Subgroups — C₃₁×#22694 #21479453

Order 7936.

812 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#2957	C₂	1	2	yes	maximal
2	C₂×C₃₁×#443	C₂	1	1	yes	maximal, characteristic
3	C₃₁×#2916	C₂	1	2	yes	maximal, complemented
4	C₃₁×#1953	C₂	1	2	yes	maximal, complemented
5	C₃₁×#1861	C₂	1	4	yes	maximal, complemented
6	C₃₁×#1848	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#1814	C₂	1	2	yes	maximal, complemented
8	C₃₁×#1772	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₃₁×#135	C₂²	1	1	yes	characteristic
10	C₃₁×#568	C₂²	1	4	yes	—
11	C₂×C₃₁×#131	C₂²	1	2	yes	—
12	C₃₁×#444	—	2	4	no	—
13	C₃₁×#443	—	2	4	no	—
14	C₃₁×#443	C₄	1	2	yes	complemented
15	C₃₁×#443	C₄	1	2	yes	complemented
16	C₃₁×#443	C₄	1	2	yes	complemented
17	C₃₁×#443	C₄	1	2	yes	complemented
18	C₃₁×#430	—	2	4	no	—
19	C₃₁×#430	C₂²	1	4	yes	—
20	C₂×C₃₁×#108	—	2	4	no	—
21	C₂×C₃₁×#108	C₂²	1	2	yes	—
22	C₂×C₃₁×#108	C₂²	1	2	yes	—
23	C₂×C₃₁×#108	C₂²	1	1	yes	characteristic
24	C₂×C₃₁×#108	C₂²	1	1	yes	characteristic
25	C₃₁×#427	C₂²	1	1	yes	characteristic
26	C₃₁×#423	C₂²	1	2	yes	—
27	C₃₁×#421	C₂²	1	4	yes	—
28	C₂×C₃₁×#104	C₂²	1	2	yes	—
29	C₃₁×#405	C₂²	1	2	yes	—
30	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
31	C₃₁×#344	C₂²	1	4	yes	—
32	C₃₁×#339	C₂²	1	2	yes	—
33	C₂×#41×C₃₁	C₂³	1	2	yes	—
34	C₃₁×#135	C₂×C₄	1	2	yes	—
35	C₃₁×#135	C₂×C₄	1	2	yes	—
36	C₃₁×#135	D₄	1	2	yes	—
37	C₃₁×#135	D₄	1	2	yes	—
38	C₂×Q₁₆×C₃₁	Q₈	1	1	yes	characteristic
39	C₂×SD₁₆×C₃₁	Q₈	1	2	yes	—
40	C₂×D₈×C₃₁	Q₈	1	1	yes	characteristic
41	C₃₁×#131	—	2	2	no	—
42	C₃₁×#131	—	2	2	no	—
43	C₃₁×#131	—	2	8	no	—
44	C₃₁×#131	—	4	4	no	—
45	C₃₁×#131	C₂×C₄	1	4	yes	—
46	C₃₁×#131	C₂×C₄	1	4	yes	—
47	C₂×M₁₆×C₃₁	—	2	2	no	—
48	C₂×M₁₆×C₃₁	—	2	8	no	—
49	C₂×M₁₆×C₃₁	C₂³	1	4	yes	—
50	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
51	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
52	C₂²×C₈×C₃₁	—	2	2	no	—
53	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
54	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
55	C₃₁×#117	C₂³	1	2	yes	—
56	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
57	C₃₁×#108	—	2	8	no	—
58	C₃₁×#108	—	2	2	no	—
59	C₃₁×#108	—	2	2	no	—
60	C₃₁×#108	—	2	2	no	—
61	C₃₁×#108	—	2	2	no	—
62	C₃₁×#108	C₂×C₄	1	2	yes	—
63	C₃₁×#108	C₂×C₄	1	2	yes	—
64	C₃₁×#108	D₄	1	2	yes	—
65	C₃₁×#108	D₄	1	2	yes	—
66	C₃₁×#107	—	2	1	no	—
67	C₃₁×#106	—	2	1	no	—
68	C₃₁×C₄⋊C₈	—	4	2	no	—
69	C₃₁×#104	—	2	8	no	—
70	C₃₁×#104	C₂×C₄	1	4	yes	—
71	C₃₁×#104	C₂×C₄	1	4	yes	—
72	C₃₁×#97	—	2	2	no	—
73	C₄×C₈×C₃₁	—	2	2	no	—
74	C₄×C₈×C₃₁	C₂×C₄	1	1	yes	characteristic
75	C₄×C₈×C₃₁	C₂×C₄	1	1	yes	characteristic
76	C₄×C₈×C₃₁	C₂×C₄	1	1	yes	characteristic
77	C₄×C₈×C₃₁	C₂×C₄	1	1	yes	characteristic
78	#41×C₃₁	—	2	2	no	—
79	#41×C₃₁	—	2	2	no	—
80	#41×C₃₁	C₂²×C₄	1	4	yes	—
81	#41×C₃₁	C₂×D₄	1	4	yes	—
82	C₂×Q₈×C₃₁	C₂×Q₈	1	2	yes	—
83	C₂×D₄×C₃₁	—	2	2	no	—
84	C₂×D₄×C₃₁	C₂×Q₈	1	2	yes	—
85	C₂²×C₄×C₃₁	—	2	2	no	—
86	C₂²×C₄×C₃₁	—	2	1	no	—
87	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
88	Q₁₆×C₃₁	C₄⋊C₄	1	2	yes	—
89	Q₁₆×C₃₁	C₄⋊C₄	1	2	yes	—
90	SD₁₆×C₃₁	C₄⋊C₄	1	4	yes	—
91	SD₁₆×C₃₁	C₄⋊C₄	1	4	yes	—
92	D₈×C₃₁	C₄⋊C₄	1	2	yes	—
93	D₈×C₃₁	C₄⋊C₄	1	2	yes	—
94	M₁₆×C₃₁	—	2	2	no	—
95	M₁₆×C₃₁	—	2	2	no	—
96	M₁₆×C₃₁	—	2	4	no	—
97	M₁₆×C₃₁	—	2	4	no	—
98	M₁₆×C₃₁	—	2	4	no	—
99	M₁₆×C₃₁	—	2	4	no	—
100	M₁₆×C₃₁	—	4	8	no	—
101	M₁₆×C₃₁	C₂²×C₄	1	4	yes	—
102	M₁₆×C₃₁	C₂×D₄	1	4	yes	—
103	C₂×C₈×C₃₁	—	2	2	no	—
104	C₂×C₈×C₃₁	—	2	2	no	—
105	C₂×C₈×C₃₁	—	2	4	no	—
106	C₂×C₈×C₃₁	—	2	4	no	—
107	C₂×C₈×C₃₁	—	2	4	no	—
108	C₂×C₈×C₃₁	—	4	8	no	—
109	C₂×C₈×C₃₁	C₂²×C₄	1	1	yes	characteristic
110	C₂×C₈×C₃₁	C₂²×C₄	1	1	yes	characteristic
111	C₂×C₈×C₃₁	C₂²×C₄	1	1	yes	characteristic
112	C₂×C₈×C₃₁	C₂²×C₄	1	1	yes	characteristic
113	C₂×C₈×C₃₁	C₂×D₄	1	1	yes	characteristic
114	C₂×C₈×C₃₁	C₂×D₄	1	1	yes	characteristic
115	C₂×C₈×C₃₁	C₂×D₄	1	1	yes	characteristic
116	C₂×C₈×C₃₁	C₂×D₄	1	1	yes	characteristic
117	C₂×C₈×C₃₁	C₂×Q₈	1	1	yes	characteristic
118	C₂×C₈×C₃₁	C₂×Q₈	1	1	yes	characteristic
119	C₂×C₈×C₃₁	#41	1	1	yes	characteristic
120	C₂×C₈×C₃₁	#41	1	1	yes	characteristic
121	C₄⋊C₄×C₃₁	—	2	2	no	—
122	C₂²⋊C₄×C₃₁	—	2	2	no	—
123	C₄²×C₃₁	—	2	1	no	—
124	C₄²×C₃₁	—	2	2	no	—
125	C₄²×C₃₁	C₂²×C₄	1	1	yes	characteristic
126	C₄²×C₃₁	C₂²×C₄	1	1	yes	characteristic
127	#22694	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
128	C₂³×C₃₁	—	2	2	no	—
129	C₂³×C₃₁	2₋¹⁺⁴	1	1	yes	characteristic
130	Q₈×C₃₁	—	2	2	no	—
131	Q₈×C₃₁	C₂×C₄⋊C₄	1	4	yes	—
132	D₄×C₃₁	—	2	4	no	—
133	D₄×C₃₁	—	2	4	no	—
134	D₄×C₃₁	—	2	2	no	—
135	D₄×C₃₁	C₂×C₄⋊C₄	1	4	yes	—
136	C₂×C₄×C₃₁	—	2	1	no	—
137	C₂×C₄×C₃₁	—	2	2	no	—
138	C₂×C₄×C₃₁	—	2	4	no	—
139	C₂×C₄×C₃₁	—	2	4	no	—
140	C₂×C₄×C₃₁	—	2	1	no	—
141	C₂×C₄×C₃₁	—	4	2	no	—
142	C₂×C₄×C₃₁	—	4	2	no	—
143	C₂×C₄×C₃₁	C₂³×C₄	1	1	yes	characteristic
144	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
145	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
146	C₂×C₄×C₃₁	C₂²×Q₈	1	1	yes	characteristic
147	C₂×C₄×C₃₁	C₂×#41	1	1	yes	characteristic
148	C₂×C₄×C₃₁	H(5,𝔽₂)	1	1	yes	characteristic
149	C₈×C₃₁	—	2	4	no	—
150	C₈×C₃₁	—	2	4	no	—
151	C₈×C₃₁	—	4	4	no	—
152	C₈×C₃₁	C₂×C₄⋊C₄	1	1	yes	characteristic
153	C₈×C₃₁	C₂×C₄⋊C₄	1	1	yes	characteristic
154	C₈×C₃₁	C₂×C₄⋊C₄	1	1	yes	characteristic
155	C₈×C₃₁	C₂×C₄⋊C₄	1	1	yes	characteristic
156	C₈×C₃₁	C₄×D₄	1	1	yes	characteristic
157	C₈×C₃₁	C₄×D₄	1	1	yes	characteristic
158	C₈×C₃₁	C₄×D₄	1	1	yes	characteristic
159	C₈×C₃₁	C₄×D₄	1	1	yes	characteristic
160	#2957	C₂×C₃₁	1	2	yes	—
161	C₂×#443	C₂×C₃₁	1	1	yes	characteristic
162	#2916	C₂×C₃₁	1	2	yes	complemented
163	#1953	C₂×C₃₁	1	2	yes	complemented
164	#1861	C₂×C₃₁	1	4	yes	complemented
165	#1848	C₂×C₃₁	1	1	yes	characteristic, complemented
166	#1814	C₂×C₃₁	1	2	yes	complemented
167	#1772	C₂×C₃₁	1	1	yes	characteristic, complemented
168	C₂²×C₃₁	—	2	4	no	—
169	C₂²×C₃₁	—	4	1	no	—
170	C₂²×C₃₁	—	8	2	no	—
171	C₂²×C₃₁	#520	1	1	yes	characteristic
172	C₂²×C₃₁	#547	1	1	yes	characteristic
173	C₂²×C₃₁	D₄×Q₈	1	1	yes	characteristic
174	C₄×C₃₁	—	2	2	no	—
175	C₄×C₃₁	—	2	4	no	—
176	C₄×C₃₁	—	4	1	no	—
177	C₄×C₃₁	—	8	2	no	—
178	C₄×C₃₁	C₂²×C₄⋊C₄	1	1	yes	characteristic
179	C₄×C₃₁	C₂×C₄×D₄	1	1	yes	characteristic
180	C₄×C₃₁	D₄²	1	1	yes	characteristic
181	C₄×C₃₁	#554	1	1	yes	characteristic
182	C₂×#135	C₂²×C₃₁	1	1	yes	characteristic
183	#568	C₂²×C₃₁	1	4	yes	—
184	C₂×#131	C₂²×C₃₁	1	2	yes	—
185	#444	—	2	4	no	—
186	#443	—	2	4	no	—
187	#443	C₄×C₃₁	1	2	yes	complemented
188	#443	C₄×C₃₁	1	2	yes	complemented
189	#443	C₄×C₃₁	1	2	yes	complemented
190	#443	C₄×C₃₁	1	2	yes	complemented
191	#430	—	2	4	no	—
192	#430	C₂²×C₃₁	1	4	yes	—
193	C₂×#108	—	2	4	no	—
194	C₂×#108	C₂²×C₃₁	1	2	yes	—
195	C₂×#108	C₂²×C₃₁	1	2	yes	—
196	C₂×#108	C₂²×C₃₁	1	1	yes	characteristic
197	C₂×#108	C₂²×C₃₁	1	1	yes	characteristic
198	#427	C₂²×C₃₁	1	1	yes	characteristic
199	#423	C₂²×C₃₁	1	2	yes	—
200	#421	C₂²×C₃₁	1	4	yes	—
201	C₂×#104	C₂²×C₃₁	1	2	yes	—
202	#405	C₂²×C₃₁	1	2	yes	—
203	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
204	#344	C₂²×C₃₁	1	4	yes	—
205	#339	C₂²×C₃₁	1	2	yes	—
206	C₂×C₃₁	—	2	1	no	—
207	C₂×C₃₁	—	2	1	no	—
208	C₂×C₃₁	—	2	1	no	—
209	C₂×C₃₁	—	4	4	no	—
210	C₂×C₃₁	D₄×C₄⋊C₄	1	1	yes	characteristic
211	C₂×#41	C₂³×C₃₁	1	2	yes	—
212	#135	C₂×C₄×C₃₁	1	2	yes	—
213	#135	C₂×C₄×C₃₁	1	2	yes	—
214	#135	D₄×C₃₁	1	2	yes	—
215	#135	D₄×C₃₁	1	2	yes	—
216	C₂×Q₁₆	Q₈×C₃₁	1	1	yes	characteristic
217	C₂×SD₁₆	Q₈×C₃₁	1	2	yes	—
218	C₂×D₈	Q₈×C₃₁	1	1	yes	characteristic
219	#131	—	2	2	no	—
220	#131	—	2	2	no	—
221	#131	—	2	8	no	—
222	#131	—	4	4	no	—
223	#131	C₂×C₄×C₃₁	1	4	yes	—
224	#131	C₂×C₄×C₃₁	1	4	yes	—
225	C₂×M₁₆	—	2	2	no	—
226	C₂×M₁₆	—	2	8	no	—
227	C₂×M₁₆	C₂³×C₃₁	1	4	yes	—
228	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
229	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
230	C₂²×C₈	—	2	2	no	—
231	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
232	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
233	#117	C₂³×C₃₁	1	2	yes	—
234	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
235	#108	—	2	8	no	—
236	#108	—	2	2	no	—
237	#108	—	2	2	no	—
238	#108	—	2	2	no	—
239	#108	—	2	2	no	—
240	#108	C₂×C₄×C₃₁	1	2	yes	—
241	#108	C₂×C₄×C₃₁	1	2	yes	—
242	#108	D₄×C₃₁	1	2	yes	—
243	#108	D₄×C₃₁	1	2	yes	—
244	#107	—	2	1	no	—
245	#106	—	2	1	no	—
246	C₄⋊C₈	—	4	2	no	—
247	#104	—	2	8	no	—
248	#104	C₂×C₄×C₃₁	1	4	yes	—
249	#104	C₂×C₄×C₃₁	1	4	yes	—
250	#97	—	2	2	no	—
251	C₄×C₈	—	2	2	no	—
252	C₄×C₈	C₂×C₄×C₃₁	1	1	yes	characteristic
253	C₄×C₈	C₂×C₄×C₃₁	1	1	yes	characteristic
254	C₄×C₈	C₂×C₄×C₃₁	1	1	yes	characteristic
255	C₄×C₈	C₂×C₄×C₃₁	1	1	yes	characteristic
256	C₃₁	#22694	1	1	yes	characteristic, direct product factor, Sylow
257	#41	—	2	2	no	—
258	#41	—	2	2	no	—
259	#41	C₂²×C₄×C₃₁	1	4	yes	—
260	#41	C₂×D₄×C₃₁	1	4	yes	—
261	C₂×Q₈	C₂×Q₈×C₃₁	1	2	yes	—
262	C₂×D₄	—	2	2	no	—
263	C₂×D₄	C₂×Q₈×C₃₁	1	2	yes	—
264	C₂²×C₄	—	2	2	no	—
265	C₂²×C₄	—	2	1	no	—
266	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
267	Q₁₆	C₄⋊C₄×C₃₁	1	2	yes	—
268	Q₁₆	C₄⋊C₄×C₃₁	1	2	yes	—
269	SD₁₆	C₄⋊C₄×C₃₁	1	4	yes	—
270	SD₁₆	C₄⋊C₄×C₃₁	1	4	yes	—
271	D₈	C₄⋊C₄×C₃₁	1	2	yes	—
272	D₈	C₄⋊C₄×C₃₁	1	2	yes	—
273	M₁₆	—	2	2	no	—
274	M₁₆	—	2	2	no	—
275	M₁₆	—	2	4	no	—
276	M₁₆	—	2	4	no	—
277	M₁₆	—	2	4	no	—
278	M₁₆	—	2	4	no	—
279	M₁₆	—	4	8	no	—
280	M₁₆	C₂²×C₄×C₃₁	1	4	yes	—
281	M₁₆	C₂×D₄×C₃₁	1	4	yes	—
282	C₂×C₈	—	2	2	no	—
283	C₂×C₈	—	2	2	no	—
284	C₂×C₈	—	2	4	no	—
285	C₂×C₈	—	2	4	no	—
286	C₂×C₈	—	2	4	no	—
287	C₂×C₈	—	4	8	no	—
288	C₂×C₈	C₂²×C₄×C₃₁	1	1	yes	characteristic
289	C₂×C₈	C₂²×C₄×C₃₁	1	1	yes	characteristic
290	C₂×C₈	C₂²×C₄×C₃₁	1	1	yes	characteristic
291	C₂×C₈	C₂²×C₄×C₃₁	1	1	yes	characteristic
292	C₂×C₈	C₂×D₄×C₃₁	1	1	yes	characteristic
293	C₂×C₈	C₂×D₄×C₃₁	1	1	yes	characteristic
294	C₂×C₈	C₂×D₄×C₃₁	1	1	yes	characteristic
295	C₂×C₈	C₂×D₄×C₃₁	1	1	yes	characteristic
296	C₂×C₈	C₂×Q₈×C₃₁	1	1	yes	characteristic
297	C₂×C₈	C₂×Q₈×C₃₁	1	1	yes	characteristic
298	C₂×C₈	#41×C₃₁	1	1	yes	characteristic
299	C₂×C₈	#41×C₃₁	1	1	yes	characteristic
300	C₄⋊C₄	—	2	2	no	—
301	C₂²⋊C₄	—	2	2	no	—
302	C₄²	—	2	1	no	—
303	C₄²	—	2	2	no	—
304	C₄²	C₂²×C₄×C₃₁	1	1	yes	characteristic
305	C₄²	C₂²×C₄×C₃₁	1	1	yes	characteristic
306	C₂³	—	2	2	no	—
307	C₂³	C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
308	Q₈	—	2	2	no	—
309	Q₈	C₂×C₄⋊C₄×C₃₁	1	4	yes	—
310	D₄	—	2	4	no	—
311	D₄	—	2	4	no	—
312	D₄	—	2	2	no	—
313	D₄	C₂×C₄⋊C₄×C₃₁	1	4	yes	—
314	C₂×C₄	—	2	1	no	—
315	C₂×C₄	—	2	2	no	—
316	C₂×C₄	—	2	4	no	—
317	C₂×C₄	—	2	4	no	—
318	C₂×C₄	—	2	1	no	—
319	C₂×C₄	—	4	2	no	—
320	C₂×C₄	—	4	2	no	—
321	C₂×C₄	C₂³×C₄×C₃₁	1	1	yes	characteristic
322	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
323	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
324	C₂×C₄	C₂²×Q₈×C₃₁	1	1	yes	characteristic
325	C₂×C₄	C₂×#41×C₃₁	1	1	yes	characteristic
326	C₂×C₄	C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
327	C₈	—	2	4	no	—
328	C₈	—	2	4	no	—
329	C₈	—	4	4	no	—
330	C₈	C₂×C₄⋊C₄×C₃₁	1	1	yes	characteristic
331	C₈	C₂×C₄⋊C₄×C₃₁	1	1	yes	characteristic
332	C₈	C₂×C₄⋊C₄×C₃₁	1	1	yes	characteristic
333	C₈	C₂×C₄⋊C₄×C₃₁	1	1	yes	characteristic
334	C₈	C₄×D₄×C₃₁	1	1	yes	characteristic
335	C₈	C₄×D₄×C₃₁	1	1	yes	characteristic
336	C₈	C₄×D₄×C₃₁	1	1	yes	characteristic
337	C₈	C₄×D₄×C₃₁	1	1	yes	characteristic
338	C₂²	—	2	4	no	—
339	C₂²	—	4	1	no	—
340	C₂²	—	8	2	no	—
341	C₂²	C₃₁×#520	1	1	yes	characteristic
342	C₂²	C₃₁×#547	1	1	yes	characteristic
343	C₂²	D₄×Q₈×C₃₁	1	1	yes	characteristic
344	C₄	—	2	2	no	—
345	C₄	—	2	4	no	—
346	C₄	—	4	1	no	—
347	C₄	—	8	2	no	—
348	C₄	C₂²×C₄⋊C₄×C₃₁	1	1	yes	characteristic
349	C₄	C₂×C₄×D₄×C₃₁	1	1	yes	characteristic
350	C₄	D₄²×C₃₁	1	1	yes	characteristic
351	C₄	C₃₁×#554	1	1	yes	characteristic
352	C₂	—	2	1	no	—
353	C₂	—	2	1	no	—
354	C₂	—	2	1	no	—
355	C₂	—	4	4	no	—
356	C₂	D₄×C₄⋊C₄×C₃₁	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₃₁	D₄²
commutator	C₂×C₄	C₂³×C₄×C₃₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₃₁
socle	C₂×C₃₁	D₄×C₄⋊C₄
prime radical	C₂×C₃₁×#135	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₃₁ ◁ C₂²×C₄×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₃₁×#2916	C₂	semidirect
4. C₃₁×#1953	C₂	semidirect
5. C₃₁×#1861	C₂	semidirect
6. C₃₁×#1848	C₂	semidirect
7. C₃₁×#1814	C₂	semidirect
8. C₃₁×#1772	C₂	semidirect
14. C₃₁×#443	C₄	semidirect
15. C₃₁×#443	C₄	semidirect
16. C₃₁×#443	C₄	semidirect
17. C₃₁×#443	C₄	semidirect
127. #22694	C₃₁	direct (N × H)
162. #2916	C₂×C₃₁	semidirect
163. #1953	C₂×C₃₁	semidirect
164. #1861	C₂×C₃₁	semidirect
165. #1848	C₂×C₃₁	semidirect
166. #1814	C₂×C₃₁	semidirect
167. #1772	C₂×C₃₁	semidirect
187. #443	C₄×C₃₁	semidirect
188. #443	C₄×C₃₁	semidirect
189. #443	C₄×C₃₁	semidirect
190. #443	C₄×C₃₁	semidirect
256. C₃₁	#22694	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×#2957	2
C₂×C₃₁×#443	2
C₃₁×#2916	2
C₃₁×#1953	2
C₃₁×#1861	2
C₃₁×#1848	2
C₃₁×#1814	2
C₃₁×#1772	2
#22694	31

Subgroups — C31×#22694 #21479453

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#22694 #21479453