Subgroups — C₃₁×#20007 #21476766

Order 7936.

570 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3395	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3381	C₂	1	2	yes	maximal
3	C₃₁×#3338	C₂	1	1	yes	maximal, characteristic
4	C₃₁×#1707	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#1676	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#1672	C₂	1	2	yes	maximal, complemented
7	C₃₁×#1669	C₂	1	1	yes	maximal, characteristic
8	C₃₁×#1644	C₂	1	2	yes	maximal
9	C₃₁×#1636	C₂	1	2	yes	maximal, complemented
10	C₈×Q₁₆×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×SD₁₆×C₃₁	C₂	1	1	yes	maximal, characteristic
12	C₃₁×#557	C₂²	1	2	yes	—
13	C₃₁×#554	C₂²	1	2	yes	—
14	C₃₁×#500	C₂²	1	1	yes	characteristic
15	C₃₁×#499	—	2	2	no	—
16	C₃₁×#498	C₂²	1	2	yes	—
17	C₃₁×#494	—	2	1	no	—
18	C₃₁×#494	C₂²	1	1	yes	characteristic
19	C₃₁×#487	C₂²	1	2	yes	—
20	C₃₁×#484	—	2	2	no	—
21	C₃₁×#479	—	2	2	no	—
22	C₃₁×#478	—	2	2	no	—
23	C₃₁×#477	C₂²	1	2	yes	—
24	C₃₁×#477	C₂²	1	2	yes	—
25	C₃₁×#474	C₂²	1	2	yes	—
26	C₃₁×#467	—	2	1	no	—
27	C₃₁×#462	—	2	2	no	—
28	C₃₁×#462	C₂²	1	2	yes	—
29	C₈×Q₈×C₃₁	C₂²	1	1	yes	characteristic
30	C₈×Q₈×C₃₁	C₂²	1	2	yes	—
31	C₄×Q₁₆×C₃₁	—	2	1	no	—
32	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
33	C₄×SD₁₆×C₃₁	—	2	2	no	—
34	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
35	C₈×D₄×C₃₁	C₂²	1	1	yes	characteristic
36	C₂×C₃₁×#107	—	2	1	no	—
37	C₃₁×#335	C₂²	1	1	yes	characteristic
38	C₃₁×#334	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	2	yes	—
43	C₃₁×D₄⋊C₈	C₂²	1	1	yes	characteristic
44	C₈²×C₃₁	C₂²	1	1	yes	characteristic
45	C₂×Q₁₆×C₃₁	—	2	2	no	—
46	C₂×Q₁₆×C₃₁	—	2	1	no	—
47	C₂×Q₁₆×C₃₁	—	2	1	no	—
48	C₂×Q₁₆×C₃₁	D₄	1	1	yes	characteristic
49	C₂×SD₁₆×C₃₁	D₄	1	1	yes	characteristic
50	C₂²×C₈×C₃₁	—	2	1	no	—
51	C₃₁×C₄⋊Q₈	—	2	2	no	—
52	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
53	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
54	C₃₁×#125	—	2	2	no	—
55	C₃₁×#125	—	2	2	no	—
56	C₃₁×#125	—	4	2	no	—
57	C₃₁×C₂²⋊Q₈	—	2	2	no	—
58	C₃₁×C₂²⋊Q₈	—	4	2	no	—
59	C₄×Q₈×C₃₁	—	2	2	no	—
60	C₄×Q₈×C₃₁	—	2	2	no	—
61	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
62	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
63	C₄×D₄×C₃₁	—	2	2	no	—
64	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
65	C₂×C₄⋊C₄×C₃₁	—	2	2	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	—	2	2	no	—
71	C₃₁×#107	D₄	1	1	yes	characteristic
72	C₃₁×#106	—	2	2	no	—
73	C₃₁×#106	—	2	2	no	—
74	C₃₁×#106	D₄	1	1	yes	characteristic
75	C₃₁×C₄⋊C₈	—	2	1	no	—
76	C₃₁×C₄⋊C₈	—	2	2	no	—
77	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
78	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
79	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
80	C₃₁×#103	—	2	2	no	—
81	C₃₁×#103	—	2	2	no	—
82	C₃₁×#103	—	2	2	no	—
83	C₃₁×#103	—	4	2	no	—
84	C₃₁×#103	D₄	1	1	yes	characteristic
85	C₃₁×#103	D₄	1	2	yes	—
86	C₃₁×#102	—	2	2	no	—
87	C₃₁×#102	D₄	1	1	yes	characteristic
88	C₃₁×C₂²⋊C₈	—	2	1	no	—
89	C₄×C₈×C₃₁	—	2	2	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	C₂×D₄	1	2	yes	—
97	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
98	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₃₁	—	2	1	no	—
100	C₂²×C₄×C₃₁	—	4	2	no	—
101	Q₁₆×C₃₁	—	2	2	no	—
102	Q₁₆×C₃₁	—	4	2	no	—
103	Q₁₆×C₃₁	—	8	1	no	—
104	Q₁₆×C₃₁	—	8	2	no	—
105	SD₁₆×C₃₁	Q₁₆	1	4	yes	complemented
106	C₂×C₈×C₃₁	—	2	2	no	—
107	C₂×C₈×C₃₁	—	2	1	no	—
108	C₂×C₈×C₃₁	—	2	1	no	—
109	C₂×C₈×C₃₁	—	2	1	no	—
110	C₂×C₈×C₃₁	—	4	2	no	—
111	C₂×C₈×C₃₁	C₂×D₄	1	1	yes	characteristic
112	C₂×C₈×C₃₁	C₂×D₄	1	1	yes	characteristic
113	C₂×C₈×C₃₁	C₂×D₄	1	1	yes	characteristic
114	C₂×C₈×C₃₁	C₂×D₄	1	1	yes	characteristic
115	C₄⋊C₄×C₃₁	—	2	2	no	—
116	C₄⋊C₄×C₃₁	—	2	1	no	—
117	C₄⋊C₄×C₃₁	—	2	2	no	—
118	C₄⋊C₄×C₃₁	—	2	2	no	—
119	C₄⋊C₄×C₃₁	—	2	2	no	—
120	C₄⋊C₄×C₃₁	—	2	2	no	—
121	C₄⋊C₄×C₃₁	—	4	2	no	—
122	C₄⋊C₄×C₃₁	—	4	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	1	yes	characteristic
127	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
128	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
129	C₂²⋊C₄×C₃₁	—	2	1	no	—
130	C₂²⋊C₄×C₃₁	—	4	2	no	—
131	C₄²×C₃₁	—	2	2	no	—
132	C₄²×C₃₁	—	2	1	no	—
133	C₄²×C₃₁	—	4	2	no	—
134	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
135	#20007	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
136	C₂³×C₃₁	—	2	1	no	—
137	Q₈×C₃₁	—	2	1	no	—
138	Q₈×C₃₁	—	2	2	no	—
139	Q₈×C₃₁	—	2	2	no	—
140	Q₈×C₃₁	—	4	2	no	—
141	Q₈×C₃₁	—	4	2	no	—
142	Q₈×C₃₁	—	8	2	no	—
143	Q₈×C₃₁	C₂×Q₁₆	1	2	yes	—
144	D₄×C₃₁	—	2	1	no	—
145	D₄×C₃₁	C₂×Q₁₆	1	2	yes	—
146	C₂×C₄×C₃₁	—	2	1	no	—
147	C₂×C₄×C₃₁	—	2	2	no	—
148	C₂×C₄×C₃₁	—	2	2	no	—
149	C₂×C₄×C₃₁	—	2	1	no	—
150	C₂×C₄×C₃₁	—	2	1	no	—
151	C₂×C₄×C₃₁	—	4	1	no	—
152	C₂×C₄×C₃₁	—	4	1	no	—
153	C₂×C₄×C₃₁	—	4	2	no	—
154	C₂×C₄×C₃₁	—	4	2	no	—
155	C₂×C₄×C₃₁	—	16	2	no	—
156	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
157	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
158	C₂×C₄×C₃₁	H(5,𝔽₂)	1	1	yes	characteristic
159	C₈×C₃₁	—	2	1	no	—
160	C₈×C₃₁	—	2	1	no	—
161	C₈×C₃₁	—	4	1	no	—
162	C₈×C₃₁	—	4	1	no	—
163	C₈×C₃₁	—	4	1	no	—
164	C₈×C₃₁	—	4	2	no	—
165	C₈×C₃₁	C₂×Q₁₆	1	2	yes	—
166	C₈×C₃₁	#135	1	2	yes	—
167	#3395	C₂×C₃₁	1	1	yes	characteristic, complemented
168	#3381	C₂×C₃₁	1	2	yes	—
169	#3338	C₂×C₃₁	1	1	yes	characteristic
170	#1707	C₂×C₃₁	1	1	yes	characteristic, complemented
171	#1676	C₂×C₃₁	1	1	yes	characteristic, complemented
172	#1672	C₂×C₃₁	1	2	yes	complemented
173	#1669	C₂×C₃₁	1	1	yes	characteristic
174	#1644	C₂×C₃₁	1	2	yes	—
175	#1636	C₂×C₃₁	1	2	yes	complemented
176	C₈×Q₁₆	C₂×C₃₁	1	1	yes	characteristic, complemented
177	C₈×SD₁₆	C₂×C₃₁	1	1	yes	characteristic
178	C₂²×C₃₁	—	2	2	no	—
179	C₂²×C₃₁	—	4	1	no	—
180	C₂²×C₃₁	—	4	1	no	—
181	C₂²×C₃₁	D₄²	1	1	yes	characteristic
182	C₄×C₃₁	—	2	2	no	—
183	C₄×C₃₁	—	2	1	no	—
184	C₄×C₃₁	—	4	1	no	—
185	C₄×C₃₁	—	4	2	no	—
186	C₄×C₃₁	—	4	1	no	—
187	C₄×C₃₁	—	4	2	no	—
188	C₄×C₃₁	—	8	2	no	—
189	C₄×C₃₁	—	8	2	no	—
190	C₄×C₃₁	C₂²×Q₁₆	1	1	yes	characteristic
191	C₄×C₃₁	C₂×#135	1	1	yes	characteristic
192	C₄×C₃₁	#577	1	1	yes	characteristic
193	C₄×C₃₁	#578	1	1	yes	characteristic
194	#557	C₂²×C₃₁	1	2	yes	—
195	#554	C₂²×C₃₁	1	2	yes	—
196	#500	C₂²×C₃₁	1	1	yes	characteristic
197	#499	—	2	2	no	—
198	#498	C₂²×C₃₁	1	2	yes	—
199	#494	—	2	1	no	—
200	#494	C₂²×C₃₁	1	1	yes	characteristic
201	#487	C₂²×C₃₁	1	2	yes	—
202	#484	—	2	2	no	—
203	#479	—	2	2	no	—
204	#478	—	2	2	no	—
205	#477	C₂²×C₃₁	1	2	yes	—
206	#477	C₂²×C₃₁	1	2	yes	—
207	#474	C₂²×C₃₁	1	2	yes	—
208	#467	—	2	1	no	—
209	#462	—	2	2	no	—
210	#462	C₂²×C₃₁	1	2	yes	—
211	C₈×Q₈	C₂²×C₃₁	1	1	yes	characteristic
212	C₈×Q₈	C₂²×C₃₁	1	2	yes	—
213	C₄×Q₁₆	—	2	1	no	—
214	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
215	C₄×SD₁₆	—	2	2	no	—
216	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
217	C₈×D₄	C₂²×C₃₁	1	1	yes	characteristic
218	C₂×#107	—	2	1	no	—
219	#335	C₂²×C₃₁	1	1	yes	characteristic
220	#334	C₂²×C₃₁	1	1	yes	characteristic
221	#333	C₂²×C₃₁	1	2	yes	—
222	#332	C₂²×C₃₁	1	2	yes	—
223	Q₈⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
224	Q₈⋊C₈	C₂²×C₃₁	1	2	yes	—
225	D₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
226	C₈²	C₂²×C₃₁	1	1	yes	characteristic
227	C₂×C₃₁	—	4	2	no	—
228	C₂×C₃₁	#3284	1	1	yes	characteristic
229	C₂×C₃₁	D₄×Q₁₆	1	1	yes	characteristic
230	C₂×C₃₁	#3290	1	1	yes	characteristic
231	C₂×Q₁₆	—	2	2	no	—
232	C₂×Q₁₆	—	2	1	no	—
233	C₂×Q₁₆	—	2	1	no	—
234	C₂×Q₁₆	D₄×C₃₁	1	1	yes	characteristic
235	C₂×SD₁₆	D₄×C₃₁	1	1	yes	characteristic
236	C₂²×C₈	—	2	1	no	—
237	C₄⋊Q₈	—	2	2	no	—
238	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
239	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
240	#125	—	2	2	no	—
241	#125	—	2	2	no	—
242	#125	—	4	2	no	—
243	C₂²⋊Q₈	—	2	2	no	—
244	C₂²⋊Q₈	—	4	2	no	—
245	C₄×Q₈	—	2	2	no	—
246	C₄×Q₈	—	2	2	no	—
247	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
248	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
249	C₄×D₄	—	2	2	no	—
250	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
251	C₂×C₄⋊C₄	—	2	2	no	—
252	#107	—	2	1	no	—
253	#107	—	2	1	no	—
254	#107	—	2	2	no	—
255	#107	—	2	2	no	—
256	#107	—	2	2	no	—
257	#107	D₄×C₃₁	1	1	yes	characteristic
258	#106	—	2	2	no	—
259	#106	—	2	2	no	—
260	#106	D₄×C₃₁	1	1	yes	characteristic
261	C₄⋊C₈	—	2	1	no	—
262	C₄⋊C₈	—	2	2	no	—
263	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
264	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
265	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
266	#103	—	2	2	no	—
267	#103	—	2	2	no	—
268	#103	—	2	2	no	—
269	#103	—	4	2	no	—
270	#103	D₄×C₃₁	1	1	yes	characteristic
271	#103	D₄×C₃₁	1	2	yes	—
272	#102	—	2	2	no	—
273	#102	D₄×C₃₁	1	1	yes	characteristic
274	C₂²⋊C₈	—	2	1	no	—
275	C₄×C₈	—	2	2	no	—
276	C₄×C₈	—	2	1	no	—
277	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
278	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
279	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
280	C₃₁	#20007	1	1	yes	characteristic, direct product factor, Sylow
281	C₂×Q₈	—	2	2	no	—
282	C₂×Q₈	—	2	2	no	—
283	C₂×Q₈	C₂×D₄×C₃₁	1	2	yes	—
284	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
285	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
286	C₂²×C₄	—	2	1	no	—
287	C₂²×C₄	—	4	2	no	—
288	Q₁₆	—	2	2	no	—
289	Q₁₆	—	4	2	no	—
290	Q₁₆	—	8	1	no	—
291	Q₁₆	—	8	2	no	—
292	SD₁₆	Q₁₆×C₃₁	1	4	yes	complemented
293	C₂×C₈	—	2	2	no	—
294	C₂×C₈	—	2	1	no	—
295	C₂×C₈	—	2	1	no	—
296	C₂×C₈	—	2	1	no	—
297	C₂×C₈	—	4	2	no	—
298	C₂×C₈	C₂×D₄×C₃₁	1	1	yes	characteristic
299	C₂×C₈	C₂×D₄×C₃₁	1	1	yes	characteristic
300	C₂×C₈	C₂×D₄×C₃₁	1	1	yes	characteristic
301	C₂×C₈	C₂×D₄×C₃₁	1	1	yes	characteristic
302	C₄⋊C₄	—	2	2	no	—
303	C₄⋊C₄	—	2	1	no	—
304	C₄⋊C₄	—	2	2	no	—
305	C₄⋊C₄	—	2	2	no	—
306	C₄⋊C₄	—	2	2	no	—
307	C₄⋊C₄	—	2	2	no	—
308	C₄⋊C₄	—	4	2	no	—
309	C₄⋊C₄	—	4	2	no	—
310	C₄⋊C₄	—	4	2	no	—
311	C₄⋊C₄	—	4	2	no	—
312	C₄⋊C₄	—	4	2	no	—
313	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
314	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
315	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
316	C₂²⋊C₄	—	2	1	no	—
317	C₂²⋊C₄	—	4	2	no	—
318	C₄²	—	2	2	no	—
319	C₄²	—	2	1	no	—
320	C₄²	—	4	2	no	—
321	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
322	C₂³	—	2	1	no	—
323	Q₈	—	2	1	no	—
324	Q₈	—	2	2	no	—
325	Q₈	—	2	2	no	—
326	Q₈	—	4	2	no	—
327	Q₈	—	4	2	no	—
328	Q₈	—	8	2	no	—
329	Q₈	C₂×Q₁₆×C₃₁	1	2	yes	—
330	D₄	—	2	1	no	—
331	D₄	C₂×Q₁₆×C₃₁	1	2	yes	—
332	C₂×C₄	—	2	1	no	—
333	C₂×C₄	—	2	2	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	2	1	no	—
336	C₂×C₄	—	2	1	no	—
337	C₂×C₄	—	4	1	no	—
338	C₂×C₄	—	4	1	no	—
339	C₂×C₄	—	4	2	no	—
340	C₂×C₄	—	4	2	no	—
341	C₂×C₄	—	16	2	no	—
342	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
343	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
344	C₂×C₄	C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
345	C₈	—	2	1	no	—
346	C₈	—	2	1	no	—
347	C₈	—	4	1	no	—
348	C₈	—	4	1	no	—
349	C₈	—	4	1	no	—
350	C₈	—	4	2	no	—
351	C₈	C₂×Q₁₆×C₃₁	1	2	yes	—
352	C₈	C₃₁×#135	1	2	yes	—
353	C₂²	—	2	2	no	—
354	C₂²	—	4	1	no	—
355	C₂²	—	4	1	no	—
356	C₂²	D₄²×C₃₁	1	1	yes	characteristic
357	C₄	—	2	2	no	—
358	C₄	—	2	1	no	—
359	C₄	—	4	1	no	—
360	C₄	—	4	2	no	—
361	C₄	—	4	2	no	—
362	C₄	—	4	1	no	—
363	C₄	—	8	2	no	—
364	C₄	—	8	2	no	—
365	C₄	C₂²×Q₁₆×C₃₁	1	1	yes	characteristic
366	C₄	C₂×C₃₁×#135	1	1	yes	characteristic
367	C₄	C₃₁×#577	1	1	yes	characteristic
368	C₄	C₃₁×#578	1	1	yes	characteristic
369	C₂	—	4	2	no	—
370	C₂	C₃₁×#3284	1	1	yes	characteristic
371	C₂	D₄×Q₁₆×C₃₁	1	1	yes	characteristic
372	C₂	C₃₁×#3290	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×#3395	C₂	semidirect
4. C₃₁×#1707	C₂	semidirect
5. C₃₁×#1676	C₂	semidirect
6. C₃₁×#1672	C₂	semidirect
9. C₃₁×#1636	C₂	semidirect
10. C₈×Q₁₆×C₃₁	C₂	semidirect
105. SD₁₆×C₃₁	Q₁₆	semidirect
135. #20007	C₃₁	direct (N × H)
167. #3395	C₂×C₃₁	semidirect
170. #1707	C₂×C₃₁	semidirect
171. #1676	C₂×C₃₁	semidirect
172. #1672	C₂×C₃₁	semidirect
175. #1636	C₂×C₃₁	semidirect
176. C₈×Q₁₆	C₂×C₃₁	semidirect
280. C₃₁	#20007	direct (N × H)
292. SD₁₆	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×#3395	2
C₃₁×#3381	2
C₃₁×#3338	2
C₃₁×#1707	2
C₃₁×#1676	2
C₃₁×#1672	2
C₃₁×#1669	2
C₃₁×#1644	2
C₃₁×#1636	2
C₈×Q₁₆×C₃₁	2
C₈×SD₁₆×C₃₁	2
#20007	31

Subgroups — C31×#20007 #21476766

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#20007 #21476766