Subgroups — C₃₁×#19983 #21476742

Order 7936.

622 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×#3383	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3359	C₂	1	2	yes	maximal
3	D₄×Q₁₆×C₃₁	C₂	1	1	yes	maximal, characteristic
4	C₃₁×#1707	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#1680	C₂	1	2	yes	maximal, complemented
6	C₃₁×#1673	C₂	1	1	yes	maximal, characteristic
7	C₃₁×#1670	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#1653	C₂	1	2	yes	maximal, complemented
9	C₃₁×#1651	C₂	1	2	yes	maximal
10	C₈×Q₁₆×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×SD₁₆×C₃₁	C₂	1	1	yes	maximal, characteristic
12	C₂²×Q₁₆×C₃₁	—	2	1	no	—
13	C₃₁×#557	C₂²	1	2	yes	—
14	D₄×Q₈×C₃₁	C₂²	1	2	yes	—
15	C₃₁×#500	C₂²	1	1	yes	characteristic
16	C₃₁×#499	—	2	1	no	—
17	C₃₁×#498	C₂²	1	2	yes	—
18	C₃₁×#494	C₂²	1	1	yes	characteristic
19	C₃₁×#487	—	2	2	no	—
20	C₃₁×#487	C₂²	1	2	yes	—
21	C₃₁×#479	—	2	2	no	—
22	C₃₁×#475	—	2	2	no	—
23	C₃₁×#475	C₂²	1	2	yes	—
24	C₃₁×#475	C₂²	1	2	yes	—
25	C₃₁×#467	—	2	1	no	—
26	C₃₁×#462	C₂²	1	2	yes	—
27	C₃₁×#461	—	2	2	no	—
28	C₃₁×#461	C₂²	1	2	yes	—
29	C₃₁×#451	—	2	2	no	—
30	C₈×Q₈×C₃₁	C₂²	1	2	yes	—
31	C₈×Q₈×C₃₁	C₂²	1	1	yes	characteristic
32	C₄×Q₁₆×C₃₁	—	2	1	no	—
33	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
34	C₄×SD₁₆×C₃₁	—	2	2	no	—
35	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
36	C₈×D₄×C₃₁	C₂²	1	1	yes	characteristic
37	C₃₁×#335	C₂²	1	1	yes	characteristic
38	C₃₁×#334	C₂²	1	1	yes	characteristic
39	C₃₁×#332	C₂²	1	2	yes	—
40	C₃₁×#332	C₂²	1	2	yes	—
41	C₃₁×Q₈⋊C₈	C₂²	1	1	yes	characteristic
42	C₃₁×Q₈⋊C₈	C₂²	1	2	yes	—
43	C₃₁×D₄⋊C₈	C₂²	1	1	yes	characteristic
44	C₈²×C₃₁	C₂²	1	1	yes	characteristic
45	C₂²×Q₈×C₃₁	—	2	2	no	—
46	C₂×Q₁₆×C₃₁	—	2	2	no	—
47	C₂×Q₁₆×C₃₁	—	2	1	no	—
48	C₂×Q₁₆×C₃₁	—	2	1	no	—
49	C₂×Q₁₆×C₃₁	—	4	4	no	—
50	C₂×Q₁₆×C₃₁	D₄	1	1	yes	characteristic
51	C₂×SD₁₆×C₃₁	—	2	2	no	—
52	C₂×SD₁₆×C₃₁	D₄	1	1	yes	characteristic
53	C₂²×C₈×C₃₁	—	2	1	no	—
54	C₃₁×C₄⋊Q₈	—	2	2	no	—
55	C₃₁×C₄⋊Q₈	—	2	2	no	—
56	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
57	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
58	C₃₁×#125	—	2	2	no	—
59	C₃₁×#125	—	4	2	no	—
60	C₃₁×C₂²⋊Q₈	—	2	2	no	—
61	C₃₁×C₂²⋊Q₈	—	4	2	no	—
62	C₄×Q₈×C₃₁	—	2	2	no	—
63	C₄×Q₈×C₃₁	—	2	2	no	—
64	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
65	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
66	C₄×D₄×C₃₁	—	2	2	no	—
67	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
68	C₃₁×#107	—	2	1	no	—
69	C₃₁×#107	—	2	1	no	—
70	C₃₁×#107	D₄	1	1	yes	characteristic
71	C₃₁×#106	—	2	2	no	—
72	C₃₁×#106	—	2	2	no	—
73	C₃₁×#106	—	4	2	no	—
74	C₃₁×#106	D₄	1	1	yes	characteristic
75	C₃₁×C₄⋊C₈	—	2	2	no	—
76	C₃₁×C₄⋊C₈	—	2	1	no	—
77	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
78	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
79	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
80	C₃₁×#103	—	2	2	no	—
81	C₃₁×#103	—	2	2	no	—
82	C₃₁×#103	—	2	2	no	—
83	C₃₁×#103	—	2	2	no	—
84	C₃₁×#103	—	2	2	no	—
85	C₃₁×#103	—	2	2	no	—
86	C₃₁×#103	D₄	1	1	yes	characteristic
87	C₃₁×#103	D₄	1	2	yes	—
88	C₃₁×#102	D₄	1	1	yes	characteristic
89	C₃₁×C₂²⋊C₈	—	2	1	no	—
90	C₄×C₈×C₃₁	—	2	2	no	—
91	C₄×C₈×C₃₁	—	2	1	no	—
92	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
93	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
94	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
95	C₂×Q₈×C₃₁	—	2	2	no	—
96	C₂×Q₈×C₃₁	—	2	2	no	—
97	C₂×Q₈×C₃₁	—	4	2	no	—
98	C₂×Q₈×C₃₁	—	4	4	no	—
99	C₂×Q₈×C₃₁	—	8	2	no	—
100	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
101	C₂×Q₈×C₃₁	C₂×D₄	1	2	yes	—
102	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₃₁	—	2	1	no	—
104	C₂²×C₄×C₃₁	—	4	2	no	—
105	Q₁₆×C₃₁	—	4	4	no	—
106	Q₁₆×C₃₁	—	4	2	no	—
107	Q₁₆×C₃₁	—	8	1	no	—
108	Q₁₆×C₃₁	SD₁₆	1	4	yes	complemented
109	SD₁₆×C₃₁	—	2	2	no	—
110	SD₁₆×C₃₁	—	4	4	no	—
111	C₂×C₈×C₃₁	—	2	1	no	—
112	C₂×C₈×C₃₁	—	2	1	no	—
113	C₂×C₈×C₃₁	—	2	2	no	—
114	C₂×C₈×C₃₁	—	2	1	no	—
115	C₂×C₈×C₃₁	—	4	2	no	—
116	C₂×C₈×C₃₁	C₂×D₄	1	1	yes	characteristic
117	C₂×C₈×C₃₁	C₂×D₄	1	1	yes	characteristic
118	C₂×C₈×C₃₁	C₂×D₄	1	1	yes	characteristic
119	C₂×C₈×C₃₁	C₂×D₄	1	1	yes	characteristic
120	C₄⋊C₄×C₃₁	—	2	2	no	—
121	C₄⋊C₄×C₃₁	—	2	1	no	—
122	C₄⋊C₄×C₃₁	—	2	2	no	—
123	C₄⋊C₄×C₃₁	—	2	2	no	—
124	C₄⋊C₄×C₃₁	—	2	2	no	—
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	—	4	2	no	—
130	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
131	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
132	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
133	C₂²⋊C₄×C₃₁	—	2	1	no	—
134	C₂²⋊C₄×C₃₁	—	4	2	no	—
135	C₄²×C₃₁	—	2	2	no	—
136	C₄²×C₃₁	—	2	1	no	—
137	C₄²×C₃₁	—	4	2	no	—
138	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
139	#19983	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
140	C₂³×C₃₁	—	2	1	no	—
141	Q₈×C₃₁	—	2	2	no	—
142	Q₈×C₃₁	—	2	1	no	—
143	Q₈×C₃₁	—	2	1	no	—
144	Q₈×C₃₁	—	4	2	no	—
145	Q₈×C₃₁	—	4	2	no	—
146	Q₈×C₃₁	—	4	2	no	—
147	Q₈×C₃₁	—	4	2	no	—
148	Q₈×C₃₁	—	8	4	no	—
149	Q₈×C₃₁	C₂×SD₁₆	1	4	yes	—
150	D₄×C₃₁	—	2	1	no	—
151	D₄×C₃₁	#135	1	2	yes	—
152	C₂×C₄×C₃₁	—	2	2	no	—
153	C₂×C₄×C₃₁	—	2	1	no	—
154	C₂×C₄×C₃₁	—	2	2	no	—
155	C₂×C₄×C₃₁	—	2	1	no	—
156	C₂×C₄×C₃₁	—	2	1	no	—
157	C₂×C₄×C₃₁	—	4	1	no	—
158	C₂×C₄×C₃₁	—	4	1	no	—
159	C₂×C₄×C₃₁	—	4	2	no	—
160	C₂×C₄×C₃₁	—	4	2	no	—
161	C₂×C₄×C₃₁	—	8	4	no	—
162	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
163	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
164	C₂×C₄×C₃₁	H(5,𝔽₂)	1	1	yes	characteristic
165	C₈×C₃₁	—	2	2	no	—
166	C₈×C₃₁	—	2	1	no	—
167	C₈×C₃₁	—	2	1	no	—
168	C₈×C₃₁	—	2	1	no	—
169	C₈×C₃₁	—	4	1	no	—
170	C₈×C₃₁	—	4	2	no	—
171	C₈×C₃₁	—	4	1	no	—
172	C₈×C₃₁	C₂×SD₁₆	1	2	yes	—
173	#3383	C₂×C₃₁	1	1	yes	characteristic, complemented
174	#3359	C₂×C₃₁	1	2	yes	—
175	D₄×Q₁₆	C₂×C₃₁	1	1	yes	characteristic
176	#1707	C₂×C₃₁	1	1	yes	characteristic, complemented
177	#1680	C₂×C₃₁	1	2	yes	complemented
178	#1673	C₂×C₃₁	1	1	yes	characteristic
179	#1670	C₂×C₃₁	1	1	yes	characteristic, complemented
180	#1653	C₂×C₃₁	1	2	yes	complemented
181	#1651	C₂×C₃₁	1	2	yes	—
182	C₈×Q₁₆	C₂×C₃₁	1	1	yes	characteristic, complemented
183	C₈×SD₁₆	C₂×C₃₁	1	1	yes	characteristic
184	C₂²×C₃₁	—	2	2	no	—
185	C₂²×C₃₁	—	4	1	no	—
186	C₂²×C₃₁	—	4	1	no	—
187	C₂²×C₃₁	D₄²	1	1	yes	characteristic
188	C₄×C₃₁	—	2	4	no	—
189	C₄×C₃₁	—	2	1	no	—
190	C₄×C₃₁	—	4	1	no	—
191	C₄×C₃₁	—	4	1	no	—
192	C₄×C₃₁	—	4	1	no	—
193	C₄×C₃₁	—	4	2	no	—
194	C₄×C₃₁	—	8	2	no	—
195	C₄×C₃₁	—	8	2	no	—
196	C₄×C₃₁	C₂²×SD₁₆	1	1	yes	characteristic
197	C₄×C₃₁	C₂×#135	1	1	yes	characteristic
198	C₄×C₃₁	#577	1	1	yes	characteristic
199	C₄×C₃₁	#578	1	1	yes	characteristic
200	C₂²×Q₁₆	—	2	1	no	—
201	#557	C₂²×C₃₁	1	2	yes	—
202	D₄×Q₈	C₂²×C₃₁	1	2	yes	—
203	#500	C₂²×C₃₁	1	1	yes	characteristic
204	#499	—	2	1	no	—
205	#498	C₂²×C₃₁	1	2	yes	—
206	#494	C₂²×C₃₁	1	1	yes	characteristic
207	#487	—	2	2	no	—
208	#487	C₂²×C₃₁	1	2	yes	—
209	#479	—	2	2	no	—
210	#475	—	2	2	no	—
211	#475	C₂²×C₃₁	1	2	yes	—
212	#475	C₂²×C₃₁	1	2	yes	—
213	#467	—	2	1	no	—
214	#462	C₂²×C₃₁	1	2	yes	—
215	#461	—	2	2	no	—
216	#461	C₂²×C₃₁	1	2	yes	—
217	#451	—	2	2	no	—
218	C₈×Q₈	C₂²×C₃₁	1	2	yes	—
219	C₈×Q₈	C₂²×C₃₁	1	1	yes	characteristic
220	C₄×Q₁₆	—	2	1	no	—
221	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
222	C₄×SD₁₆	—	2	2	no	—
223	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
224	C₈×D₄	C₂²×C₃₁	1	1	yes	characteristic
225	#335	C₂²×C₃₁	1	1	yes	characteristic
226	#334	C₂²×C₃₁	1	1	yes	characteristic
227	#332	C₂²×C₃₁	1	2	yes	—
228	#332	C₂²×C₃₁	1	2	yes	—
229	Q₈⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
230	Q₈⋊C₈	C₂²×C₃₁	1	2	yes	—
231	D₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
232	C₈²	C₂²×C₃₁	1	1	yes	characteristic
233	C₂×C₃₁	—	4	2	no	—
234	C₂×C₃₁	D₄×SD₁₆	1	1	yes	characteristic
235	C₂×C₃₁	#3285	1	1	yes	characteristic
236	C₂×C₃₁	#3293	1	1	yes	characteristic
237	C₂²×Q₈	—	2	2	no	—
238	C₂×Q₁₆	—	2	2	no	—
239	C₂×Q₁₆	—	2	1	no	—
240	C₂×Q₁₆	—	2	1	no	—
241	C₂×Q₁₆	—	4	4	no	—
242	C₂×Q₁₆	D₄×C₃₁	1	1	yes	characteristic
243	C₂×SD₁₆	—	2	2	no	—
244	C₂×SD₁₆	D₄×C₃₁	1	1	yes	characteristic
245	C₂²×C₈	—	2	1	no	—
246	C₄⋊Q₈	—	2	2	no	—
247	C₄⋊Q₈	—	2	2	no	—
248	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
249	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
250	#125	—	2	2	no	—
251	#125	—	4	2	no	—
252	C₂²⋊Q₈	—	2	2	no	—
253	C₂²⋊Q₈	—	4	2	no	—
254	C₄×Q₈	—	2	2	no	—
255	C₄×Q₈	—	2	2	no	—
256	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
257	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
258	C₄×D₄	—	2	2	no	—
259	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
260	#107	—	2	1	no	—
261	#107	—	2	1	no	—
262	#107	D₄×C₃₁	1	1	yes	characteristic
263	#106	—	2	2	no	—
264	#106	—	2	2	no	—
265	#106	—	4	2	no	—
266	#106	D₄×C₃₁	1	1	yes	characteristic
267	C₄⋊C₈	—	2	2	no	—
268	C₄⋊C₈	—	2	1	no	—
269	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
270	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
271	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
272	#103	—	2	2	no	—
273	#103	—	2	2	no	—
274	#103	—	2	2	no	—
275	#103	—	2	2	no	—
276	#103	—	2	2	no	—
277	#103	—	2	2	no	—
278	#103	D₄×C₃₁	1	1	yes	characteristic
279	#103	D₄×C₃₁	1	2	yes	—
280	#102	D₄×C₃₁	1	1	yes	characteristic
281	C₂²⋊C₈	—	2	1	no	—
282	C₄×C₈	—	2	2	no	—
283	C₄×C₈	—	2	1	no	—
284	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
285	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
286	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
287	C₃₁	#19983	1	1	yes	characteristic, direct product factor, Sylow
288	C₂×Q₈	—	2	2	no	—
289	C₂×Q₈	—	2	2	no	—
290	C₂×Q₈	—	4	2	no	—
291	C₂×Q₈	—	4	4	no	—
292	C₂×Q₈	—	8	2	no	—
293	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
294	C₂×Q₈	C₂×D₄×C₃₁	1	2	yes	—
295	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
296	C₂²×C₄	—	2	1	no	—
297	C₂²×C₄	—	4	2	no	—
298	Q₁₆	—	4	4	no	—
299	Q₁₆	—	4	2	no	—
300	Q₁₆	—	8	1	no	—
301	Q₁₆	SD₁₆×C₃₁	1	4	yes	complemented
302	SD₁₆	—	2	2	no	—
303	SD₁₆	—	4	4	no	—
304	C₂×C₈	—	2	1	no	—
305	C₂×C₈	—	2	1	no	—
306	C₂×C₈	—	2	2	no	—
307	C₂×C₈	—	2	1	no	—
308	C₂×C₈	—	4	2	no	—
309	C₂×C₈	C₂×D₄×C₃₁	1	1	yes	characteristic
310	C₂×C₈	C₂×D₄×C₃₁	1	1	yes	characteristic
311	C₂×C₈	C₂×D₄×C₃₁	1	1	yes	characteristic
312	C₂×C₈	C₂×D₄×C₃₁	1	1	yes	characteristic
313	C₄⋊C₄	—	2	2	no	—
314	C₄⋊C₄	—	2	1	no	—
315	C₄⋊C₄	—	2	2	no	—
316	C₄⋊C₄	—	2	2	no	—
317	C₄⋊C₄	—	2	2	no	—
318	C₄⋊C₄	—	2	2	no	—
319	C₄⋊C₄	—	4	2	no	—
320	C₄⋊C₄	—	4	2	no	—
321	C₄⋊C₄	—	4	2	no	—
322	C₄⋊C₄	—	4	2	no	—
323	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
324	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
325	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
326	C₂²⋊C₄	—	2	1	no	—
327	C₂²⋊C₄	—	4	2	no	—
328	C₄²	—	2	2	no	—
329	C₄²	—	2	1	no	—
330	C₄²	—	4	2	no	—
331	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
332	C₂³	—	2	1	no	—
333	Q₈	—	2	2	no	—
334	Q₈	—	2	1	no	—
335	Q₈	—	2	1	no	—
336	Q₈	—	4	2	no	—
337	Q₈	—	4	2	no	—
338	Q₈	—	4	2	no	—
339	Q₈	—	4	2	no	—
340	Q₈	—	8	4	no	—
341	Q₈	C₂×SD₁₆×C₃₁	1	4	yes	—
342	D₄	—	2	1	no	—
343	D₄	C₃₁×#135	1	2	yes	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	1	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	1	no	—
348	C₂×C₄	—	2	1	no	—
349	C₂×C₄	—	4	1	no	—
350	C₂×C₄	—	4	1	no	—
351	C₂×C₄	—	4	2	no	—
352	C₂×C₄	—	4	2	no	—
353	C₂×C₄	—	8	4	no	—
354	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
355	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
356	C₂×C₄	C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
357	C₈	—	2	2	no	—
358	C₈	—	2	1	no	—
359	C₈	—	2	1	no	—
360	C₈	—	2	1	no	—
361	C₈	—	4	1	no	—
362	C₈	—	4	2	no	—
363	C₈	—	4	1	no	—
364	C₈	C₂×SD₁₆×C₃₁	1	2	yes	—
365	C₂²	—	2	2	no	—
366	C₂²	—	4	1	no	—
367	C₂²	—	4	1	no	—
368	C₂²	D₄²×C₃₁	1	1	yes	characteristic
369	C₄	—	2	4	no	—
370	C₄	—	2	1	no	—
371	C₄	—	4	1	no	—
372	C₄	—	4	1	no	—
373	C₄	—	4	1	no	—
374	C₄	—	4	2	no	—
375	C₄	—	8	2	no	—
376	C₄	—	8	2	no	—
377	C₄	C₂²×SD₁₆×C₃₁	1	1	yes	characteristic
378	C₄	C₂×C₃₁×#135	1	1	yes	characteristic
379	C₄	C₃₁×#577	1	1	yes	characteristic
380	C₄	C₃₁×#578	1	1	yes	characteristic
381	C₂	—	4	2	no	—
382	C₂	D₄×SD₁₆×C₃₁	1	1	yes	characteristic
383	C₂	C₃₁×#3285	1	1	yes	characteristic
384	C₂	C₃₁×#3293	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	D₄²
commutator, Frattini, cosocle	C₄²	C₂⁴×C₃₁
prime radical	C₂×D₄×C₃₁	C₂×D₄
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₄²×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3383	C₂	semidirect
4. C₃₁×#1707	C₂	semidirect
5. C₃₁×#1680	C₂	semidirect
7. C₃₁×#1670	C₂	semidirect
8. C₃₁×#1653	C₂	semidirect
10. C₈×Q₁₆×C₃₁	C₂	semidirect
108. Q₁₆×C₃₁	SD₁₆	semidirect
139. #19983	C₃₁	direct (N × H)
173. #3383	C₂×C₃₁	semidirect
176. #1707	C₂×C₃₁	semidirect
177. #1680	C₂×C₃₁	semidirect
179. #1670	C₂×C₃₁	semidirect
180. #1653	C₂×C₃₁	semidirect
182. C₈×Q₁₆	C₂×C₃₁	semidirect
287. C₃₁	#19983	direct (N × H)
301. Q₁₆	SD₁₆×C₃₁	semidirect

Maximal subgroups

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

subgroup	index
C₃₁×#3383	2
C₃₁×#3359	2
D₄×Q₁₆×C₃₁	2
C₃₁×#1707	2
C₃₁×#1680	2
C₃₁×#1673	2
C₃₁×#1670	2
C₃₁×#1653	2
C₃₁×#1651	2
C₈×Q₁₆×C₃₁	2
C₈×SD₁₆×C₃₁	2
#19983	31

Subgroups — C31×#19983 #21476742

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#19983 #21476742