Subgroups — C₃₁×#19993 #21476752

Order 7936.

606 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3380	C₂	1	1	yes	maximal, characteristic
2	Q₈×D₈×C₃₁	C₂	1	1	yes	maximal, characteristic
3	C₃₁×#3299	C₂	1	2	yes	maximal, complemented
4	C₃₁×#1710	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#1683	C₂	1	2	yes	maximal, complemented
6	C₃₁×#1676	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#1674	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#1644	C₂	1	2	yes	maximal, complemented
9	C₃₁×#1637	C₂	1	2	yes	maximal, complemented
10	C₈×Q₁₆×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×D₈×C₃₁	C₂	1	1	yes	maximal, characteristic
12	C₃₁×#554	C₂²	1	2	yes	—
13	D₄×Q₈×C₃₁	C₂²	1	2	yes	—
14	C₃₁×#500	—	2	1	no	—
15	C₃₁×#500	C₂²	1	1	yes	characteristic
16	C₃₁×#500	C₂²	1	1	yes	characteristic
17	C₃₁×#499	—	2	1	no	—
18	C₃₁×#487	C₂²	1	2	yes	—
19	C₃₁×#487	C₂²	1	2	yes	—
20	C₃₁×#484	—	2	2	no	—
21	C₃₁×#478	—	2	2	no	—
22	C₃₁×#477	C₂²	1	2	yes	—
23	C₃₁×#476	C₂²	1	2	yes	—
24	C₃₁×#474	—	2	2	no	—
25	C₃₁×#474	C₂²	1	2	yes	—
26	C₃₁×#467	—	2	2	no	—
27	C₃₁×#462	C₂²	1	2	yes	—
28	C₃₁×#451	—	2	2	no	—
29	C₈×Q₈×C₃₁	C₂²	1	1	yes	characteristic
30	C₈×Q₈×C₃₁	C₂²	1	1	yes	characteristic
31	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
32	C₄×D₈×C₃₁	—	2	1	no	—
33	C₄×D₈×C₃₁	—	2	1	no	—
34	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic
35	C₈×D₄×C₃₁	C₂²	1	2	yes	—
36	C₂×C₃₁×#103	—	2	2	no	—
37	C₃₁×#335	C₂²	1	1	yes	characteristic
38	C₃₁×#335	C₂²	1	1	yes	characteristic
39	C₃₁×#333	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	1	yes	characteristic
43	C₃₁×D₄⋊C₈	C₂²	1	2	yes	—
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	D₄	1	1	yes	characteristic
48	C₂×D₈×C₃₁	D₄	1	1	yes	characteristic
49	C₂²×C₈×C₃₁	—	2	2	no	—
50	C₃₁×C₄⋊Q₈	—	2	2	no	—
51	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
52	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
53	C₃₁×#125	—	2	2	no	—
54	C₃₁×C₂²⋊Q₈	—	2	2	no	—
55	C₃₁×C₂²⋊Q₈	—	2	2	no	—
56	C₃₁×C₂²⋊Q₈	—	4	2	no	—
57	C₃₁×C₂²⋊Q₈	—	4	2	no	—
58	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
59	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
60	C₄×D₄×C₃₁	—	2	2	no	—
61	C₄×D₄×C₃₁	—	2	2	no	—
62	C₄×D₄×C₃₁	C₂³	1	2	yes	—
63	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
64	C₃₁×#107	—	2	1	no	—
65	C₃₁×#107	—	2	1	no	—
66	C₃₁×#107	—	2	1	no	—
67	C₃₁×#107	—	2	1	no	—
68	C₃₁×#107	—	2	2	no	—
69	C₃₁×#107	—	2	2	no	—
70	C₃₁×#107	D₄	1	1	yes	characteristic
71	C₃₁×#107	D₄	1	1	yes	characteristic
72	C₃₁×#106	—	2	2	no	—
73	C₃₁×C₄⋊C₈	—	2	1	no	—
74	C₃₁×C₄⋊C₈	—	2	1	no	—
75	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
76	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
77	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
78	C₃₁×#103	—	2	2	no	—
79	C₃₁×#103	—	2	2	no	—
80	C₃₁×#103	—	2	2	no	—
81	C₃₁×#103	—	2	2	no	—
82	C₃₁×#103	—	4	2	no	—
83	C₃₁×#103	D₄	1	1	yes	characteristic
84	C₃₁×#103	D₄	1	1	yes	characteristic
85	C₃₁×#102	—	2	2	no	—
86	C₃₁×#102	—	2	2	no	—
87	C₃₁×#102	D₄	1	2	yes	—
88	C₃₁×C₂²⋊C₈	—	2	2	no	—
89	C₄×C₈×C₃₁	—	2	1	no	—
90	C₄×C₈×C₃₁	—	2	1	no	—
91	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
92	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
93	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
94	C₂×Q₈×C₃₁	—	2	2	no	—
95	C₂×Q₈×C₃₁	—	2	2	no	—
96	C₂×Q₈×C₃₁	—	4	2	no	—
97	C₂×Q₈×C₃₁	—	4	4	no	—
98	C₂×Q₈×C₃₁	—	8	2	no	—
99	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
100	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
101	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
102	C₂²×C₄×C₃₁	—	2	2	no	—
103	C₂²×C₄×C₃₁	—	4	2	no	—
104	C₂²×C₄×C₃₁	—	4	2	no	—
105	Q₁₆×C₃₁	—	2	2	no	—
106	Q₁₆×C₃₁	—	8	2	no	—
107	D₈×C₃₁	Q₁₆	1	4	yes	complemented
108	C₂×C₈×C₃₁	—	2	1	no	—
109	C₂×C₈×C₃₁	—	2	1	no	—
110	C₂×C₈×C₃₁	—	2	2	no	—
111	C₂×C₈×C₃₁	—	2	1	no	—
112	C₂×C₈×C₃₁	—	8	2	no	—
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	C₄⋊C₄×C₃₁	—	2	1	no	—
118	C₄⋊C₄×C₃₁	—	2	1	no	—
119	C₄⋊C₄×C₃₁	—	2	2	no	—
120	C₄⋊C₄×C₃₁	—	2	2	no	—
121	C₄⋊C₄×C₃₁	—	2	2	no	—
122	C₄⋊C₄×C₃₁	—	2	2	no	—
123	C₄⋊C₄×C₃₁	—	4	2	no	—
124	C₄⋊C₄×C₃₁	—	4	2	no	—
125	C₄⋊C₄×C₃₁	—	4	2	no	—
126	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
127	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
128	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
129	C₂²⋊C₄×C₃₁	—	2	2	no	—
130	C₂²⋊C₄×C₃₁	—	4	2	no	—
131	C₂²⋊C₄×C₃₁	—	4	2	no	—
132	C₄²×C₃₁	—	2	1	no	—
133	C₄²×C₃₁	—	2	1	no	—
134	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
135	#19993	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
136	C₂³×C₃₁	—	2	2	no	—
137	Q₈×C₃₁	—	2	1	no	—
138	Q₈×C₃₁	—	2	1	no	—
139	Q₈×C₃₁	—	2	1	no	—
140	Q₈×C₃₁	—	4	2	no	—
141	Q₈×C₃₁	—	4	2	no	—
142	Q₈×C₃₁	—	8	4	no	—
143	Q₈×C₃₁	—	8	2	no	—
144	Q₈×C₃₁	#135	1	2	yes	—
145	D₄×C₃₁	—	2	2	no	—
146	D₄×C₃₁	C₂×Q₁₆	1	4	yes	—
147	C₂×C₄×C₃₁	—	2	1	no	—
148	C₂×C₄×C₃₁	—	2	1	no	—
149	C₂×C₄×C₃₁	—	2	1	no	—
150	C₂×C₄×C₃₁	—	2	1	no	—
151	C₂×C₄×C₃₁	—	2	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	—	8	4	no	—
157	C₂×C₄×C₃₁	—	16	2	no	—
158	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
159	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
160	C₂×C₄×C₃₁	H(5,𝔽₂)	1	1	yes	characteristic
161	C₈×C₃₁	—	2	1	no	—
162	C₈×C₃₁	—	2	1	no	—
163	C₈×C₃₁	—	2	1	no	—
164	C₈×C₃₁	—	4	1	no	—
165	C₈×C₃₁	—	4	2	no	—
166	C₈×C₃₁	—	4	1	no	—
167	C₈×C₃₁	—	4	1	no	—
168	C₈×C₃₁	C₂×Q₁₆	1	2	yes	—
169	#3380	C₂×C₃₁	1	1	yes	characteristic
170	Q₈×D₈	C₂×C₃₁	1	1	yes	characteristic
171	#3299	C₂×C₃₁	1	2	yes	complemented
172	#1710	C₂×C₃₁	1	1	yes	characteristic, complemented
173	#1683	C₂×C₃₁	1	2	yes	complemented
174	#1676	C₂×C₃₁	1	1	yes	characteristic, complemented
175	#1674	C₂×C₃₁	1	1	yes	characteristic, complemented
176	#1644	C₂×C₃₁	1	2	yes	complemented
177	#1637	C₂×C₃₁	1	2	yes	complemented
178	C₈×Q₁₆	C₂×C₃₁	1	1	yes	characteristic, complemented
179	C₈×D₈	C₂×C₃₁	1	1	yes	characteristic
180	C₂²×C₃₁	—	2	4	no	—
181	C₂²×C₃₁	—	4	2	no	—
182	C₂²×C₃₁	—	4	2	no	—
183	C₂²×C₃₁	D₄²	1	1	yes	characteristic
184	C₄×C₃₁	—	2	2	no	—
185	C₄×C₃₁	—	2	1	no	—
186	C₄×C₃₁	—	4	2	no	—
187	C₄×C₃₁	—	4	1	no	—
188	C₄×C₃₁	—	4	1	no	—
189	C₄×C₃₁	—	4	1	no	—
190	C₄×C₃₁	—	8	2	no	—
191	C₄×C₃₁	—	8	2	no	—
192	C₄×C₃₁	C₂²×Q₁₆	1	1	yes	characteristic
193	C₄×C₃₁	C₂×#135	1	1	yes	characteristic
194	C₄×C₃₁	#576	1	1	yes	characteristic
195	C₄×C₃₁	#578	1	1	yes	characteristic
196	#554	C₂²×C₃₁	1	2	yes	—
197	D₄×Q₈	C₂²×C₃₁	1	2	yes	—
198	#500	—	2	1	no	—
199	#500	C₂²×C₃₁	1	1	yes	characteristic
200	#500	C₂²×C₃₁	1	1	yes	characteristic
201	#499	—	2	1	no	—
202	#487	C₂²×C₃₁	1	2	yes	—
203	#487	C₂²×C₃₁	1	2	yes	—
204	#484	—	2	2	no	—
205	#478	—	2	2	no	—
206	#477	C₂²×C₃₁	1	2	yes	—
207	#476	C₂²×C₃₁	1	2	yes	—
208	#474	—	2	2	no	—
209	#474	C₂²×C₃₁	1	2	yes	—
210	#467	—	2	2	no	—
211	#462	C₂²×C₃₁	1	2	yes	—
212	#451	—	2	2	no	—
213	C₈×Q₈	C₂²×C₃₁	1	1	yes	characteristic
214	C₈×Q₈	C₂²×C₃₁	1	1	yes	characteristic
215	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
216	C₄×D₈	—	2	1	no	—
217	C₄×D₈	—	2	1	no	—
218	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic
219	C₈×D₄	C₂²×C₃₁	1	2	yes	—
220	C₂×#103	—	2	2	no	—
221	#335	C₂²×C₃₁	1	1	yes	characteristic
222	#335	C₂²×C₃₁	1	1	yes	characteristic
223	#333	C₂²×C₃₁	1	2	yes	—
224	#332	C₂²×C₃₁	1	2	yes	—
225	Q₈⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
226	Q₈⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
227	D₄⋊C₈	C₂²×C₃₁	1	2	yes	—
228	C₈²	C₂²×C₃₁	1	1	yes	characteristic
229	C₂×C₃₁	—	4	4	no	—
230	C₂×C₃₁	#3280	1	1	yes	characteristic
231	C₂×C₃₁	D₄×Q₁₆	1	1	yes	characteristic
232	C₂×C₃₁	#3290	1	1	yes	characteristic
233	C₂²×Q₈	—	2	2	no	—
234	C₂×Q₁₆	—	2	2	no	—
235	C₂×Q₁₆	D₄×C₃₁	1	1	yes	characteristic
236	C₂×D₈	D₄×C₃₁	1	1	yes	characteristic
237	C₂²×C₈	—	2	2	no	—
238	C₄⋊Q₈	—	2	2	no	—
239	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
240	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
241	#125	—	2	2	no	—
242	C₂²⋊Q₈	—	2	2	no	—
243	C₂²⋊Q₈	—	2	2	no	—
244	C₂²⋊Q₈	—	4	2	no	—
245	C₂²⋊Q₈	—	4	2	no	—
246	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
247	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
248	C₄×D₄	—	2	2	no	—
249	C₄×D₄	—	2	2	no	—
250	C₄×D₄	C₂³×C₃₁	1	2	yes	—
251	C₂×C₄⋊C₄	—	2	2	no	—
252	#107	—	2	1	no	—
253	#107	—	2	1	no	—
254	#107	—	2	1	no	—
255	#107	—	2	1	no	—
256	#107	—	2	2	no	—
257	#107	—	2	2	no	—
258	#107	D₄×C₃₁	1	1	yes	characteristic
259	#107	D₄×C₃₁	1	1	yes	characteristic
260	#106	—	2	2	no	—
261	C₄⋊C₈	—	2	1	no	—
262	C₄⋊C₈	—	2	1	no	—
263	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
264	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
265	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
266	#103	—	2	2	no	—
267	#103	—	2	2	no	—
268	#103	—	2	2	no	—
269	#103	—	2	2	no	—
270	#103	—	4	2	no	—
271	#103	D₄×C₃₁	1	1	yes	characteristic
272	#103	D₄×C₃₁	1	1	yes	characteristic
273	#102	—	2	2	no	—
274	#102	—	2	2	no	—
275	#102	D₄×C₃₁	1	2	yes	—
276	C₂²⋊C₈	—	2	2	no	—
277	C₄×C₈	—	2	1	no	—
278	C₄×C₈	—	2	1	no	—
279	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
280	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
281	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
282	C₃₁	#19993	1	1	yes	characteristic, direct product factor, Sylow
283	C₂×Q₈	—	2	2	no	—
284	C₂×Q₈	—	2	2	no	—
285	C₂×Q₈	—	4	2	no	—
286	C₂×Q₈	—	4	4	no	—
287	C₂×Q₈	—	8	2	no	—
288	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
289	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
290	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
291	C₂²×C₄	—	2	2	no	—
292	C₂²×C₄	—	4	2	no	—
293	C₂²×C₄	—	4	2	no	—
294	Q₁₆	—	2	2	no	—
295	Q₁₆	—	8	2	no	—
296	D₈	Q₁₆×C₃₁	1	4	yes	complemented
297	C₂×C₈	—	2	1	no	—
298	C₂×C₈	—	2	1	no	—
299	C₂×C₈	—	2	2	no	—
300	C₂×C₈	—	2	1	no	—
301	C₂×C₈	—	8	2	no	—
302	C₂×C₈	C₂×D₄×C₃₁	1	1	yes	characteristic
303	C₂×C₈	C₂×D₄×C₃₁	1	1	yes	characteristic
304	C₂×C₈	C₂×D₄×C₃₁	1	1	yes	characteristic
305	C₂×C₈	C₂×D₄×C₃₁	1	1	yes	characteristic
306	C₄⋊C₄	—	2	1	no	—
307	C₄⋊C₄	—	2	1	no	—
308	C₄⋊C₄	—	2	2	no	—
309	C₄⋊C₄	—	2	2	no	—
310	C₄⋊C₄	—	2	2	no	—
311	C₄⋊C₄	—	2	2	no	—
312	C₄⋊C₄	—	4	2	no	—
313	C₄⋊C₄	—	4	2	no	—
314	C₄⋊C₄	—	4	2	no	—
315	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
316	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
317	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
318	C₂²⋊C₄	—	2	2	no	—
319	C₂²⋊C₄	—	4	2	no	—
320	C₂²⋊C₄	—	4	2	no	—
321	C₄²	—	2	1	no	—
322	C₄²	—	2	1	no	—
323	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
324	C₂³	—	2	2	no	—
325	Q₈	—	2	1	no	—
326	Q₈	—	2	1	no	—
327	Q₈	—	2	1	no	—
328	Q₈	—	4	2	no	—
329	Q₈	—	4	2	no	—
330	Q₈	—	8	4	no	—
331	Q₈	—	8	2	no	—
332	Q₈	C₃₁×#135	1	2	yes	—
333	D₄	—	2	2	no	—
334	D₄	C₂×Q₁₆×C₃₁	1	4	yes	—
335	C₂×C₄	—	2	1	no	—
336	C₂×C₄	—	2	1	no	—
337	C₂×C₄	—	2	1	no	—
338	C₂×C₄	—	2	1	no	—
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	4	2	no	—
341	C₂×C₄	—	4	2	no	—
342	C₂×C₄	—	4	2	no	—
343	C₂×C₄	—	4	2	no	—
344	C₂×C₄	—	8	4	no	—
345	C₂×C₄	—	16	2	no	—
346	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
347	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
348	C₂×C₄	C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
349	C₈	—	2	1	no	—
350	C₈	—	2	1	no	—
351	C₈	—	2	1	no	—
352	C₈	—	4	1	no	—
353	C₈	—	4	2	no	—
354	C₈	—	4	1	no	—
355	C₈	—	4	1	no	—
356	C₈	C₂×Q₁₆×C₃₁	1	2	yes	—
357	C₂²	—	2	4	no	—
358	C₂²	—	4	2	no	—
359	C₂²	—	4	2	no	—
360	C₂²	D₄²×C₃₁	1	1	yes	characteristic
361	C₄	—	2	2	no	—
362	C₄	—	2	1	no	—
363	C₄	—	4	2	no	—
364	C₄	—	4	1	no	—
365	C₄	—	4	1	no	—
366	C₄	—	4	1	no	—
367	C₄	—	8	2	no	—
368	C₄	—	8	2	no	—
369	C₄	C₂²×Q₁₆×C₃₁	1	1	yes	characteristic
370	C₄	C₂×C₃₁×#135	1	1	yes	characteristic
371	C₄	C₃₁×#576	1	1	yes	characteristic
372	C₄	C₃₁×#578	1	1	yes	characteristic
373	C₂	—	4	4	no	—
374	C₂	C₃₁×#3280	1	1	yes	characteristic
375	C₂	D₄×Q₁₆×C₃₁	1	1	yes	characteristic
376	C₂	C₃₁×#3290	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	D₄²
commutator, Frattini, cosocle	C₄²	C₂⁴×C₃₁
prime radical	C₂×D₈×C₃₁	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
3. C₃₁×#3299	C₂	semidirect
4. C₃₁×#1710	C₂	semidirect
5. C₃₁×#1683	C₂	semidirect
6. C₃₁×#1676	C₂	semidirect
7. C₃₁×#1674	C₂	semidirect
8. C₃₁×#1644	C₂	semidirect
9. C₃₁×#1637	C₂	semidirect
10. C₈×Q₁₆×C₃₁	C₂	semidirect
107. D₈×C₃₁	Q₁₆	semidirect
135. #19993	C₃₁	direct (N × H)
171. #3299	C₂×C₃₁	semidirect
172. #1710	C₂×C₃₁	semidirect
173. #1683	C₂×C₃₁	semidirect
174. #1676	C₂×C₃₁	semidirect
175. #1674	C₂×C₃₁	semidirect
176. #1644	C₂×C₃₁	semidirect
177. #1637	C₂×C₃₁	semidirect
178. C₈×Q₁₆	C₂×C₃₁	semidirect
282. C₃₁	#19993	direct (N × H)
296. D₈	Q₁₆×C₃₁	semidirect

Maximal subgroups

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

subgroup	index
C₃₁×#3380	2
Q₈×D₈×C₃₁	2
C₃₁×#3299	2
C₃₁×#1710	2
C₃₁×#1683	2
C₃₁×#1676	2
C₃₁×#1674	2
C₃₁×#1644	2
C₃₁×#1637	2
C₈×Q₁₆×C₃₁	2
C₈×D₈×C₃₁	2
#19993	31

Subgroups — C31×#19993 #21476752

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#19993 #21476752