Subgroups — C₃₁×#33787 #21490546

Order 7936.

586 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3176	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3156	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#2250	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#2248	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#2245	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#2242	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#2210	C₂	1	2	yes	maximal, complemented
8	C₃₁×#2208	C₂	1	2	yes	maximal, complemented
9	C₃₁×#2186	C₂	1	2	yes	maximal, complemented
10	C₃₁×#2185	C₂	1	2	yes	maximal, complemented
11	C₃₁×#2164	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₃₁×#137	—	2	1	no	—
13	C₂×C₃₁×#135	C₂²	1	1	yes	characteristic
14	C₂²×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
15	C₃₁×#540	—	2	1	no	—
16	C₃₁×#536	—	2	1	no	—
17	C₂×C₃₁×SD₃₂	C₂²	1	2	yes	—
18	C₂×C₃₁×SD₃₂	C₂²	1	2	yes	—
19	C₂×C₃₁×SD₃₂	C₂²	1	2	yes	—
20	C₂×C₃₁×D₁₆	C₂²	1	2	yes	—
21	C₃₁×#499	C₂²	1	1	yes	characteristic
22	C₃₁×#497	—	2	1	no	—
23	C₃₁×#497	—	2	1	no	—
24	C₃₁×#495	C₂²	1	1	yes	characteristic
25	C₃₁×#495	C₂²	1	1	yes	characteristic
26	C₃₁×#494	C₂²	1	1	yes	characteristic
27	C₃₁×#494	C₂²	1	1	yes	characteristic
28	C₃₁×#493	C₂²	1	1	yes	characteristic
29	C₃₁×#490	—	2	1	no	—
30	C₃₁×#469	—	2	1	no	—
31	C₃₁×#466	C₂²	1	2	yes	—
32	C₃₁×#442	—	2	1	no	—
33	C₄×D₈×C₃₁	C₂²	1	2	yes	—
34	C₃₁×#405	C₂²	1	1	yes	characteristic
35	C₃₁×C₄⋊C₁₆	C₂²	1	2	yes	—
36	C₃₁×#358	C₂²	1	2	yes	—
37	C₃₁×#358	C₂²	1	2	yes	—
38	C₃₁×#358	C₂²	1	2	yes	—
39	C₃₁×#357	C₂²	1	2	yes	—
40	C₃₁×C₂²⋊C₁₆	C₂²	1	2	yes	—
41	C₃₁×#346	C₂²	1	1	yes	characteristic
42	C₄×C₁₆×C₃₁	C₂²	1	1	yes	characteristic
43	C₂×#41×C₃₁	—	2	1	no	—
44	C₂²×Q₈×C₃₁	—	2	1	no	—
45	C₃₁×#137	—	4	4	no	—
46	C₃₁×#135	—	4	2	no	—
47	C₂×Q₁₆×C₃₁	—	2	1	no	—
48	C₂×Q₁₆×C₃₁	—	2	1	no	—
49	C₂×Q₁₆×C₃₁	—	2	1	no	—
50	C₂×Q₁₆×C₃₁	—	4	2	no	—
51	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
52	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
53	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
54	C₂×SD₁₆×C₃₁	—	2	1	no	—
55	C₂×SD₁₆×C₃₁	—	2	1	no	—
56	C₂×SD₁₆×C₃₁	—	2	1	no	—
57	C₂×D₈×C₃₁	—	2	1	no	—
58	C₂×D₈×C₃₁	C₂³	1	2	yes	—
59	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
60	C₂×M₁₆×C₃₁	D₄	1	1	yes	characteristic
61	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
62	C₃₁×C₄⋊Q₈	—	2	1	no	—
63	C₃₁×C₄⋊Q₈	—	2	1	no	—
64	C₃₁×#127	—	2	1	no	—
65	C₃₁×#125	—	2	1	no	—
66	C₃₁×#124	—	2	1	no	—
67	C₃₁×#124	—	2	1	no	—
68	C₃₁×#123	—	4	2	no	—
69	C₃₁×#123	—	4	2	no	—
70	C₃₁×C₂²⋊Q₈	—	4	2	no	—
71	C₃₁×#121	—	2	2	no	—
72	C₃₁×#121	—	4	2	no	—
73	C₄×D₄×C₃₁	—	2	2	no	—
74	C₃₁×#117	D₄	1	1	yes	characteristic
75	C₃₁×SD₃₂	—	4	2	no	—
76	C₃₁×SD₃₂	—	4	2	no	—
77	C₃₁×SD₃₂	—	4	2	no	—
78	C₃₁×D₁₆	—	4	2	no	—
79	C₂×C₁₆×C₃₁	C₂³	1	2	yes	—
80	C₂×C₁₆×C₃₁	C₂³	1	2	yes	—
81	C₃₁×#107	C₂³	1	2	yes	—
82	C₃₁×#106	—	2	1	no	—
83	C₃₁×#102	—	2	2	no	—
84	C₃₁×#102	—	2	2	no	—
85	C₃₁×#97	D₄	1	1	yes	characteristic
86	C₃₁×#97	D₄	1	1	yes	characteristic
87	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
88	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
89	#41×C₃₁	—	4	2	no	—
90	#41×C₃₁	—	4	2	no	—
91	C₂×Q₈×C₃₁	—	2	1	no	—
92	C₂×Q₈×C₃₁	—	2	1	no	—
93	C₂×Q₈×C₃₁	—	2	1	no	—
94	C₂×Q₈×C₃₁	—	4	2	no	—
95	C₂×Q₈×C₃₁	—	4	2	no	—
96	C₂×Q₈×C₃₁	—	4	1	no	—
97	C₂×D₄×C₃₁	—	2	2	no	—
98	C₂×D₄×C₃₁	—	2	1	no	—
99	C₂×D₄×C₃₁	—	4	1	no	—
100	C₂×D₄×C₃₁	—	4	2	no	—
101	C₂×D₄×C₃₁	—	4	2	no	—
102	C₂²×C₄×C₃₁	—	4	1	no	—
103	C₂²×C₄×C₃₁	—	4	1	no	—
104	C₂²×C₄×C₃₁	—	4	2	no	—
105	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
106	Q₁₆×C₃₁	—	2	2	no	—
107	Q₁₆×C₃₁	—	2	2	no	—
108	Q₁₆×C₃₁	—	2	2	no	—
109	Q₁₆×C₃₁	—	4	2	no	—
110	Q₁₆×C₃₁	—	4	2	no	—
111	Q₁₆×C₃₁	—	4	2	no	—
112	SD₁₆×C₃₁	—	4	2	no	—
113	SD₁₆×C₃₁	—	4	2	no	—
114	SD₁₆×C₃₁	—	4	2	no	—
115	D₈×C₃₁	—	2	2	no	—
116	D₈×C₃₁	—	2	2	no	—
117	D₈×C₃₁	—	2	2	no	—
118	D₈×C₃₁	—	4	2	no	—
119	M₁₆×C₃₁	—	2	2	no	—
120	C₂×C₈×C₃₁	—	2	2	no	—
121	C₂×C₈×C₃₁	C₂×D₄	1	1	yes	characteristic
122	C₂×C₈×C₃₁	C₂×D₄	1	1	yes	characteristic
123	C₂×C₈×C₃₁	C₂×D₄	1	1	yes	characteristic
124	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
125	C₄⋊C₄×C₃₁	—	2	2	no	—
126	C₄⋊C₄×C₃₁	—	4	2	no	—
127	C₄⋊C₄×C₃₁	—	4	2	no	—
128	C₄⋊C₄×C₃₁	—	4	2	no	—
129	C₄⋊C₄×C₃₁	D₈	1	2	yes	—
130	C₂²⋊C₄×C₃₁	—	4	2	no	—
131	C₂²⋊C₄×C₃₁	—	4	2	no	—
132	C₂²⋊C₄×C₃₁	—	4	2	no	—
133	C₂²⋊C₄×C₃₁	—	4	2	no	—
134	C₂²⋊C₄×C₃₁	D₈	1	2	yes	—
135	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
136	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
137	C₁₆×C₃₁	—	2	2	no	—
138	C₁₆×C₃₁	—	2	2	no	—
139	#33787	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
140	C₂³×C₃₁	—	4	1	no	—
141	C₂³×C₃₁	—	4	2	no	—
142	C₂³×C₃₁	C₂×D₈	1	1	yes	characteristic
143	Q₈×C₃₁	—	4	1	no	—
144	Q₈×C₃₁	—	4	1	no	—
145	Q₈×C₃₁	—	4	1	no	—
146	Q₈×C₃₁	—	4	1	no	—
147	Q₈×C₃₁	—	4	1	no	—
148	Q₈×C₃₁	—	4	1	no	—
149	Q₈×C₃₁	—	8	2	no	—
150	D₄×C₃₁	—	4	1	no	—
151	D₄×C₃₁	—	4	2	no	—
152	D₄×C₃₁	—	4	2	no	—
153	D₄×C₃₁	—	4	1	no	—
154	D₄×C₃₁	—	8	2	no	—
155	D₄×C₃₁	—	16	2	no	—
156	D₄×C₃₁	—	16	2	no	—
157	C₂×C₄×C₃₁	—	2	1	no	—
158	C₂×C₄×C₃₁	—	2	1	no	—
159	C₂×C₄×C₃₁	—	4	2	no	—
160	C₂×C₄×C₃₁	—	4	1	no	—
161	C₂×C₄×C₃₁	—	4	1	no	—
162	C₂×C₄×C₃₁	—	4	1	no	—
163	C₂×C₄×C₃₁	—	8	2	no	—
164	C₂×C₄×C₃₁	—	8	2	no	—
165	C₂×C₄×C₃₁	—	16	2	no	—
166	C₂×C₄×C₃₁	C₂×D₈	1	2	yes	—
167	C₂×C₄×C₃₁	C₂×D₈	1	2	yes	—
168	C₂×C₄×C₃₁	C₂×D₈	1	1	yes	characteristic
169	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
170	C₈×C₃₁	—	2	1	no	—
171	C₈×C₃₁	—	2	1	no	—
172	C₈×C₃₁	AGL(1,ℤ/8)	1	2	yes	—
173	C₈×C₃₁	H(5,𝔽₂)	1	2	yes	—
174	#3176	C₂×C₃₁	1	1	yes	characteristic, complemented
175	#3156	C₂×C₃₁	1	1	yes	characteristic, complemented
176	#2250	C₂×C₃₁	1	1	yes	characteristic, complemented
177	#2248	C₂×C₃₁	1	1	yes	characteristic, complemented
178	#2245	C₂×C₃₁	1	1	yes	characteristic, complemented
179	#2242	C₂×C₃₁	1	1	yes	characteristic, complemented
180	#2210	C₂×C₃₁	1	2	yes	complemented
181	#2208	C₂×C₃₁	1	2	yes	complemented
182	#2186	C₂×C₃₁	1	2	yes	complemented
183	#2185	C₂×C₃₁	1	2	yes	complemented
184	#2164	C₂×C₃₁	1	1	yes	characteristic, complemented
185	C₂²×C₃₁	—	2	2	no	—
186	C₂²×C₃₁	—	2	1	no	—
187	C₂²×C₃₁	—	8	2	no	—
188	C₂²×C₃₁	—	8	2	no	—
189	C₂²×C₃₁	—	8	2	no	—
190	C₂²×C₃₁	—	8	1	no	—
191	C₂²×C₃₁	—	8	2	no	—
192	C₂²×C₃₁	C₂²×D₈	1	1	yes	characteristic
193	C₄×C₃₁	—	2	2	no	—
194	C₄×C₃₁	—	2	2	no	—
195	C₄×C₃₁	—	2	1	no	—
196	C₄×C₃₁	—	8	2	no	—
197	C₄×C₃₁	—	8	1	no	—
198	C₄×C₃₁	—	8	1	no	—
199	C₄×C₃₁	—	8	1	no	—
200	C₄×C₃₁	#535	1	1	yes	characteristic
201	C₄×C₃₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
202	C₂×#137	—	2	1	no	—
203	C₂×#135	C₂²×C₃₁	1	1	yes	characteristic
204	C₂²×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
205	#540	—	2	1	no	—
206	#536	—	2	1	no	—
207	C₂×SD₃₂	C₂²×C₃₁	1	2	yes	—
208	C₂×SD₃₂	C₂²×C₃₁	1	2	yes	—
209	C₂×SD₃₂	C₂²×C₃₁	1	2	yes	—
210	C₂×D₁₆	C₂²×C₃₁	1	2	yes	—
211	#499	C₂²×C₃₁	1	1	yes	characteristic
212	#497	—	2	1	no	—
213	#497	—	2	1	no	—
214	#495	C₂²×C₃₁	1	1	yes	characteristic
215	#495	C₂²×C₃₁	1	1	yes	characteristic
216	#494	C₂²×C₃₁	1	1	yes	characteristic
217	#494	C₂²×C₃₁	1	1	yes	characteristic
218	#493	C₂²×C₃₁	1	1	yes	characteristic
219	#490	—	2	1	no	—
220	#469	—	2	1	no	—
221	#466	C₂²×C₃₁	1	2	yes	—
222	#442	—	2	1	no	—
223	C₄×D₈	C₂²×C₃₁	1	2	yes	—
224	#405	C₂²×C₃₁	1	1	yes	characteristic
225	C₄⋊C₁₆	C₂²×C₃₁	1	2	yes	—
226	#358	C₂²×C₃₁	1	2	yes	—
227	#358	C₂²×C₃₁	1	2	yes	—
228	#358	C₂²×C₃₁	1	2	yes	—
229	#357	C₂²×C₃₁	1	2	yes	—
230	C₂²⋊C₁₆	C₂²×C₃₁	1	2	yes	—
231	#346	C₂²×C₃₁	1	1	yes	characteristic
232	C₄×C₁₆	C₂²×C₃₁	1	1	yes	characteristic
233	C₂×C₃₁	—	4	1	no	—
234	C₂×C₃₁	—	16	2	no	—
235	C₂×C₃₁	—	16	1	no	—
236	C₂×C₃₁	#3205	1	1	yes	characteristic
237	C₂×C₃₁	#3416	1	2	yes	—
238	C₂×#41	—	2	1	no	—
239	C₂²×Q₈	—	2	1	no	—
240	#137	—	4	4	no	—
241	#135	—	4	2	no	—
242	C₂×Q₁₆	—	2	1	no	—
243	C₂×Q₁₆	—	2	1	no	—
244	C₂×Q₁₆	—	2	1	no	—
245	C₂×Q₁₆	—	4	2	no	—
246	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
247	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
248	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
249	C₂×SD₁₆	—	2	1	no	—
250	C₂×SD₁₆	—	2	1	no	—
251	C₂×SD₁₆	—	2	1	no	—
252	C₂×D₈	—	2	1	no	—
253	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
254	C₂×D₈	C₂³×C₃₁	1	2	yes	—
255	C₂×M₁₆	D₄×C₃₁	1	1	yes	characteristic
256	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
257	C₄⋊Q₈	—	2	1	no	—
258	C₄⋊Q₈	—	2	1	no	—
259	#127	—	2	1	no	—
260	#125	—	2	1	no	—
261	#124	—	2	1	no	—
262	#124	—	2	1	no	—
263	#123	—	4	2	no	—
264	#123	—	4	2	no	—
265	C₂²⋊Q₈	—	4	2	no	—
266	#121	—	2	2	no	—
267	#121	—	4	2	no	—
268	C₄×D₄	—	2	2	no	—
269	#117	D₄×C₃₁	1	1	yes	characteristic
270	SD₃₂	—	4	2	no	—
271	SD₃₂	—	4	2	no	—
272	SD₃₂	—	4	2	no	—
273	D₁₆	—	4	2	no	—
274	C₂×C₁₆	C₂³×C₃₁	1	2	yes	—
275	C₂×C₁₆	C₂³×C₃₁	1	2	yes	—
276	#107	C₂³×C₃₁	1	2	yes	—
277	#106	—	2	1	no	—
278	#102	—	2	2	no	—
279	#102	—	2	2	no	—
280	#97	D₄×C₃₁	1	1	yes	characteristic
281	#97	D₄×C₃₁	1	1	yes	characteristic
282	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
283	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
284	C₃₁	#33787	1	1	yes	characteristic, direct product factor, Sylow
285	#41	—	4	2	no	—
286	#41	—	4	2	no	—
287	C₂×Q₈	—	2	1	no	—
288	C₂×Q₈	—	2	1	no	—
289	C₂×Q₈	—	2	1	no	—
290	C₂×Q₈	—	4	2	no	—
291	C₂×Q₈	—	4	2	no	—
292	C₂×Q₈	—	4	1	no	—
293	C₂×D₄	—	2	2	no	—
294	C₂×D₄	—	2	1	no	—
295	C₂×D₄	—	4	1	no	—
296	C₂×D₄	—	4	2	no	—
297	C₂×D₄	—	4	2	no	—
298	C₂²×C₄	—	4	1	no	—
299	C₂²×C₄	—	4	1	no	—
300	C₂²×C₄	—	4	2	no	—
301	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
302	Q₁₆	—	2	2	no	—
303	Q₁₆	—	2	2	no	—
304	Q₁₆	—	2	2	no	—
305	Q₁₆	—	4	2	no	—
306	Q₁₆	—	4	2	no	—
307	Q₁₆	—	4	2	no	—
308	SD₁₆	—	4	2	no	—
309	SD₁₆	—	4	2	no	—
310	SD₁₆	—	4	2	no	—
311	D₈	—	2	2	no	—
312	D₈	—	2	2	no	—
313	D₈	—	2	2	no	—
314	D₈	—	4	2	no	—
315	M₁₆	—	2	2	no	—
316	C₂×C₈	—	2	2	no	—
317	C₂×C₈	C₂×D₄×C₃₁	1	1	yes	characteristic
318	C₂×C₈	C₂×D₄×C₃₁	1	1	yes	characteristic
319	C₂×C₈	C₂×D₄×C₃₁	1	1	yes	characteristic
320	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
321	C₄⋊C₄	—	2	2	no	—
322	C₄⋊C₄	—	4	2	no	—
323	C₄⋊C₄	—	4	2	no	—
324	C₄⋊C₄	—	4	2	no	—
325	C₄⋊C₄	D₈×C₃₁	1	2	yes	—
326	C₂²⋊C₄	—	4	2	no	—
327	C₂²⋊C₄	—	4	2	no	—
328	C₂²⋊C₄	—	4	2	no	—
329	C₂²⋊C₄	—	4	2	no	—
330	C₂²⋊C₄	D₈×C₃₁	1	2	yes	—
331	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
332	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
333	C₁₆	—	2	2	no	—
334	C₁₆	—	2	2	no	—
335	C₂³	—	4	1	no	—
336	C₂³	—	4	2	no	—
337	C₂³	C₂×D₈×C₃₁	1	1	yes	characteristic
338	Q₈	—	4	1	no	—
339	Q₈	—	4	1	no	—
340	Q₈	—	4	1	no	—
341	Q₈	—	4	1	no	—
342	Q₈	—	4	1	no	—
343	Q₈	—	4	1	no	—
344	Q₈	—	8	2	no	—
345	D₄	—	4	1	no	—
346	D₄	—	4	2	no	—
347	D₄	—	4	2	no	—
348	D₄	—	4	1	no	—
349	D₄	—	8	2	no	—
350	D₄	—	16	2	no	—
351	D₄	—	16	2	no	—
352	C₂×C₄	—	2	1	no	—
353	C₂×C₄	—	2	1	no	—
354	C₂×C₄	—	4	2	no	—
355	C₂×C₄	—	4	1	no	—
356	C₂×C₄	—	4	1	no	—
357	C₂×C₄	—	4	1	no	—
358	C₂×C₄	—	8	2	no	—
359	C₂×C₄	—	8	2	no	—
360	C₂×C₄	—	16	2	no	—
361	C₂×C₄	C₂×D₈×C₃₁	1	2	yes	—
362	C₂×C₄	C₂×D₈×C₃₁	1	2	yes	—
363	C₂×C₄	C₂×D₈×C₃₁	1	1	yes	characteristic
364	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
365	C₈	—	2	1	no	—
366	C₈	—	2	1	no	—
367	C₈	C₃₁×AGL(1,ℤ/8)	1	2	yes	—
368	C₈	C₃₁×H(5,𝔽₂)	1	2	yes	—
369	C₂²	—	2	2	no	—
370	C₂²	—	2	1	no	—
371	C₂²	—	8	2	no	—
372	C₂²	—	8	2	no	—
373	C₂²	—	8	2	no	—
374	C₂²	—	8	1	no	—
375	C₂²	—	8	2	no	—
376	C₂²	C₂²×D₈×C₃₁	1	1	yes	characteristic
377	C₄	—	2	2	no	—
378	C₄	—	2	2	no	—
379	C₄	—	2	1	no	—
380	C₄	—	8	2	no	—
381	C₄	—	8	1	no	—
382	C₄	—	8	1	no	—
383	C₄	—	8	1	no	—
384	C₄	C₃₁×#535	1	1	yes	characteristic
385	C₄	C₂×C₃₁×AGL(1,ℤ/8)	1	1	yes	characteristic
386	C₂	—	4	1	no	—
387	C₂	—	16	2	no	—
388	C₂	—	16	1	no	—
389	C₂	C₃₁×#3205	1	1	yes	characteristic
390	C₂	C₃₁×#3416	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₃₁
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₃₁×#117 ◁ C₃₁×#405 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3176	C₂	semidirect
2. C₃₁×#3156	C₂	semidirect
3. C₃₁×#2250	C₂	semidirect
4. C₃₁×#2248	C₂	semidirect
5. C₃₁×#2245	C₂	semidirect
6. C₃₁×#2242	C₂	semidirect
7. C₃₁×#2210	C₂	semidirect
8. C₃₁×#2208	C₂	semidirect
9. C₃₁×#2186	C₂	semidirect
10. C₃₁×#2185	C₂	semidirect
11. C₃₁×#2164	C₂	semidirect
139. #33787	C₃₁	direct (N × H)
174. #3176	C₂×C₃₁	semidirect
175. #3156	C₂×C₃₁	semidirect
176. #2250	C₂×C₃₁	semidirect
177. #2248	C₂×C₃₁	semidirect
178. #2245	C₂×C₃₁	semidirect
179. #2242	C₂×C₃₁	semidirect
180. #2210	C₂×C₃₁	semidirect
181. #2208	C₂×C₃₁	semidirect
182. #2186	C₂×C₃₁	semidirect
183. #2185	C₂×C₃₁	semidirect
184. #2164	C₂×C₃₁	semidirect
284. C₃₁	#33787	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×#3176	2
C₃₁×#3156	2
C₃₁×#2250	2
C₃₁×#2248	2
C₃₁×#2245	2
C₃₁×#2242	2
C₃₁×#2210	2
C₃₁×#2208	2
C₃₁×#2186	2
C₃₁×#2185	2
C₃₁×#2164	2
#33787	31

Subgroups — C31×#33787 #21490546

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#33787 #21490546