Subgroups — C₃₁×#29199 #21485958

Order 7936.

706 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#2647	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#2326	C₂	1	1	yes	maximal, characteristic
3	C₃₁×#2066	C₂	1	2	yes	maximal, complemented
4	C₃₁×#2065	C₂	1	2	yes	maximal
5	C₃₁×#1959	C₂	1	1	yes	maximal, characteristic
6	C₃₁×#1958	C₂	1	1	yes	maximal, characteristic
7	C₃₁×#1865	C₂	1	2	yes	maximal, complemented
8	C₃₁×#1864	C₂	1	2	yes	maximal
9	C₃₁×#1844	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#1836	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#1768	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₃₁×#124	C₂²	1	1	yes	characteristic
13	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
14	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
15	C₂×C₃₁×#106	C₂²	1	2	yes	—
16	C₂×C₃₁×#106	C₂²	1	2	yes	—
17	C₂×C₃₁×C₄⋊C₈	C₂²	1	2	yes	—
18	C₂×C₃₁×#103	C₂²	1	2	yes	—
19	C₂×C₃₁×#103	C₂²	1	2	yes	—
20	C₂×C₃₁×#102	C₂²	1	2	yes	—
21	C₂×C₃₁×#102	C₂²	1	2	yes	—
22	C₂×C₃₁×#97	C₂²	1	1	yes	characteristic
23	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
24	C₃₁×#400	—	2	2	no	—
25	C₃₁×#398	—	2	2	no	—
26	C₃₁×#391	C₂²	1	1	yes	characteristic
27	C₃₁×#390	C₂²	1	1	yes	characteristic
28	C₃₁×#389	C₂²	1	2	yes	—
29	C₃₁×#389	C₂²	1	2	yes	—
30	C₃₁×#388	—	2	2	no	—
31	C₃₁×#385	—	2	2	no	—
32	C₃₁×#384	C₂²	1	1	yes	characteristic
33	C₃₁×#384	C₂²	1	1	yes	characteristic
34	C₃₁×#382	C₂²	1	1	yes	characteristic
35	C₃₁×#376	C₂²	1	1	yes	characteristic
36	C₃₁×#340	C₂²	1	2	yes	—
37	C₃₁×#340	C₂²	1	2	yes	—
38	C₃₁×#336	C₂²	1	2	yes	—
39	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
40	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
41	C₂³×C₄×C₃₁	—	2	1	no	—
42	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
43	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
44	C₃₁×#124	—	2	2	no	—
45	C₃₁×#124	Q₈	1	4	yes	—
46	C₄×Q₈×C₃₁	—	4	2	no	—
47	C₄×D₄×C₃₁	—	4	2	no	—
48	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
49	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
50	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
51	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
52	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
53	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
54	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
55	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
56	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
57	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
58	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
59	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
60	C₂×C₄²×C₃₁	—	2	1	no	—
61	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
62	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
63	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
64	C₃₁×#106	—	4	2	no	—
65	C₃₁×#106	—	4	2	no	—
66	C₃₁×C₄⋊C₈	—	2	4	no	—
67	C₃₁×#103	—	2	4	no	—
68	C₃₁×#103	—	4	2	no	—
69	C₃₁×#102	—	2	4	no	—
70	C₃₁×#102	—	4	2	no	—
71	C₃₁×#97	—	2	2	no	—
72	C₄×C₈×C₃₁	—	2	2	no	—
73	C₃₁×#95	—	2	2	no	—
74	C₃₁×#95	—	2	2	no	—
75	C₃₁×#95	—	2	2	no	—
76	C₃₁×#95	—	2	2	no	—
77	C₃₁×#95	D₄	1	2	yes	—
78	C₃₁×#95	D₄	1	2	yes	—
79	C₂⁴×C₃₁	—	2	1	no	—
80	C₂×Q₈×C₃₁	—	2	1	no	—
81	C₂×Q₈×C₃₁	—	2	2	no	—
82	C₂×Q₈×C₃₁	—	2	2	no	—
83	C₂×Q₈×C₃₁	C₂×Q₈	1	2	yes	—
84	C₂×D₄×C₃₁	—	2	2	no	—
85	C₂×D₄×C₃₁	—	2	1	no	—
86	C₂×D₄×C₃₁	—	2	2	no	—
87	C₂×D₄×C₃₁	C₂×Q₈	1	2	yes	—
88	C₂²×C₄×C₃₁	—	2	1	no	—
89	C₂²×C₄×C₃₁	—	2	2	no	—
90	C₂²×C₄×C₃₁	—	2	1	no	—
91	C₂²×C₄×C₃₁	—	2	2	no	—
92	C₂²×C₄×C₃₁	—	2	1	no	—
93	C₂²×C₄×C₃₁	—	4	2	no	—
94	C₂²×C₄×C₃₁	—	8	2	no	—
95	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
96	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
97	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
99	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
100	C₂×C₈×C₃₁	—	2	2	no	—
101	C₂×C₈×C₃₁	—	2	2	no	—
102	C₂×C₈×C₃₁	—	2	2	no	—
103	C₂×C₈×C₃₁	—	2	2	no	—
104	C₂×C₈×C₃₁	—	2	2	no	—
105	C₂×C₈×C₃₁	#41	1	4	yes	—
106	C₄⋊C₄×C₃₁	—	2	2	no	—
107	C₄⋊C₄×C₃₁	—	2	2	no	—
108	C₄⋊C₄×C₃₁	—	2	2	no	—
109	C₄⋊C₄×C₃₁	—	2	2	no	—
110	C₄⋊C₄×C₃₁	—	2	2	no	—
111	C₄⋊C₄×C₃₁	—	2	2	no	—
112	C₄⋊C₄×C₃₁	—	4	2	no	—
113	C₄⋊C₄×C₃₁	—	8	2	no	—
114	C₄⋊C₄×C₃₁	—	8	2	no	—
115	C₄⋊C₄×C₃₁	—	8	2	no	—
116	C₄⋊C₄×C₃₁	—	8	2	no	—
117	C₂²⋊C₄×C₃₁	—	2	8	no	—
118	C₂²⋊C₄×C₃₁	—	4	2	no	—
119	C₂²⋊C₄×C₃₁	—	8	2	no	—
120	C₄²×C₃₁	—	2	2	no	—
121	C₄²×C₃₁	—	2	2	no	—
122	C₄²×C₃₁	—	4	2	no	—
123	C₄²×C₃₁	C₂×Q₈	1	2	yes	—
124	C₄²×C₃₁	#41	1	2	yes	—
125	#29199	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
126	C₂³×C₃₁	—	2	2	no	—
127	C₂³×C₃₁	—	4	1	no	—
128	C₂³×C₃₁	—	4	1	no	—
129	C₂³×C₃₁	—	4	2	no	—
130	C₂³×C₃₁	—	4	2	no	—
131	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
132	Q₈×C₃₁	—	2	4	no	—
133	Q₈×C₃₁	—	4	2	no	—
134	D₄×C₃₁	—	2	4	no	—
135	D₄×C₃₁	—	4	2	no	—
136	C₂×C₄×C₃₁	—	2	2	no	—
137	C₂×C₄×C₃₁	—	2	2	no	—
138	C₂×C₄×C₃₁	—	2	2	no	—
139	C₂×C₄×C₃₁	—	2	2	no	—
140	C₂×C₄×C₃₁	—	2	1	no	—
141	C₂×C₄×C₃₁	—	2	1	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	—	4	1	no	—
147	C₂×C₄×C₃₁	—	4	1	no	—
148	C₂×C₄×C₃₁	—	4	2	no	—
149	C₂×C₄×C₃₁	—	4	1	no	—
150	C₂×C₄×C₃₁	—	4	1	no	—
151	C₂×C₄×C₃₁	—	4	2	no	—
152	C₂×C₄×C₃₁	—	4	2	no	—
153	C₂×C₄×C₃₁	—	4	2	no	—
154	C₂×C₄×C₃₁	—	4	2	no	—
155	C₂×C₄×C₃₁	—	4	2	no	—
156	C₂×C₄×C₃₁	—	4	2	no	—
157	C₂×C₄×C₃₁	—	4	2	no	—
158	C₂×C₄×C₃₁	—	8	4	no	—
159	C₂×C₄×C₃₁	C₂²⋊Q₈	1	4	yes	—
160	C₂×C₄×C₃₁	C₂²×Q₈	1	1	yes	characteristic
161	C₂×C₄×C₃₁	C₂×#41	1	1	yes	characteristic
162	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
163	C₂×C₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
164	C₈×C₃₁	—	2	4	no	—
165	C₈×C₃₁	—	4	2	no	—
166	#2647	C₂×C₃₁	1	1	yes	characteristic, complemented
167	#2326	C₂×C₃₁	1	1	yes	characteristic
168	#2066	C₂×C₃₁	1	2	yes	complemented
169	#2065	C₂×C₃₁	1	2	yes	—
170	#1959	C₂×C₃₁	1	1	yes	characteristic
171	#1958	C₂×C₃₁	1	1	yes	characteristic
172	#1865	C₂×C₃₁	1	2	yes	complemented
173	#1864	C₂×C₃₁	1	2	yes	—
174	#1844	C₂×C₃₁	1	1	yes	characteristic, complemented
175	#1836	C₂×C₃₁	1	1	yes	characteristic, complemented
176	#1768	C₂×C₃₁	1	1	yes	characteristic, complemented
177	C₂²×C₃₁	—	4	2	no	—
178	C₂²×C₃₁	—	4	4	no	—
179	C₂²×C₃₁	—	8	2	no	—
180	C₂²×C₃₁	—	8	1	no	—
181	C₂²×C₃₁	—	8	1	no	—
182	C₂²×C₃₁	C₂×C₂²⋊Q₈	1	1	yes	characteristic
183	C₂²×C₃₁	#532	1	1	yes	characteristic
184	C₂²×C₃₁	#535	1	1	yes	characteristic
185	C₂²×C₃₁	#577	1	2	yes	—
186	C₂²×C₃₁	#577	1	2	yes	—
187	C₄×C₃₁	—	2	4	no	—
188	C₄×C₃₁	—	4	2	no	—
189	C₄×C₃₁	—	4	2	no	—
190	C₄×C₃₁	—	4	1	no	—
191	C₄×C₃₁	—	4	1	no	—
192	C₄×C₃₁	—	8	2	no	—
193	C₄×C₃₁	—	8	2	no	—
194	C₄×C₃₁	—	8	1	no	—
195	C₄×C₃₁	—	8	1	no	—
196	C₄×C₃₁	#553	1	2	yes	—
197	C₄×C₃₁	#554	1	2	yes	—
198	C₂×#124	C₂²×C₃₁	1	1	yes	characteristic
199	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
200	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
201	C₂×#106	C₂²×C₃₁	1	2	yes	—
202	C₂×#106	C₂²×C₃₁	1	2	yes	—
203	C₂×C₄⋊C₈	C₂²×C₃₁	1	2	yes	—
204	C₂×#103	C₂²×C₃₁	1	2	yes	—
205	C₂×#103	C₂²×C₃₁	1	2	yes	—
206	C₂×#102	C₂²×C₃₁	1	2	yes	—
207	C₂×#102	C₂²×C₃₁	1	2	yes	—
208	C₂×#97	C₂²×C₃₁	1	1	yes	characteristic
209	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
210	#400	—	2	2	no	—
211	#398	—	2	2	no	—
212	#391	C₂²×C₃₁	1	1	yes	characteristic
213	#390	C₂²×C₃₁	1	1	yes	characteristic
214	#389	C₂²×C₃₁	1	2	yes	—
215	#389	C₂²×C₃₁	1	2	yes	—
216	#388	—	2	2	no	—
217	#385	—	2	2	no	—
218	#384	C₂²×C₃₁	1	1	yes	characteristic
219	#384	C₂²×C₃₁	1	1	yes	characteristic
220	#382	C₂²×C₃₁	1	1	yes	characteristic
221	#376	C₂²×C₃₁	1	1	yes	characteristic
222	#340	C₂²×C₃₁	1	2	yes	—
223	#340	C₂²×C₃₁	1	2	yes	—
224	#336	C₂²×C₃₁	1	2	yes	—
225	C₂×C₃₁	—	8	2	no	—
226	C₂×C₃₁	#2566	1	1	yes	characteristic
227	C₂×C₃₁	#3084	1	2	yes	—
228	C₂×C₃₁	#3173	1	2	yes	—
229	C₂×C₃₁	#3221	1	1	yes	characteristic
230	C₂×C₃₁	#3222	1	1	yes	characteristic
231	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
232	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
233	C₂³×C₄	—	2	1	no	—
234	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
235	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
236	#124	—	2	2	no	—
237	#124	Q₈×C₃₁	1	4	yes	—
238	C₄×Q₈	—	4	2	no	—
239	C₄×D₄	—	4	2	no	—
240	C₂×C₄⋊C₄	—	2	1	no	—
241	C₂×C₄⋊C₄	—	2	2	no	—
242	C₂×C₄⋊C₄	—	2	2	no	—
243	C₂×C₄⋊C₄	—	2	2	no	—
244	C₂×C₄⋊C₄	—	2	2	no	—
245	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
246	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
247	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
248	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
249	C₂×C₂²⋊C₄	—	2	2	no	—
250	C₂×C₂²⋊C₄	—	2	1	no	—
251	C₂×C₂²⋊C₄	—	2	2	no	—
252	C₂×C₄²	—	2	1	no	—
253	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
254	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
255	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
256	#106	—	4	2	no	—
257	#106	—	4	2	no	—
258	C₄⋊C₈	—	2	4	no	—
259	#103	—	2	4	no	—
260	#103	—	4	2	no	—
261	#102	—	2	4	no	—
262	#102	—	4	2	no	—
263	#97	—	2	2	no	—
264	C₄×C₈	—	2	2	no	—
265	#95	—	2	2	no	—
266	#95	—	2	2	no	—
267	#95	—	2	2	no	—
268	#95	—	2	2	no	—
269	#95	D₄×C₃₁	1	2	yes	—
270	#95	D₄×C₃₁	1	2	yes	—
271	C₃₁	#29199	1	1	yes	characteristic, direct product factor, Sylow
272	C₂⁴	—	2	1	no	—
273	C₂×Q₈	—	2	1	no	—
274	C₂×Q₈	—	2	2	no	—
275	C₂×Q₈	—	2	2	no	—
276	C₂×Q₈	C₂×Q₈×C₃₁	1	2	yes	—
277	C₂×D₄	—	2	2	no	—
278	C₂×D₄	—	2	1	no	—
279	C₂×D₄	—	2	2	no	—
280	C₂×D₄	C₂×Q₈×C₃₁	1	2	yes	—
281	C₂²×C₄	—	2	1	no	—
282	C₂²×C₄	—	2	2	no	—
283	C₂²×C₄	—	2	1	no	—
284	C₂²×C₄	—	2	2	no	—
285	C₂²×C₄	—	2	1	no	—
286	C₂²×C₄	—	4	2	no	—
287	C₂²×C₄	—	8	2	no	—
288	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
289	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
290	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
291	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
292	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
293	C₂×C₈	—	2	2	no	—
294	C₂×C₈	—	2	2	no	—
295	C₂×C₈	—	2	2	no	—
296	C₂×C₈	—	2	2	no	—
297	C₂×C₈	—	2	2	no	—
298	C₂×C₈	#41×C₃₁	1	4	yes	—
299	C₄⋊C₄	—	2	2	no	—
300	C₄⋊C₄	—	2	2	no	—
301	C₄⋊C₄	—	2	2	no	—
302	C₄⋊C₄	—	2	2	no	—
303	C₄⋊C₄	—	2	2	no	—
304	C₄⋊C₄	—	2	2	no	—
305	C₄⋊C₄	—	4	2	no	—
306	C₄⋊C₄	—	8	2	no	—
307	C₄⋊C₄	—	8	2	no	—
308	C₄⋊C₄	—	8	2	no	—
309	C₄⋊C₄	—	8	2	no	—
310	C₂²⋊C₄	—	2	8	no	—
311	C₂²⋊C₄	—	4	2	no	—
312	C₂²⋊C₄	—	8	2	no	—
313	C₄²	—	2	2	no	—
314	C₄²	—	2	2	no	—
315	C₄²	—	4	2	no	—
316	C₄²	C₂×Q₈×C₃₁	1	2	yes	—
317	C₄²	#41×C₃₁	1	2	yes	—
318	C₂³	—	2	2	no	—
319	C₂³	—	4	1	no	—
320	C₂³	—	4	1	no	—
321	C₂³	—	4	2	no	—
322	C₂³	—	4	2	no	—
323	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
324	Q₈	—	2	4	no	—
325	Q₈	—	4	2	no	—
326	D₄	—	2	4	no	—
327	D₄	—	4	2	no	—
328	C₂×C₄	—	2	2	no	—
329	C₂×C₄	—	2	2	no	—
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	2	1	no	—
333	C₂×C₄	—	2	1	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	4	1	no	—
339	C₂×C₄	—	4	1	no	—
340	C₂×C₄	—	4	2	no	—
341	C₂×C₄	—	4	1	no	—
342	C₂×C₄	—	4	1	no	—
343	C₂×C₄	—	4	2	no	—
344	C₂×C₄	—	4	2	no	—
345	C₂×C₄	—	4	2	no	—
346	C₂×C₄	—	4	2	no	—
347	C₂×C₄	—	4	2	no	—
348	C₂×C₄	—	4	2	no	—
349	C₂×C₄	—	4	2	no	—
350	C₂×C₄	—	8	4	no	—
351	C₂×C₄	C₃₁×C₂²⋊Q₈	1	4	yes	—
352	C₂×C₄	C₂²×Q₈×C₃₁	1	1	yes	characteristic
353	C₂×C₄	C₂×#41×C₃₁	1	1	yes	characteristic
354	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
355	C₂×C₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
356	C₈	—	2	4	no	—
357	C₈	—	4	2	no	—
358	C₂²	—	4	2	no	—
359	C₂²	—	4	4	no	—
360	C₂²	—	8	2	no	—
361	C₂²	—	8	1	no	—
362	C₂²	—	8	1	no	—
363	C₂²	C₂×C₃₁×C₂²⋊Q₈	1	1	yes	characteristic
364	C₂²	C₃₁×#532	1	1	yes	characteristic
365	C₂²	C₃₁×#535	1	1	yes	characteristic
366	C₂²	C₃₁×#577	1	2	yes	—
367	C₂²	C₃₁×#577	1	2	yes	—
368	C₄	—	2	4	no	—
369	C₄	—	4	2	no	—
370	C₄	—	4	2	no	—
371	C₄	—	4	1	no	—
372	C₄	—	4	1	no	—
373	C₄	—	8	2	no	—
374	C₄	—	8	2	no	—
375	C₄	—	8	1	no	—
376	C₄	—	8	1	no	—
377	C₄	C₃₁×#553	1	2	yes	—
378	C₄	C₃₁×#554	1	2	yes	—
379	C₂	—	8	2	no	—
380	C₂	C₃₁×#2566	1	1	yes	characteristic
381	C₂	C₃₁×#3084	1	2	yes	—
382	C₂	C₃₁×#3173	1	2	yes	—
383	C₂	C₃₁×#3221	1	1	yes	characteristic
384	C₂	C₃₁×#3222	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₃₁
prime radical	C₂²×D₄×C₃₁	C₂³
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₃₁ ◁ C₃₁×#376 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#2647	C₂	semidirect
3. C₃₁×#2066	C₂	semidirect
7. C₃₁×#1865	C₂	semidirect
9. C₃₁×#1844	C₂	semidirect
10. C₃₁×#1836	C₂	semidirect
11. C₃₁×#1768	C₂	semidirect
125. #29199	C₃₁	direct (N × H)
166. #2647	C₂×C₃₁	semidirect
168. #2066	C₂×C₃₁	semidirect
172. #1865	C₂×C₃₁	semidirect
174. #1844	C₂×C₃₁	semidirect
175. #1836	C₂×C₃₁	semidirect
176. #1768	C₂×C₃₁	semidirect
271. C₃₁	#29199	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×#2647	2
C₃₁×#2326	2
C₃₁×#2066	2
C₃₁×#2065	2
C₃₁×#1959	2
C₃₁×#1958	2
C₃₁×#1865	2
C₃₁×#1864	2
C₃₁×#1844	2
C₃₁×#1836	2
C₃₁×#1768	2
#29199	31

Subgroups — C31×#29199 #21485958

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#29199 #21485958