2	2	no	—
122	C₄⋊C₄×C₃₁	—	2	2	no	—
123	C₄⋊C₄×C₃₁	C₂²×C₄	1	2	yes	—
124	C₄⋊C₄×C₃₁	C₂²×C₄	1	2	yes	—
125	C₂²⋊C₄×C₃₁	—	2	2	no	—
126	C₄²×C₃₁	—	2	2	no	—
127	C₄²×C₃₁	—	2	2	no	—
128	C₄²×C₃₁	—	2	2	no	—
129	C₄²×C₃₁	C₂²×C₄	1	1	yes	characteristic
130	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
131	C₄²×C₃₁	#41	1	1	yes	characteristic
132	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
133	#17925	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
134	C₂³×C₃₁	C₄×D₄	1	1	yes	characteristic
135	Q₈×C₃₁	—	2	4	no	—
136	Q₈×C₃₁	—	2	2	no	—
137	Q₈×C₃₁	—	2	2	no	—
138	Q₈×C₃₁	—	2	2	no	—
139	Q₈×C₃₁	—	8	1	no	—
140	Q₈×C₃₁	#131	1	4	yes	—
141	C₂×C₄×C₃₁	—	2	4	no	—
142	C₂×C₄×C₃₁	—	2	2	no	—
143	C₂×C₄×C₃₁	—	2	2	no	—
144	C₂×C₄×C₃₁	—	2	2	no	—
145	C₂×C₄×C₃₁	—	2	2	no	—
146	C₂×C₄×C₃₁	—	2	2	no	—
147	C₂×C₄×C₃₁	—	2	2	no	—
148	C₂×C₄×C₃₁	—	4	1	no	—
149	C₂×C₄×C₃₁	—	8	1	no	—
150	C₂×C₄×C₃₁	C₄×D₄	1	1	yes	characteristic
151	C₂×C₄×C₃₁	C₄×D₄	1	1	yes	characteristic
152	C₂×C₄×C₃₁	C₄×D₄	1	1	yes	characteristic
153	C₂×C₄×C₃₁	C₂³×C₄	1	1	yes	characteristic
154	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
155	C₂×C₄×C₃₁	C₂×#41	1	1	yes	characteristic
156	C₈×C₃₁	—	2	2	no	—
157	C₈×C₃₁	—	2	2	no	—
158	C₈×C₃₁	—	2	2	no	—
159	C₈×C₃₁	—	2	2	no	—
160	C₈×C₃₁	—	2	2	no	—
161	C₈×C₃₁	—	4	1	no	—
162	C₈×C₃₁	—	4	2	no	—
163	C₈×C₃₁	—	4	2	no	—
164	#3104	C₂×C₃₁	1	1	yes	characteristic
165	#2985	C₂×C₃₁	1	1	yes	characteristic
166	#2982	C₂×C₃₁	1	1	yes	characteristic
167	#1587	C₂×C₃₁	1	2	yes	complemented
168	#1584	C₂×C₃₁	1	2	yes	complemented
169	#1579	C₂×C₃₁	1	2	yes	complemented
170	C₈×Q₁₆	C₂×C₃₁	1	2	yes	complemented
171	#1572	C₂×C₃₁	1	1	yes	characteristic
172	#1491	C₂×C₃₁	1	1	yes	characteristic
173	#1485	C₂×C₃₁	1	1	yes	characteristic
174	#1453	C₂×C₃₁	1	1	yes	characteristic
175	C₂²×C₃₁	—	2	1	no	—
176	C₂²×C₃₁	—	2	1	no	—
177	C₂²×C₃₁	—	2	1	no	—
178	C₂²×C₃₁	C₂×C₄×D₄	1	1	yes	characteristic
179	C₄×C₃₁	—	2	4	no	—
180	C₄×C₃₁	—	2	1	no	—
181	C₄×C₃₁	—	2	1	no	—
182	C₄×C₃₁	—	2	1	no	—
183	C₄×C₃₁	—	2	1	no	—
184	C₄×C₃₁	—	4	2	no	—
185	C₄×C₃₁	—	4	2	no	—
186	C₄×C₃₁	—	4	2	no	—
187	C₄×C₃₁	C₂×#131	1	2	yes	—
188	C₄×C₃₁	#578	1	2	yes	—
189	#533	C₂²×C₃₁	1	1	yes	characteristic
190	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
191	#484	C₄×C₃₁	1	2	yes	—
192	#477	C₄×C₃₁	1	2	yes	—
193	#462	C₄×C₃₁	1	2	yes	—
194	#451	C₄×C₃₁	1	2	yes	—
195	#446	—	2	2	no	—
196	#446	C₂²×C₃₁	1	2	yes	—
197	C₈×Q₈	—	2	2	no	—
198	C₈×Q₈	C₂²×C₃₁	1	2	yes	—
199	C₈×Q₈	C₂²×C₃₁	1	2	yes	—
200	C₈×Q₈	C₂²×C₃₁	1	2	yes	—
201	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	—
202	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	—
203	#433	—	2	2	no	—
204	#432	C₂²×C₃₁	1	1	yes	characteristic
205	#431	—	2	2	no	—
206	#431	C₂²×C₃₁	1	1	yes	characteristic
207	#431	C₂²×C₃₁	1	1	yes	characteristic
208	#431	C₂²×C₃₁	1	1	yes	characteristic
209	C₄×M₁₆	C₂²×C₃₁	1	1	yes	characteristic
210	#335	C₂²×C₃₁	1	2	yes	—
211	#334	C₂²×C₃₁	1	2	yes	—
212	Q₈⋊C₈	C₂²×C₃₁	1	2	yes	—
213	Q₈⋊C₈	C₂²×C₃₁	1	2	yes	—
214	Q₈⋊C₈	C₂²×C₃₁	1	2	yes	—
215	Q₈⋊C₈	C₂²×C₃₁	1	2	yes	—
216	#322	C₂²×C₃₁	1	1	yes	characteristic
217	#322	C₂²×C₃₁	1	1	yes	characteristic
218	#322	C₂²×C₃₁	1	1	yes	characteristic
219	C₈²	C₂²×C₃₁	1	1	yes	characteristic
220	C₂×C₃₁	—	4	1	no	—
221	C₂×C₃₁	#2929	1	1	yes	characteristic
222	C₂×C₃₁	#2950	1	1	yes	characteristic
223	C₂×C₃₁	#2956	1	1	yes	characteristic
224	C₂²×Q₈	C₂×C₄×C₃₁	1	1	yes	characteristic
225	C₂×Q₁₆	C₂×C₄×C₃₁	1	2	yes	—
226	C₂×Q₁₆	C₂×C₄×C₃₁	1	2	yes	—
227	C₂×M₁₆	—	2	1	no	—
228	C₄⋊Q₈	C₂×C₄×C₃₁	1	1	yes	characteristic
229	C₄⋊Q₈	C₂×C₄×C₃₁	1	1	yes	characteristic
230	#125	—	2	1	no	—
231	C₂²⋊Q₈	—	2	1	no	—
232	C₂²⋊Q₈	C₂×C₄×C₃₁	1	2	yes	—
233	C₄×Q₈	—	2	1	no	—
234	C₄×Q₈	—	2	1	no	—
235	C₄×Q₈	—	2	1	no	—
236	C₄×Q₈	C₂×C₄×C₃₁	1	2	yes	—
237	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
238	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
239	#117	—	2	1	no	—
240	C₂×C₄⋊C₄	—	2	1	no	—
241	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	1	yes	characteristic
242	C₂×C₄²	—	2	1	no	—
243	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
244	#107	C₂×C₄×C₃₁	1	2	yes	—
245	#107	C₂×C₄×C₃₁	1	2	yes	—
246	C₄⋊C₈	—	2	2	no	—
247	C₄⋊C₈	—	2	2	no	—
248	C₄⋊C₈	—	2	2	no	—
249	C₄⋊C₈	—	2	2	no	—
250	C₄⋊C₈	C₂×C₄×C₃₁	1	2	yes	—
251	C₄⋊C₈	D₄×C₃₁	1	2	yes	—
252	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
253	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
254	#103	C₂×C₄×C₃₁	1	2	yes	—
255	#103	C₂×C₄×C₃₁	1	2	yes	—
256	#103	C₂×C₄×C₃₁	1	2	yes	—
257	#103	C₂×C₄×C₃₁	1	2	yes	—
258	C₂²⋊C₈	—	2	1	no	—
259	C₂²⋊C₈	—	2	1	no	—
260	C₂²⋊C₈	C₂×C₄×C₃₁	1	2	yes	—
261	C₂²⋊C₈	D₄×C₃₁	1	2	yes	—
262	#97	—	2	2	no	—
263	#97	—	2	1	no	—
264	#97	—	2	1	no	—
265	C₄×C₈	—	2	2	no	—
266	C₄×C₈	—	2	2	no	—
267	C₄×C₈	—	2	2	no	—
268	C₄×C₈	—	2	1	no	—
269	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
270	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
271	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
272	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
273	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
274	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
275	C₃₁	#17925	1	1	yes	characteristic, direct product factor, Sylow
276	C₂×Q₈	—	2	4	no	—
277	C₂×Q₈	—	2	1	no	—
278	C₂×Q₈	—	2	1	no	—
279	C₂×Q₈	C₂²×C₄×C₃₁	1	2	yes	—
280	C₂×Q₈	C₂²×C₄×C₃₁	1	2	yes	—
281	C₂²×C₄	—	2	1	no	—
282	C₂²×C₄	—	2	1	no	—
283	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
284	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
285	C₂²×C₄	#41×C₃₁	1	1	yes	characteristic
286	Q₁₆	—	2	4	no	—
287	Q₁₆	—	2	4	no	—
288	M₁₆	—	4	2	no	—
289	C₂×C₈	—	2	1	no	—
290	C₂×C₈	—	2	2	no	—
291	C₂×C₈	—	2	2	no	—
292	C₂×C₈	—	2	1	no	—
293	C₂×C₈	C₂²×C₄×C₃₁	1	2	yes	—
294	C₂×C₈	C₂²×C₄×C₃₁	1	2	yes	—
295	C₂×C₈	C₂×D₄×C₃₁	1	2	yes	—
296	C₂×C₈	C₂×D₄×C₃₁	1	2	yes	—
297	C₄⋊C₄	—	2	2	no	—
298	C₄⋊C₄	—	2	1	no	—
299	C₄⋊C₄	—	2	1	no	—
300	C₄⋊C₄	—	2	1	no	—
301	C₄⋊C₄	—	2	1	no	—
302	C₄⋊C₄	—	2	2	no	—
303	C₄⋊C₄	—	2	2	no	—
304	C₄⋊C₄	—	2	2	no	—
305	C₄⋊C₄	C₂²×C₄×C₃₁	1	2	yes	—
306	C₄⋊C₄	C₂²×C₄×C₃₁	1	2	yes	—
307	C₂²⋊C₄	—	2	2	no	—
308	C₄²	—	2	2	no	—
309	C₄²	—	2	2	no	—
310	C₄²	—	2	2	no	—
311	C₄²	C₂²×C₄×C₃₁	1	1	yes	characteristic
312	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
313	C₄²	#41×C₃₁	1	1	yes	characteristic
314	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
315	C₂³	C₄×D₄×C₃₁	1	1	yes	characteristic
316	Q₈	—	2	4	no	—
317	Q₈	—	2	2	no	—
318	Q₈	—	2	2	no	—
319	Q₈	—	2	2	no	—
320	Q₈	—	8	1	no	—
321	Q₈	C₃₁×#131	1	4	yes	—
322	C₂×C₄	—	2	4	no	—
323	C₂×C₄	—	2	2	no	—
324	C₂×C₄	—	2	2	no	—
325	C₂×C₄	—	2	2	no	—
326	C₂×C₄	—	2	2	no	—
327	C₂×C₄	—	2	2	no	—
328	C₂×C₄	—	2	2	no	—
329	C₂×C₄	—	4	1	no	—
330	C₂×C₄	—	8	1	no	—
331	C₂×C₄	C₄×D₄×C₃₁	1	1	yes	characteristic
332	C₂×C₄	C₄×D₄×C₃₁	1	1	yes	characteristic
333	C₂×C₄	C₄×D₄×C₃₁	1	1	yes	characteristic
334	C₂×C₄	C₂³×C₄×C₃₁	1	1	yes	characteristic
335	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
336	C₂×C₄	C₂×#41×C₃₁	1	1	yes	characteristic
337	C₈	—	2	2	no	—
338	C₈	—	2	2	no	—
339	C₈	—	2	2	no	—
340	C₈	—	2	2	no	—
341	C₈	—	2	2	no	—
342	C₈	—	4	1	no	—
343	C₈	—	4	2	no	—
344	C₈	—	4	2	no	—
345	C₂²	—	2	1	no	—
346	C₂²	—	2	1	no	—
347	C₂²	—	2	1	no	—
348	C₂²	C₂×C₄×D₄×C₃₁	1	1	yes	characteristic
349	C₄	—	2	4	no	—
350	C₄	—	2	1	no	—
351	C₄	—	2	1	no	—
352	C₄	—	2	1	no	—
353	C₄	—	2	1	no	—
354	C₄	—	4	2	no	—
355	C₄	—	4	2	no	—
356	C₄	—	4	2	no	—
357	C₄	C₂×C₃₁×#131	1	2	yes	—
358	C₄	C₃₁×#578	1	2	yes	—
359	C₂	—	4	1	no	—
360	C₂	C₃₁×#2929	1	1	yes	characteristic
361	C₂	C₃₁×#2950	1	1	yes	characteristic
362	C₂	C₃₁×#2956	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₃₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₃₁
Frattini, cosocle	C₄²	C₂⁴×C₃₁
socle	C₂²×C₃₁	C₂×C₄×D₄
prime radical	C₂³×C₃₁	C₄×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₃₁ ◁ C₃₁×#431 ◁ G

Complements

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

N	H ≅ G/N	type
4. C₃₁×#1587	C₂	semidirect
5. C₃₁×#1584	C₂	semidirect
6. C₃₁×#1579	C₂	semidirect
7. C₈×Q₁₆×C₃₁	C₂	semidirect
133. #17925	C₃₁	direct (N × H)
167. #1587	C₂×C₃₁	semidirect
168. #1584	C₂×C₃₁	semidirect
169. #1579	C₂×C₃₁	semidirect
170. C₈×Q₁₆	C₂×C₃₁	semidirect
275. C₃₁	#17925	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×#3104	2
C₃₁×#2985	2
C₃₁×#2982	2
C₃₁×#1587	2
C₃₁×#1584	2
C₃₁×#1579	2
C₈×Q₁₆×C₃₁	2
C₃₁×#1572	2
C₃₁×#1491	2
C₃₁×#1485	2
C₃₁×#1453	2
#17925	31

Subgroups — C31×#17925 #21474684

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#17925 #21474684