Subgroups — C₃₁×#22438 #21479197

Order 7936.

1494 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	C₂²×C₃₁×#135	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃₁×#442	C₂	1	2	yes	maximal, complemented
3	C₃₁×#2339	C₂	1	2	yes	maximal, complemented
4	C₃₁×#1971	C₂	1	2	yes	maximal, complemented
5	C₃₁×#1877	C₂	1	4	yes	maximal, complemented
6	C₃₁×#1807	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#1788	C₂	1	2	yes	maximal, complemented
8	C₃₁×#1752	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#41×C₃₁	C₂²	1	2	yes	—
10	C₂×C₃₁×#135	—	2	8	no	—
11	C₂×C₃₁×#135	C₄	1	8	yes	complemented
12	C₂²×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
13	C₂²×SD₁₆×C₃₁	C₂²	1	2	yes	—
14	C₂²×D₈×C₃₁	C₂²	1	1	yes	characteristic
15	C₂³×C₈×C₃₁	C₂²	1	1	yes	characteristic
16	C₂×C₄×D₄×C₃₁	C₂²	1	4	yes	—
17	C₃₁×#442	—	2	8	no	—
18	C₂×C₃₁×#106	C₂²	1	2	yes	—
19	C₂×C₃₁×#103	C₂²	1	4	yes	—
20	C₂×C₃₁×#102	C₂²	1	4	yes	—
21	C₂×C₃₁×C₂²⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×C₃₁×#97	C₂²	1	2	yes	—
23	C₃₁×#391	C₂²	1	4	yes	—
24	C₃₁×#386	—	2	4	no	—
25	C₃₁×#381	—	2	2	no	—
26	C₃₁×#380	C₂²	1	2	yes	—
27	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
28	C₂×C₃₁×#95	—	2	2	no	—
29	C₃₁×#340	C₂²	1	2	yes	—
30	C₃₁×#336	C₂²	1	2	yes	—
31	C₂×#41×C₃₁	—	2	4	no	—
32	C₂×#41×C₃₁	—	2	8	no	—
33	C₂×#41×C₃₁	—	4	4	no	—
34	C₂×#41×C₃₁	C₂×C₄	1	8	yes	complemented
35	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
36	C₂²×D₄×C₃₁	—	2	2	no	—
37	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
38	C₂³×C₄×C₃₁	—	2	2	no	—
39	C₂³×C₄×C₃₁	—	2	4	no	—
40	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
41	C₃₁×#135	—	2	32	no	—
42	C₂×Q₁₆×C₃₁	—	2	4	no	—
43	C₂×Q₁₆×C₃₁	C₂×C₄	1	4	yes	complemented
44	C₂×SD₁₆×C₃₁	—	2	8	no	—
45	C₂×SD₁₆×C₃₁	C₂×C₄	1	8	yes	complemented
46	C₂×D₈×C₃₁	C₂×C₄	1	4	yes	—
47	C₂×D₈×C₃₁	D₄	1	8	yes	—
48	C₂²×C₈×C₃₁	—	2	4	no	—
49	C₂²×C₈×C₃₁	C₂×C₄	1	4	yes	complemented
50	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
51	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
52	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
53	C₄×D₄×C₃₁	—	2	8	no	—
54	C₄×D₄×C₃₁	—	4	4	no	—
55	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
56	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
57	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
58	C₂×C₂²⋊C₄×C₃₁	D₄	1	2	yes	—
59	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
60	C₃₁×#106	—	2	4	no	—
61	C₃₁×#103	—	4	4	no	—
62	C₃₁×#102	—	2	8	no	—
63	C₃₁×C₂²⋊C₈	—	2	2	no	—
64	C₃₁×#97	—	2	4	no	—
65	C₃₁×#95	—	2	2	no	—
66	C₃₁×#95	—	2	4	no	—
67	C₃₁×#95	—	2	4	no	—
68	C₃₁×#95	D₄	1	2	yes	—
69	C₂⁴×C₃₁	—	2	2	no	—
70	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
71	#41×C₃₁	—	2	16	no	—
72	#41×C₃₁	—	4	8	no	—
73	#41×C₃₁	—	4	16	no	—
74	C₂×Q₈×C₃₁	—	2	2	no	—
75	C₂×Q₈×C₃₁	—	2	4	no	—
76	C₂×Q₈×C₃₁	—	2	4	no	—
77	C₂×Q₈×C₃₁	C₂²×C₄	1	4	yes	—
78	C₂×D₄×C₃₁	—	2	8	no	—
79	C₂×D₄×C₃₁	—	2	2	no	—
80	C₂×D₄×C₃₁	—	2	4	no	—
81	C₂×D₄×C₃₁	—	4	8	no	—
82	C₂×D₄×C₃₁	C₂²×C₄	1	4	yes	—
83	C₂×D₄×C₃₁	C₂×D₄	1	8	yes	—
84	C₂²×C₄×C₃₁	—	2	2	no	—
85	C₂²×C₄×C₃₁	—	2	2	no	—
86	C₂²×C₄×C₃₁	—	2	2	no	—
87	C₂²×C₄×C₃₁	—	2	8	no	—
88	C₂²×C₄×C₃₁	—	2	4	no	—
89	C₂²×C₄×C₃₁	—	4	8	no	—
90	C₂²×C₄×C₃₁	—	4	8	no	—
91	C₂²×C₄×C₃₁	—	4	8	no	—
92	C₂²×C₄×C₃₁	—	8	4	no	—
93	C₂²×C₄×C₃₁	C₂²×C₄	1	2	yes	—
94	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
95	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
96	C₂²×C₄×C₃₁	#41	1	2	yes	—
97	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
98	Q₁₆×C₃₁	—	2	8	no	—
99	SD₁₆×C₃₁	—	2	16	no	—
100	D₈×C₃₁	C₂²⋊C₄	1	16	yes	complemented
101	C₂×C₈×C₃₁	—	2	2	no	—
102	C₂×C₈×C₃₁	—	2	8	no	—
103	C₂×C₈×C₃₁	—	2	2	no	—
104	C₂×C₈×C₃₁	—	2	2	no	—
105	C₂×C₈×C₃₁	—	2	2	no	—
106	C₂×C₈×C₃₁	C₂²×C₄	1	2	yes	—
107	C₂×C₈×C₃₁	C₂²×C₄	1	2	yes	—
108	C₂×C₈×C₃₁	C₂×D₄	1	4	yes	—
109	C₄⋊C₄×C₃₁	—	2	4	no	—
110	C₄⋊C₄×C₃₁	—	2	4	no	—
111	C₂²⋊C₄×C₃₁	—	4	2	no	—
112	C₂²⋊C₄×C₃₁	—	4	8	no	—
113	C₂²⋊C₄×C₃₁	—	8	2	no	—
114	C₄²×C₃₁	—	2	2	no	—
115	C₄²×C₃₁	—	2	2	no	—
116	#22438	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
117	C₂³×C₃₁	—	2	4	no	—
118	C₂³×C₃₁	—	2	8	no	—
119	C₂³×C₃₁	—	2	2	no	—
120	C₂³×C₃₁	—	2	2	no	—
121	C₂³×C₃₁	—	2	2	no	—
122	C₂³×C₃₁	—	4	4	no	—
123	C₂³×C₃₁	—	4	2	no	—
124	C₂³×C₃₁	—	4	2	no	—
125	C₂³×C₃₁	C₄×D₄	1	2	yes	—
126	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
127	Q₈×C₃₁	—	2	4	no	—
128	Q₈×C₃₁	—	2	4	no	—
129	Q₈×C₃₁	—	4	4	no	—
130	D₄×C₃₁	—	2	4	no	—
131	D₄×C₃₁	—	2	8	no	—
132	D₄×C₃₁	—	4	16	no	—
133	D₄×C₃₁	C₂×C₂²⋊C₄	1	8	yes	—
134	C₂×C₄×C₃₁	—	2	2	no	—
135	C₂×C₄×C₃₁	—	2	2	no	—
136	C₂×C₄×C₃₁	—	2	2	no	—
137	C₂×C₄×C₃₁	—	2	4	no	—
138	C₂×C₄×C₃₁	—	2	4	no	—
139	C₂×C₄×C₃₁	—	2	4	no	—
140	C₂×C₄×C₃₁	—	2	4	no	—
141	C₂×C₄×C₃₁	—	2	4	no	—
142	C₂×C₄×C₃₁	—	4	16	no	—
143	C₂×C₄×C₃₁	—	4	4	no	—
144	C₂×C₄×C₃₁	—	4	4	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	C₄×D₄	1	2	yes	—
149	C₂×C₄×C₃₁	C₂³×C₄	1	1	yes	characteristic
150	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
151	C₂×C₄×C₃₁	C₂×#41	1	1	yes	characteristic
152	C₂×C₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
153	C₈×C₃₁	—	2	2	no	—
154	C₈×C₃₁	—	4	2	no	—
155	C₈×C₃₁	C₂×C₂²⋊C₄	1	4	yes	—
156	C₂²×#135	C₂×C₃₁	1	1	yes	characteristic
157	C₂×#442	C₂×C₃₁	1	2	yes	complemented
158	#2339	C₂×C₃₁	1	2	yes	complemented
159	#1971	C₂×C₃₁	1	2	yes	complemented
160	#1877	C₂×C₃₁	1	4	yes	complemented
161	#1807	C₂×C₃₁	1	1	yes	characteristic, complemented
162	#1788	C₂×C₃₁	1	2	yes	complemented
163	#1752	C₂×C₃₁	1	1	yes	characteristic, complemented
164	C₂²×C₃₁	—	2	2	no	—
165	C₂²×C₃₁	—	2	8	no	—
166	C₂²×C₃₁	—	2	2	no	—
167	C₂²×C₃₁	—	2	2	no	—
168	C₂²×C₃₁	—	4	4	no	—
169	C₂²×C₃₁	—	4	4	no	—
170	C₂²×C₃₁	—	4	8	no	—
171	C₂²×C₃₁	—	4	4	no	—
172	C₂²×C₃₁	—	4	8	no	—
173	C₂²×C₃₁	C₂×C₄×D₄	1	1	yes	characteristic
174	C₂²×C₃₁	D₄²	1	2	yes	—
175	C₂²×C₃₁	#575	1	2	yes	—
176	C₂²×C₃₁	#577	1	2	yes	—
177	C₄×C₃₁	—	2	2	no	—
178	C₄×C₃₁	—	4	4	no	—
179	C₄×C₃₁	—	4	4	no	—
180	C₄×C₃₁	—	8	4	no	—
181	C₄×C₃₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
182	C₄×C₃₁	#518	1	1	yes	characteristic
183	C₄×C₃₁	#546	1	2	yes	—
184	C₂²×#41	C₂²×C₃₁	1	2	yes	—
185	C₂×#135	—	2	8	no	—
186	C₂×#135	C₄×C₃₁	1	8	yes	complemented
187	C₂²×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
188	C₂²×SD₁₆	C₂²×C₃₁	1	2	yes	—
189	C₂²×D₈	C₂²×C₃₁	1	1	yes	characteristic
190	C₂³×C₈	C₂²×C₃₁	1	1	yes	characteristic
191	C₂×C₄×D₄	C₂²×C₃₁	1	4	yes	—
192	#442	—	2	8	no	—
193	C₂×#106	C₂²×C₃₁	1	2	yes	—
194	C₂×#103	C₂²×C₃₁	1	4	yes	—
195	C₂×#102	C₂²×C₃₁	1	4	yes	—
196	C₂×C₂²⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
197	C₂×#97	C₂²×C₃₁	1	2	yes	—
198	#391	C₂²×C₃₁	1	4	yes	—
199	#386	—	2	4	no	—
200	#381	—	2	2	no	—
201	#380	C₂²×C₃₁	1	2	yes	—
202	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
203	C₂×#95	—	2	2	no	—
204	#340	C₂²×C₃₁	1	2	yes	—
205	#336	C₂²×C₃₁	1	2	yes	—
206	C₂×C₃₁	—	4	2	no	—
207	C₂×C₃₁	—	4	8	no	—
208	C₂×C₃₁	D₄×C₂²⋊C₄	1	1	yes	characteristic
209	C₂×C₃₁	#2943	1	1	yes	characteristic
210	C₂×C₃₁	#2952	1	1	yes	characteristic
211	C₂×C₃₁	#3267	1	4	yes	—
212	C₂×#41	—	2	4	no	—
213	C₂×#41	—	2	8	no	—
214	C₂×#41	—	4	4	no	—
215	C₂×#41	C₂×C₄×C₃₁	1	8	yes	complemented
216	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
217	C₂²×D₄	—	2	2	no	—
218	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
219	C₂³×C₄	—	2	2	no	—
220	C₂³×C₄	—	2	4	no	—
221	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
222	#135	—	2	32	no	—
223	C₂×Q₁₆	—	2	4	no	—
224	C₂×Q₁₆	C₂×C₄×C₃₁	1	4	yes	complemented
225	C₂×SD₁₆	—	2	8	no	—
226	C₂×SD₁₆	C₂×C₄×C₃₁	1	8	yes	complemented
227	C₂×D₈	C₂×C₄×C₃₁	1	4	yes	—
228	C₂×D₈	D₄×C₃₁	1	8	yes	—
229	C₂²×C₈	—	2	4	no	—
230	C₂²×C₈	C₂×C₄×C₃₁	1	4	yes	complemented
231	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
232	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
233	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
234	C₄×D₄	—	2	8	no	—
235	C₄×D₄	—	4	4	no	—
236	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
237	C₂×C₂²⋊C₄	—	2	4	no	—
238	C₂×C₂²⋊C₄	—	2	2	no	—
239	C₂×C₂²⋊C₄	D₄×C₃₁	1	2	yes	—
240	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
241	#106	—	2	4	no	—
242	#103	—	4	4	no	—
243	#102	—	2	8	no	—
244	C₂²⋊C₈	—	2	2	no	—
245	#97	—	2	4	no	—
246	#95	—	2	2	no	—
247	#95	—	2	4	no	—
248	#95	—	2	4	no	—
249	#95	D₄×C₃₁	1	2	yes	—
250	C₃₁	#22438	1	1	yes	characteristic, direct product factor, Sylow
251	C₂⁴	—	2	2	no	—
252	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
253	#41	—	2	16	no	—
254	#41	—	4	8	no	—
255	#41	—	4	16	no	—
256	C₂×Q₈	—	2	2	no	—
257	C₂×Q₈	—	2	4	no	—
258	C₂×Q₈	—	2	4	no	—
259	C₂×Q₈	C₂²×C₄×C₃₁	1	4	yes	—
260	C₂×D₄	—	2	8	no	—
261	C₂×D₄	—	2	2	no	—
262	C₂×D₄	—	2	4	no	—
263	C₂×D₄	—	4	8	no	—
264	C₂×D₄	C₂²×C₄×C₃₁	1	4	yes	—
265	C₂×D₄	C₂×D₄×C₃₁	1	8	yes	—
266	C₂²×C₄	—	2	2	no	—
267	C₂²×C₄	—	2	2	no	—
268	C₂²×C₄	—	2	2	no	—
269	C₂²×C₄	—	2	8	no	—
270	C₂²×C₄	—	2	4	no	—
271	C₂²×C₄	—	4	8	no	—
272	C₂²×C₄	—	4	8	no	—
273	C₂²×C₄	—	4	8	no	—
274	C₂²×C₄	—	8	4	no	—
275	C₂²×C₄	C₂²×C₄×C₃₁	1	2	yes	—
276	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
277	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
278	C₂²×C₄	#41×C₃₁	1	2	yes	—
279	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
280	Q₁₆	—	2	8	no	—
281	SD₁₆	—	2	16	no	—
282	D₈	C₂²⋊C₄×C₃₁	1	16	yes	complemented
283	C₂×C₈	—	2	2	no	—
284	C₂×C₈	—	2	8	no	—
285	C₂×C₈	—	2	2	no	—
286	C₂×C₈	—	2	2	no	—
287	C₂×C₈	—	2	2	no	—
288	C₂×C₈	C₂²×C₄×C₃₁	1	2	yes	—
289	C₂×C₈	C₂²×C₄×C₃₁	1	2	yes	—
290	C₂×C₈	C₂×D₄×C₃₁	1	4	yes	—
291	C₄⋊C₄	—	2	4	no	—
292	C₄⋊C₄	—	2	4	no	—
293	C₂²⋊C₄	—	4	2	no	—
294	C₂²⋊C₄	—	4	8	no	—
295	C₂²⋊C₄	—	8	2	no	—
296	C₄²	—	2	2	no	—
297	C₄²	—	2	2	no	—
298	C₂³	—	2	4	no	—
299	C₂³	—	2	8	no	—
300	C₂³	—	2	2	no	—
301	C₂³	—	2	2	no	—
302	C₂³	—	2	2	no	—
303	C₂³	—	4	4	no	—
304	C₂³	—	4	2	no	—
305	C₂³	—	4	2	no	—
306	C₂³	C₄×D₄×C₃₁	1	2	yes	—
307	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
308	Q₈	—	2	4	no	—
309	Q₈	—	2	4	no	—
310	Q₈	—	4	4	no	—
311	D₄	—	2	4	no	—
312	D₄	—	2	8	no	—
313	D₄	—	4	16	no	—
314	D₄	C₂×C₂²⋊C₄×C₃₁	1	8	yes	—
315	C₂×C₄	—	2	2	no	—
316	C₂×C₄	—	2	2	no	—
317	C₂×C₄	—	2	2	no	—
318	C₂×C₄	—	2	4	no	—
319	C₂×C₄	—	2	4	no	—
320	C₂×C₄	—	2	4	no	—
321	C₂×C₄	—	2	4	no	—
322	C₂×C₄	—	2	4	no	—
323	C₂×C₄	—	4	16	no	—
324	C₂×C₄	—	4	4	no	—
325	C₂×C₄	—	4	4	no	—
326	C₂×C₄	—	4	4	no	—
327	C₂×C₄	—	4	4	no	—
328	C₂×C₄	—	8	16	no	—
329	C₂×C₄	C₄×D₄×C₃₁	1	2	yes	—
330	C₂×C₄	C₂³×C₄×C₃₁	1	1	yes	characteristic
331	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
332	C₂×C₄	C₂×#41×C₃₁	1	1	yes	characteristic
333	C₂×C₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
334	C₈	—	2	2	no	—
335	C₈	—	4	2	no	—
336	C₈	C₂×C₂²⋊C₄×C₃₁	1	4	yes	—
337	C₂²	—	2	2	no	—
338	C₂²	—	2	8	no	—
339	C₂²	—	2	2	no	—
340	C₂²	—	2	2	no	—
341	C₂²	—	4	4	no	—
342	C₂²	—	4	4	no	—
343	C₂²	—	4	8	no	—
344	C₂²	—	4	4	no	—
345	C₂²	—	4	8	no	—
346	C₂²	C₂×C₄×D₄×C₃₁	1	1	yes	characteristic
347	C₂²	D₄²×C₃₁	1	2	yes	—
348	C₂²	C₃₁×#575	1	2	yes	—
349	C₂²	C₃₁×#577	1	2	yes	—
350	C₄	—	2	2	no	—
351	C₄	—	4	4	no	—
352	C₄	—	4	4	no	—
353	C₄	—	8	4	no	—
354	C₄	C₂²×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
355	C₄	C₃₁×#518	1	1	yes	characteristic
356	C₄	C₃₁×#546	1	2	yes	—
357	C₂	—	4	2	no	—
358	C₂	—	4	8	no	—
359	C₂	D₄×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
360	C₂	C₃₁×#2943	1	1	yes	characteristic
361	C₂	C₃₁×#2952	1	1	yes	characteristic
362	C₂	C₃₁×#3267	1	4	yes	—

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

Complements

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

N	H ≅ G/N	type
2. C₂×C₃₁×#442	C₂	semidirect
3. C₃₁×#2339	C₂	semidirect
4. C₃₁×#1971	C₂	semidirect
5. C₃₁×#1877	C₂	semidirect
6. C₃₁×#1807	C₂	semidirect
7. C₃₁×#1788	C₂	semidirect
8. C₃₁×#1752	C₂	semidirect
11. C₂×C₃₁×#135	C₄	semidirect
34. C₂×#41×C₃₁	C₂×C₄	semidirect
43. C₂×Q₁₆×C₃₁	C₂×C₄	semidirect
45. C₂×SD₁₆×C₃₁	C₂×C₄	semidirect
49. C₂²×C₈×C₃₁	C₂×C₄	semidirect
100. D₈×C₃₁	C₂²⋊C₄	semidirect
116. #22438	C₃₁	direct (N × H)
157. C₂×#442	C₂×C₃₁	semidirect
158. #2339	C₂×C₃₁	semidirect
159. #1971	C₂×C₃₁	semidirect
160. #1877	C₂×C₃₁	semidirect
161. #1807	C₂×C₃₁	semidirect
162. #1788	C₂×C₃₁	semidirect
163. #1752	C₂×C₃₁	semidirect
186. C₂×#135	C₄×C₃₁	semidirect
215. C₂×#41	C₂×C₄×C₃₁	semidirect
224. C₂×Q₁₆	C₂×C₄×C₃₁	semidirect
226. C₂×SD₁₆	C₂×C₄×C₃₁	semidirect
230. C₂²×C₈	C₂×C₄×C₃₁	semidirect
250. C₃₁	#22438	direct (N × H)
282. D₈	C₂²⋊C₄×C₃₁	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₃₁×#135	2
C₂×C₃₁×#442	2
C₃₁×#2339	2
C₃₁×#1971	2
C₃₁×#1877	2
C₃₁×#1807	2
C₃₁×#1788	2
C₃₁×#1752	2
#22438	31

Subgroups — C31×#22438 #21479197

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#22438 #21479197