Subgroups — C₃₁×#60490 #21517249

Order 7936.

2178 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×#3458	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃₁×#518	C₂	1	1	yes	maximal, characteristic
3	C₃₁×#3081	C₂	1	16	yes	maximal, complemented
4	C₃₁×#3077	C₂	1	8	yes	maximal, complemented
5	C₃₁×#2911	C₂	1	2	yes	maximal, complemented
6	C₃₁×#2905	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₃₁×#418	C₂	1	2	yes	maximal
8	C₂³×D₄×C₃₁	C₂²	1	1	yes	characteristic
9	C₂²×M₁₆×C₃₁	C₂²	1	2	yes	—
10	C₃₁×#544	—	2	2	no	—
11	C₃₁×#544	C₂²	1	8	yes	complemented
12	C₃₁×#543	—	2	2	no	—
13	C₃₁×#533	—	2	4	no	—
14	C₃₁×#533	C₂²	1	4	yes	complemented
15	C₃₁×#518	—	2	4	no	—
16	C₃₁×#518	C₂²	1	8	yes	—
17	C₂×C₄×D₄×C₃₁	—	2	2	no	—
18	C₂×C₄×D₄×C₃₁	C₂²	1	4	yes	—
19	C₂×C₃₁×#117	C₂²	1	2	yes	—
20	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
21	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
22	C₂²×C₂²⋊C₄×C₃₁	—	2	2	no	—
23	C₃₁×#478	C₂²	1	32	yes	complemented
24	C₃₁×#476	C₂²	1	16	yes	complemented
25	C₃₁×#474	C₂²	1	16	yes	complemented
26	C₃₁×#428	C₂²	1	8	yes	complemented
27	C₃₁×#428	C₂²	1	8	yes	complemented
28	C₃₁×#427	C₂²	1	8	yes	complemented
29	C₃₁×#424	C₂²	1	8	yes	complemented
30	C₃₁×#423	C₂²	1	4	yes	complemented
31	C₃₁×#418	C₂²	1	8	yes	—
32	C₃₁×#418	C₂²	1	8	yes	—
33	C₂×C₃₁×#102	C₂²	1	8	yes	—
34	C₂⁵×C₃₁	—	2	1	no	—
35	C₂²×D₄×C₃₁	—	2	1	no	—
36	C₂²×D₄×C₃₁	—	2	2	no	—
37	C₂²×D₄×C₃₁	—	2	4	no	—
38	C₂²×D₄×C₃₁	Q₈	1	8	yes	complemented
39	C₂²×D₄×C₃₁	C₂³	1	4	yes	—
40	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
41	C₂³×C₄×C₃₁	—	2	4	no	—
42	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
43	C₂×M₁₆×C₃₁	—	2	8	no	—
44	C₂×M₁₆×C₃₁	C₂³	1	4	yes	—
45	C₂×M₁₆×C₃₁	C₂³	1	4	yes	—
46	C₂²×C₈×C₃₁	C₂³	1	4	yes	—
47	C₃₁×C₄⋊Q₈	—	2	8	no	—
48	C₃₁×C₄⋊Q₈	C₂³	1	8	yes	complemented
49	C₃₁×#125	—	2	8	no	—
50	C₃₁×#125	C₂³	1	8	yes	complemented
51	C₃₁×C₂²⋊Q₈	—	2	8	no	—
52	C₃₁×C₂²⋊Q₈	—	2	16	no	—
53	C₄×Q₈×C₃₁	—	2	8	no	—
54	C₄×D₄×C₃₁	—	2	16	no	—
55	C₄×D₄×C₃₁	—	2	8	no	—
56	C₄×D₄×C₃₁	C₂³	1	16	yes	—
57	C₃₁×#117	—	2	2	no	—
58	C₃₁×#117	—	2	2	no	—
59	C₃₁×#117	—	2	2	no	—
60	C₃₁×#117	D₄	1	4	yes	—
61	C₃₁×#117	C₂³	1	4	yes	—
62	C₃₁×#117	C₂³	1	4	yes	—
63	C₃₁×#117	C₂³	1	4	yes	—
64	C₃₁×#117	C₂³	1	4	yes	—
65	C₂×C₄⋊C₄×C₃₁	D₄	1	2	yes	—
66	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
67	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
68	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
69	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
70	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
71	C₂×C₂²⋊C₄×C₃₁	—	2	16	no	—
72	C₂×C₂²⋊C₄×C₃₁	D₄	1	2	yes	—
73	C₂×C₄²×C₃₁	—	2	1	no	—
74	C₂×C₄²×C₃₁	—	2	2	no	—
75	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
76	C₃₁×#107	C₂³	1	16	yes	complemented
77	C₃₁×#106	C₂³	1	16	yes	complemented
78	C₃₁×C₄⋊C₈	C₂³	1	16	yes	complemented
79	C₃₁×#102	C₂³	1	32	yes	—
80	C₂⁴×C₃₁	—	2	2	no	—
81	C₂⁴×C₃₁	—	2	8	no	—
82	C₂⁴×C₃₁	—	2	4	no	—
83	C₂⁴×C₃₁	—	8	4	no	—
84	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
85	C₂×Q₈×C₃₁	—	2	8	no	—
86	C₂×D₄×C₃₁	—	2	8	no	—
87	C₂×D₄×C₃₁	—	2	16	no	—
88	C₂×D₄×C₃₁	—	2	2	no	—
89	C₂×D₄×C₃₁	—	2	4	no	—
90	C₂×D₄×C₃₁	—	2	8	no	—
91	C₂×D₄×C₃₁	—	2	4	no	—
92	C₂×D₄×C₃₁	C₂×Q₈	1	8	yes	—
93	C₂×D₄×C₃₁	C₂×Q₈	1	16	yes	—
94	C₂×D₄×C₃₁	C₂⁴	1	4	yes	—
95	C₂²×C₄×C₃₁	—	2	2	no	—
96	C₂²×C₄×C₃₁	—	2	4	no	—
97	C₂²×C₄×C₃₁	—	2	16	no	—
98	C₂²×C₄×C₃₁	—	8	8	no	—
99	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
100	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
102	C₂²×C₄×C₃₁	C₂×Q₈	1	4	yes	—
103	C₂²×C₄×C₃₁	#41	1	4	yes	—
104	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
105	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
106	M₁₆×C₃₁	—	2	8	no	—
107	M₁₆×C₃₁	—	2	8	no	—
108	C₂×C₈×C₃₁	—	2	8	no	—
109	C₂×C₈×C₃₁	C₂⁴	1	8	yes	—
110	C₄⋊C₄×C₃₁	—	2	2	no	—
111	C₄⋊C₄×C₃₁	—	2	4	no	—
112	C₄⋊C₄×C₃₁	—	2	8	no	—
113	C₄⋊C₄×C₃₁	—	2	16	no	—
114	C₄⋊C₄×C₃₁	C₂×D₄	1	8	yes	—
115	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
116	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
117	C₂²⋊C₄×C₃₁	—	2	4	no	—
118	C₂²⋊C₄×C₃₁	—	2	4	no	—
119	C₂²⋊C₄×C₃₁	—	2	4	no	—
120	C₂²⋊C₄×C₃₁	—	2	16	no	—
121	C₂²⋊C₄×C₃₁	C₂×D₄	1	8	yes	—
122	C₄²×C₃₁	—	2	4	no	—
123	C₄²×C₃₁	—	2	4	no	—
124	C₄²×C₃₁	—	2	4	no	—
125	C₄²×C₃₁	C₂×D₄	1	4	yes	—
126	C₄²×C₃₁	C₂⁴	1	4	yes	—
127	#60490	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
128	C₂³×C₃₁	—	2	8	no	—
129	C₂³×C₃₁	—	2	4	no	—
130	C₂³×C₃₁	—	2	16	no	—
131	C₂³×C₃₁	—	4	2	no	—
132	C₂³×C₃₁	—	4	8	no	—
133	C₂³×C₃₁	—	8	8	no	—
134	C₂³×C₃₁	—	8	16	no	—
135	C₂³×C₃₁	C₂²⋊Q₈	1	4	yes	—
136	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
137	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
138	Q₈×C₃₁	—	8	8	no	—
139	D₄×C₃₁	—	2	8	no	—
140	D₄×C₃₁	—	2	16	no	—
141	D₄×C₃₁	—	2	4	no	—
142	D₄×C₃₁	C₂²×Q₈	1	8	yes	—
143	C₂×C₄×C₃₁	—	2	4	no	—
144	C₂×C₄×C₃₁	—	2	8	no	—
145	C₂×C₄×C₃₁	—	4	4	no	—
146	C₂×C₄×C₃₁	—	4	4	no	—
147	C₂×C₄×C₃₁	—	8	16	no	—
148	C₂×C₄×C₃₁	—	8	4	no	—
149	C₂×C₄×C₃₁	C₂²⋊Q₈	1	4	yes	—
150	C₂×C₄×C₃₁	C₂²⋊Q₈	1	8	yes	—
151	C₂×C₄×C₃₁	C₂²×D₄	1	8	yes	—
152	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
153	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
154	C₂×C₄×C₃₁	C₂²×Q₈	1	2	yes	—
155	C₂×C₄×C₃₁	C₂²×Q₈	1	4	yes	—
156	C₂×C₄×C₃₁	C₂×#41	1	4	yes	—
157	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
158	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
159	C₈×C₃₁	—	2	8	no	—
160	#3458	C₂×C₃₁	1	1	yes	characteristic, complemented
161	C₂×#518	C₂×C₃₁	1	1	yes	characteristic
162	#3081	C₂×C₃₁	1	16	yes	complemented
163	#3077	C₂×C₃₁	1	8	yes	complemented
164	#2911	C₂×C₃₁	1	2	yes	complemented
165	#2905	C₂×C₃₁	1	1	yes	characteristic, complemented
166	C₂×#418	C₂×C₃₁	1	2	yes	—
167	C₂²×C₃₁	—	2	2	no	—
168	C₂²×C₃₁	—	2	4	no	—
169	C₂²×C₃₁	—	2	8	no	—
170	C₂²×C₃₁	—	4	4	no	—
171	C₂²×C₃₁	—	4	16	no	—
172	C₂²×C₃₁	—	4	8	no	—
173	C₂²×C₃₁	—	8	16	no	—
174	C₂²×C₃₁	C₂×C₂²⋊Q₈	1	2	yes	—
175	C₂²×C₃₁	C₂×C₂²⋊Q₈	1	4	yes	—
176	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
177	C₄×C₃₁	—	2	8	no	—
178	C₄×C₃₁	—	4	4	no	—
179	C₄×C₃₁	—	4	8	no	—
180	C₄×C₃₁	C₂×C₂²⋊Q₈	1	2	yes	—
181	C₄×C₃₁	C₂×C₂²⋊Q₈	1	4	yes	—
182	C₄×C₃₁	C₂³×Q₈	1	1	yes	characteristic
183	C₄×C₃₁	C₂²×#41	1	1	yes	characteristic
184	C₂³×D₄	C₂²×C₃₁	1	1	yes	characteristic
185	C₂²×M₁₆	C₂²×C₃₁	1	2	yes	—
186	#544	—	2	2	no	—
187	#544	C₂²×C₃₁	1	8	yes	complemented
188	#543	—	2	2	no	—
189	#533	—	2	4	no	—
190	#533	C₂²×C₃₁	1	4	yes	complemented
191	#518	—	2	4	no	—
192	#518	C₂²×C₃₁	1	8	yes	—
193	C₂×C₄×D₄	—	2	2	no	—
194	C₂×C₄×D₄	C₂²×C₃₁	1	4	yes	—
195	C₂×#117	C₂²×C₃₁	1	2	yes	—
196	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
197	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
198	C₂²×C₂²⋊C₄	—	2	2	no	—
199	#478	C₂²×C₃₁	1	32	yes	complemented
200	#476	C₂²×C₃₁	1	16	yes	complemented
201	#474	C₂²×C₃₁	1	16	yes	complemented
202	#428	C₂²×C₃₁	1	8	yes	complemented
203	#428	C₂²×C₃₁	1	8	yes	complemented
204	#427	C₂²×C₃₁	1	8	yes	complemented
205	#424	C₂²×C₃₁	1	8	yes	complemented
206	#423	C₂²×C₃₁	1	4	yes	complemented
207	#418	C₂²×C₃₁	1	8	yes	—
208	#418	C₂²×C₃₁	1	8	yes	—
209	C₂×#102	C₂²×C₃₁	1	8	yes	—
210	C₂×C₃₁	—	2	2	no	—
211	C₂×C₃₁	—	2	4	no	—
212	C₂×C₃₁	—	4	8	no	—
213	C₂×C₃₁	C₂²×C₂²⋊Q₈	1	1	yes	characteristic
214	C₂×C₃₁	#3585	1	2	yes	—
215	C₂⁵	—	2	1	no	—
216	C₂²×D₄	—	2	1	no	—
217	C₂²×D₄	—	2	2	no	—
218	C₂²×D₄	—	2	4	no	—
219	C₂²×D₄	Q₈×C₃₁	1	8	yes	complemented
220	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
221	C₂²×D₄	C₂³×C₃₁	1	4	yes	—
222	C₂³×C₄	—	2	4	no	—
223	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
224	C₂×M₁₆	—	2	8	no	—
225	C₂×M₁₆	C₂³×C₃₁	1	4	yes	—
226	C₂×M₁₆	C₂³×C₃₁	1	4	yes	—
227	C₂²×C₈	C₂³×C₃₁	1	4	yes	—
228	C₄⋊Q₈	—	2	8	no	—
229	C₄⋊Q₈	C₂³×C₃₁	1	8	yes	complemented
230	#125	—	2	8	no	—
231	#125	C₂³×C₃₁	1	8	yes	complemented
232	C₂²⋊Q₈	—	2	8	no	—
233	C₂²⋊Q₈	—	2	16	no	—
234	C₄×Q₈	—	2	8	no	—
235	C₄×D₄	—	2	16	no	—
236	C₄×D₄	—	2	8	no	—
237	C₄×D₄	C₂³×C₃₁	1	16	yes	—
238	#117	—	2	2	no	—
239	#117	—	2	2	no	—
240	#117	—	2	2	no	—
241	#117	D₄×C₃₁	1	4	yes	—
242	#117	C₂³×C₃₁	1	4	yes	—
243	#117	C₂³×C₃₁	1	4	yes	—
244	#117	C₂³×C₃₁	1	4	yes	—
245	#117	C₂³×C₃₁	1	4	yes	—
246	C₂×C₄⋊C₄	D₄×C₃₁	1	2	yes	—
247	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
248	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
249	C₂×C₂²⋊C₄	—	2	1	no	—
250	C₂×C₂²⋊C₄	—	2	2	no	—
251	C₂×C₂²⋊C₄	—	2	4	no	—
252	C₂×C₂²⋊C₄	—	2	16	no	—
253	C₂×C₂²⋊C₄	D₄×C₃₁	1	2	yes	—
254	C₂×C₄²	—	2	1	no	—
255	C₂×C₄²	—	2	2	no	—
256	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
257	#107	C₂³×C₃₁	1	16	yes	complemented
258	#106	C₂³×C₃₁	1	16	yes	complemented
259	C₄⋊C₈	C₂³×C₃₁	1	16	yes	complemented
260	#102	C₂³×C₃₁	1	32	yes	—
261	C₃₁	#60490	1	1	yes	characteristic, direct product factor, Sylow
262	C₂⁴	—	2	2	no	—
263	C₂⁴	—	2	8	no	—
264	C₂⁴	—	2	4	no	—
265	C₂⁴	—	8	4	no	—
266	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
267	C₂×Q₈	—	2	8	no	—
268	C₂×D₄	—	2	8	no	—
269	C₂×D₄	—	2	16	no	—
270	C₂×D₄	—	2	2	no	—
271	C₂×D₄	—	2	4	no	—
272	C₂×D₄	—	2	8	no	—
273	C₂×D₄	—	2	4	no	—
274	C₂×D₄	C₂×Q₈×C₃₁	1	8	yes	—
275	C₂×D₄	C₂×Q₈×C₃₁	1	16	yes	—
276	C₂×D₄	C₂⁴×C₃₁	1	4	yes	—
277	C₂²×C₄	—	2	2	no	—
278	C₂²×C₄	—	2	4	no	—
279	C₂²×C₄	—	2	16	no	—
280	C₂²×C₄	—	8	8	no	—
281	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
282	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
283	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
284	C₂²×C₄	C₂×Q₈×C₃₁	1	4	yes	—
285	C₂²×C₄	#41×C₃₁	1	4	yes	—
286	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
287	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
288	M₁₆	—	2	8	no	—
289	M₁₆	—	2	8	no	—
290	C₂×C₈	—	2	8	no	—
291	C₂×C₈	C₂⁴×C₃₁	1	8	yes	—
292	C₄⋊C₄	—	2	2	no	—
293	C₄⋊C₄	—	2	4	no	—
294	C₄⋊C₄	—	2	8	no	—
295	C₄⋊C₄	—	2	16	no	—
296	C₄⋊C₄	C₂×D₄×C₃₁	1	8	yes	—
297	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
298	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
299	C₂²⋊C₄	—	2	4	no	—
300	C₂²⋊C₄	—	2	4	no	—
301	C₂²⋊C₄	—	2	4	no	—
302	C₂²⋊C₄	—	2	16	no	—
303	C₂²⋊C₄	C₂×D₄×C₃₁	1	8	yes	—
304	C₄²	—	2	4	no	—
305	C₄²	—	2	4	no	—
306	C₄²	—	2	4	no	—
307	C₄²	C₂×D₄×C₃₁	1	4	yes	—
308	C₄²	C₂⁴×C₃₁	1	4	yes	—
309	C₂³	—	2	8	no	—
310	C₂³	—	2	4	no	—
311	C₂³	—	2	16	no	—
312	C₂³	—	4	2	no	—
313	C₂³	—	4	8	no	—
314	C₂³	—	8	8	no	—
315	C₂³	—	8	16	no	—
316	C₂³	C₃₁×C₂²⋊Q₈	1	4	yes	—
317	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
318	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
319	Q₈	—	8	8	no	—
320	D₄	—	2	8	no	—
321	D₄	—	2	16	no	—
322	D₄	—	2	4	no	—
323	D₄	C₂²×Q₈×C₃₁	1	8	yes	—
324	C₂×C₄	—	2	4	no	—
325	C₂×C₄	—	2	8	no	—
326	C₂×C₄	—	4	4	no	—
327	C₂×C₄	—	4	4	no	—
328	C₂×C₄	—	8	16	no	—
329	C₂×C₄	—	8	4	no	—
330	C₂×C₄	C₃₁×C₂²⋊Q₈	1	4	yes	—
331	C₂×C₄	C₃₁×C₂²⋊Q₈	1	8	yes	—
332	C₂×C₄	C₂²×D₄×C₃₁	1	8	yes	—
333	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
334	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
335	C₂×C₄	C₂²×Q₈×C₃₁	1	2	yes	—
336	C₂×C₄	C₂²×Q₈×C₃₁	1	4	yes	—
337	C₂×C₄	C₂×#41×C₃₁	1	4	yes	—
338	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
339	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
340	C₈	—	2	8	no	—
341	C₂²	—	2	2	no	—
342	C₂²	—	2	4	no	—
343	C₂²	—	2	8	no	—
344	C₂²	—	4	4	no	—
345	C₂²	—	4	16	no	—
346	C₂²	—	4	8	no	—
347	C₂²	—	8	16	no	—
348	C₂²	C₂×C₃₁×C₂²⋊Q₈	1	2	yes	—
349	C₂²	C₂×C₃₁×C₂²⋊Q₈	1	4	yes	—
350	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
351	C₄	—	2	8	no	—
352	C₄	—	4	4	no	—
353	C₄	—	4	8	no	—
354	C₄	C₂×C₃₁×C₂²⋊Q₈	1	2	yes	—
355	C₄	C₂×C₃₁×C₂²⋊Q₈	1	4	yes	—
356	C₄	C₂³×Q₈×C₃₁	1	1	yes	characteristic
357	C₄	C₂²×#41×C₃₁	1	1	yes	characteristic
358	C₂	—	2	2	no	—
359	C₂	—	2	4	no	—
360	C₂	—	4	8	no	—
361	C₂	C₂²×C₃₁×C₂²⋊Q₈	1	1	yes	characteristic
362	C₂	C₃₁×#3585	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
prime radical	C₂³×D₄×C₃₁	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₂×C₃₁×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3458	C₂	semidirect
3. C₃₁×#3081	C₂	semidirect
4. C₃₁×#3077	C₂	semidirect
5. C₃₁×#2911	C₂	semidirect
6. C₃₁×#2905	C₂	semidirect
11. C₃₁×#544	C₂²	semidirect
14. C₃₁×#533	C₂²	semidirect
23. C₃₁×#478	C₂²	semidirect
24. C₃₁×#476	C₂²	semidirect
25. C₃₁×#474	C₂²	semidirect
26. C₃₁×#428	C₂²	semidirect
27. C₃₁×#428	C₂²	semidirect
28. C₃₁×#427	C₂²	semidirect
29. C₃₁×#424	C₂²	semidirect
30. C₃₁×#423	C₂²	semidirect
38. C₂²×D₄×C₃₁	Q₈	semidirect
48. C₃₁×C₄⋊Q₈	C₂³	semidirect
50. C₃₁×#125	C₂³	semidirect
76. C₃₁×#107	C₂³	semidirect
77. C₃₁×#106	C₂³	semidirect
78. C₃₁×C₄⋊C₈	C₂³	semidirect
127. #60490	C₃₁	direct (N × H)
160. #3458	C₂×C₃₁	semidirect
162. #3081	C₂×C₃₁	semidirect
163. #3077	C₂×C₃₁	semidirect
164. #2911	C₂×C₃₁	semidirect
165. #2905	C₂×C₃₁	semidirect
187. #544	C₂²×C₃₁	semidirect
190. #533	C₂²×C₃₁	semidirect
199. #478	C₂²×C₃₁	semidirect
200. #476	C₂²×C₃₁	semidirect
201. #474	C₂²×C₃₁	semidirect
202. #428	C₂²×C₃₁	semidirect
203. #428	C₂²×C₃₁	semidirect
204. #427	C₂²×C₃₁	semidirect
205. #424	C₂²×C₃₁	semidirect
206. #423	C₂²×C₃₁	semidirect
219. C₂²×D₄	Q₈×C₃₁	semidirect
229. C₄⋊Q₈	C₂³×C₃₁	semidirect
231. #125	C₂³×C₃₁	semidirect
257. #107	C₂³×C₃₁	semidirect
258. #106	C₂³×C₃₁	semidirect
259. C₄⋊C₈	C₂³×C₃₁	semidirect
261. C₃₁	#60490	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×#3458	2
C₂×C₃₁×#518	2
C₃₁×#3081	2
C₃₁×#3077	2
C₃₁×#2911	2
C₃₁×#2905	2
C₂×C₃₁×#418	2
#60490	31

Subgroups — C31×#60490 #21517249

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#60490 #21517249