Subgroups — C₃₁×#19957 #21476716

Order 7936.

584 conjugacy classes of subgroups.

The subgroup lattice has 382 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, complemented
2	C₃₁×#3357	C₂	1	2	yes	maximal, complemented
3	C₃₁×#3341	C₂	1	1	yes	maximal, characteristic
4	C₃₁×#1713	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#1695	C₂	1	2	yes	maximal, complemented
6	C₃₁×#1676	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#1675	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#1634	C₂	1	2	yes	maximal, complemented
9	C₃₁×#1632	C₂	1	2	yes	maximal, complemented
10	C₃₁×#1589	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×SD₁₆×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#555	C₂²	1	2	yes	—
13	C₃₁×#554	C₂²	1	2	yes	—
14	C₃₁×#500	C₂²	1	1	yes	characteristic
15	C₃₁×#500	C₂²	1	2	yes	—
16	C₃₁×#500	C₂²	1	1	yes	characteristic
17	C₃₁×#499	—	2	1	no	—
18	C₃₁×#494	C₂²	1	2	yes	—
19	C₃₁×#485	—	2	2	no	—
20	C₃₁×#482	—	2	2	no	—
21	C₃₁×#480	—	2	2	no	—
22	C₃₁×#478	—	2	2	no	—
23	C₃₁×#477	C₂²	1	2	yes	—
24	C₃₁×#476	C₂²	1	2	yes	—
25	C₃₁×#476	C₂²	1	2	yes	—
26	C₃₁×#476	C₂²	1	2	yes	—
27	C₃₁×#468	—	2	2	no	—
28	C₃₁×#466	—	2	1	no	—
29	C₈×Q₈×C₃₁	C₂²	1	1	yes	characteristic
30	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
31	C₄×D₈×C₃₁	—	2	1	no	—
32	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic
33	C₃₁×#436	C₂²	1	2	yes	—
34	C₈×D₄×C₃₁	C₂²	1	1	yes	characteristic
35	C₃₁×#428	—	2	2	no	—
36	C₃₁×#427	—	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×#333	C₂²	1	2	yes	—
41	C₃₁×Q₈⋊C₈	C₂²	1	1	yes	characteristic
42	C₃₁×D₄⋊C₈	C₂²	1	1	yes	characteristic
43	C₃₁×D₄⋊C₈	C₂²	1	2	yes	—
44	C₈²×C₃₁	C₂²	1	1	yes	characteristic
45	C₂×Q₁₆×C₃₁	—	4	2	no	—
46	C₂×SD₁₆×C₃₁	D₄	1	1	yes	characteristic
47	C₂×D₈×C₃₁	D₄	1	1	yes	characteristic
48	C₂×M₁₆×C₃₁	—	2	2	no	—
49	C₂²×C₈×C₃₁	—	2	1	no	—
50	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
51	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
52	C₃₁×#125	—	2	2	no	—
53	C₃₁×#124	—	4	2	no	—
54	C₃₁×C₂²⋊Q₈	—	2	2	no	—
55	C₃₁×C₂²⋊Q₈	—	4	2	no	—
56	C₃₁×#121	—	2	2	no	—
57	C₃₁×#121	—	2	2	no	—
58	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
59	C₄×D₄×C₃₁	—	2	2	no	—
60	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
61	C₄×D₄×C₃₁	C₂³	1	2	yes	—
62	C₃₁×#117	—	2	2	no	—
63	C₃₁×#117	—	2	2	no	—
64	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
65	C₃₁×#107	—	2	1	no	—
66	C₃₁×#107	—	2	2	no	—
67	C₃₁×#107	—	2	1	no	—
68	C₃₁×#107	—	2	1	no	—
69	C₃₁×#107	—	2	2	no	—
70	C₃₁×#107	—	2	1	no	—
71	C₃₁×#107	—	2	2	no	—
72	C₃₁×#107	D₄	1	1	yes	characteristic
73	C₃₁×#106	—	2	2	no	—
74	C₃₁×#106	—	2	2	no	—
75	C₃₁×#106	—	2	2	no	—
76	C₃₁×#106	D₄	1	1	yes	characteristic
77	C₃₁×C₄⋊C₈	—	2	1	no	—
78	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
79	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
80	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
81	C₃₁×#103	—	2	2	no	—
82	C₃₁×#103	D₄	1	1	yes	characteristic
83	C₃₁×#102	—	2	2	no	—
84	C₃₁×#102	—	2	2	no	—
85	C₃₁×#102	—	2	2	no	—
86	C₃₁×#102	D₄	1	2	yes	—
87	C₃₁×#102	D₄	1	1	yes	characteristic
88	C₃₁×C₂²⋊C₈	—	2	1	no	—
89	C₃₁×C₂²⋊C₈	—	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	1	yes	characteristic
97	C₂×D₄×C₃₁	—	4	2	no	—
98	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
99	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₃₁	—	2	2	no	—
101	C₂²×C₄×C₃₁	—	2	1	no	—
102	C₂²×C₄×C₃₁	—	4	2	no	—
103	Q₁₆×C₃₁	—	8	4	no	—
104	SD₁₆×C₃₁	—	2	2	no	—
105	D₈×C₃₁	—	2	2	no	—
106	M₁₆×C₃₁	—	4	4	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	—	2	2	no	—
111	C₂×C₈×C₃₁	—	4	2	no	—
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	C₂×C₈×C₃₁	C₂×D₄	1	1	yes	characteristic
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	C₂×D₄	1	2	yes	—
124	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
125	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
126	C₂²⋊C₄×C₃₁	—	2	2	no	—
127	C₂²⋊C₄×C₃₁	—	2	1	no	—
128	C₂²⋊C₄×C₃₁	—	4	2	no	—
129	C₂²⋊C₄×C₃₁	—	4	2	no	—
130	C₂²⋊C₄×C₃₁	—	4	2	no	—
131	C₄²×C₃₁	—	2	1	no	—
132	C₄²×C₃₁	—	4	2	no	—
133	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
134	#19957	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
135	C₂³×C₃₁	—	2	2	no	—
136	C₂³×C₃₁	—	2	1	no	—
137	Q₈×C₃₁	—	2	1	no	—
138	Q₈×C₃₁	—	2	1	no	—
139	Q₈×C₃₁	—	8	2	no	—
140	Q₈×C₃₁	—	8	2	no	—
141	D₄×C₃₁	—	2	1	no	—
142	D₄×C₃₁	—	2	2	no	—
143	D₄×C₃₁	—	2	2	no	—
144	D₄×C₃₁	—	2	1	no	—
145	D₄×C₃₁	—	16	2	no	—
146	C₂×C₄×C₃₁	—	2	1	no	—
147	C₂×C₄×C₃₁	—	2	1	no	—
148	C₂×C₄×C₃₁	—	2	1	no	—
149	C₂×C₄×C₃₁	—	2	2	no	—
150	C₂×C₄×C₃₁	—	4	2	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	—	4	2	no	—
156	C₂×C₄×C₃₁	—	16	2	no	—
157	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
158	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
159	C₂×C₄×C₃₁	H(5,𝔽₂)	1	1	yes	characteristic
160	C₈×C₃₁	—	2	2	no	—
161	C₈×C₃₁	—	2	1	no	—
162	C₈×C₃₁	—	2	1	no	—
163	C₈×C₃₁	—	4	2	no	—
164	C₈×C₃₁	—	4	1	no	—
165	C₈×C₃₁	—	4	1	no	—
166	C₈×C₃₁	#135	1	2	yes	—
167	C₈×C₃₁	#137	1	2	yes	—
168	#3380	C₂×C₃₁	1	1	yes	characteristic, complemented
169	#3357	C₂×C₃₁	1	2	yes	complemented
170	#3341	C₂×C₃₁	1	1	yes	characteristic
171	#1713	C₂×C₃₁	1	1	yes	characteristic, complemented
172	#1695	C₂×C₃₁	1	2	yes	complemented
173	#1676	C₂×C₃₁	1	1	yes	characteristic, complemented
174	#1675	C₂×C₃₁	1	1	yes	characteristic, complemented
175	#1634	C₂×C₃₁	1	2	yes	complemented
176	#1632	C₂×C₃₁	1	2	yes	complemented
177	#1589	C₂×C₃₁	1	1	yes	characteristic, complemented
178	C₈×SD₁₆	C₂×C₃₁	1	1	yes	characteristic, complemented
179	C₂²×C₃₁	—	4	1	no	—
180	C₂²×C₃₁	—	4	2	no	—
181	C₂²×C₃₁	—	4	2	no	—
182	C₂²×C₃₁	—	4	1	no	—
183	C₂²×C₃₁	—	4	2	no	—
184	C₂²×C₃₁	—	4	1	no	—
185	C₂²×C₃₁	D₄²	1	1	yes	characteristic
186	C₄×C₃₁	—	2	1	no	—
187	C₄×C₃₁	—	4	1	no	—
188	C₄×C₃₁	—	4	2	no	—
189	C₄×C₃₁	—	4	1	no	—
190	C₄×C₃₁	—	4	1	no	—
191	C₄×C₃₁	—	8	2	no	—
192	C₄×C₃₁	—	8	2	no	—
193	C₄×C₃₁	C₂×#135	1	1	yes	characteristic
194	C₄×C₃₁	C₂×#137	1	1	yes	characteristic
195	C₄×C₃₁	#578	1	1	yes	characteristic
196	C₄×C₃₁	#578	1	1	yes	characteristic
197	#555	C₂²×C₃₁	1	2	yes	—
198	#554	C₂²×C₃₁	1	2	yes	—
199	#500	C₂²×C₃₁	1	1	yes	characteristic
200	#500	C₂²×C₃₁	1	2	yes	—
201	#500	C₂²×C₃₁	1	1	yes	characteristic
202	#499	—	2	1	no	—
203	#494	C₂²×C₃₁	1	2	yes	—
204	#485	—	2	2	no	—
205	#482	—	2	2	no	—
206	#480	—	2	2	no	—
207	#478	—	2	2	no	—
208	#477	C₂²×C₃₁	1	2	yes	—
209	#476	C₂²×C₃₁	1	2	yes	—
210	#476	C₂²×C₃₁	1	2	yes	—
211	#476	C₂²×C₃₁	1	2	yes	—
212	#468	—	2	2	no	—
213	#466	—	2	1	no	—
214	C₈×Q₈	C₂²×C₃₁	1	1	yes	characteristic
215	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
216	C₄×D₈	—	2	1	no	—
217	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic
218	#436	C₂²×C₃₁	1	2	yes	—
219	C₈×D₄	C₂²×C₃₁	1	1	yes	characteristic
220	#428	—	2	2	no	—
221	#427	—	2	1	no	—
222	#335	C₂²×C₃₁	1	1	yes	characteristic
223	#334	C₂²×C₃₁	1	1	yes	characteristic
224	#333	C₂²×C₃₁	1	2	yes	—
225	#333	C₂²×C₃₁	1	2	yes	—
226	Q₈⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
227	D₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
228	D₄⋊C₈	C₂²×C₃₁	1	2	yes	—
229	C₈²	C₂²×C₃₁	1	1	yes	characteristic
230	C₂×C₃₁	—	8	1	no	—
231	C₂×C₃₁	—	8	2	no	—
232	C₂×C₃₁	#3276	1	1	yes	characteristic
233	C₂×C₃₁	#3283	1	1	yes	characteristic
234	C₂×C₃₁	#3292	1	1	yes	characteristic
235	C₂×Q₁₆	—	4	2	no	—
236	C₂×SD₁₆	D₄×C₃₁	1	1	yes	characteristic
237	C₂×D₈	D₄×C₃₁	1	1	yes	characteristic
238	C₂×M₁₆	—	2	2	no	—
239	C₂²×C₈	—	2	1	no	—
240	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
241	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
242	#125	—	2	2	no	—
243	#124	—	4	2	no	—
244	C₂²⋊Q₈	—	2	2	no	—
245	C₂²⋊Q₈	—	4	2	no	—
246	#121	—	2	2	no	—
247	#121	—	2	2	no	—
248	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
249	C₄×D₄	—	2	2	no	—
250	C₄×D₄	C₂³×C₃₁	1	2	yes	—
251	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
252	#117	—	2	2	no	—
253	#117	—	2	2	no	—
254	C₂×C₄⋊C₄	—	2	2	no	—
255	#107	—	2	1	no	—
256	#107	—	2	2	no	—
257	#107	—	2	1	no	—
258	#107	—	2	1	no	—
259	#107	—	2	2	no	—
260	#107	—	2	1	no	—
261	#107	—	2	2	no	—
262	#107	D₄×C₃₁	1	1	yes	characteristic
263	#106	—	2	2	no	—
264	#106	—	2	2	no	—
265	#106	—	2	2	no	—
266	#106	D₄×C₃₁	1	1	yes	characteristic
267	C₄⋊C₈	—	2	1	no	—
268	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
269	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
270	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
271	#103	—	2	2	no	—
272	#103	D₄×C₃₁	1	1	yes	characteristic
273	#102	—	2	2	no	—
274	#102	—	2	2	no	—
275	#102	—	2	2	no	—
276	#102	D₄×C₃₁	1	2	yes	—
277	#102	D₄×C₃₁	1	1	yes	characteristic
278	C₂²⋊C₈	—	2	1	no	—
279	C₂²⋊C₈	—	2	2	no	—
280	C₄×C₈	—	2	1	no	—
281	C₄×C₈	C₂³×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	#19957	1	1	yes	characteristic, direct product factor, Sylow
285	C₂×Q₈	—	2	2	no	—
286	C₂×Q₈	—	2	2	no	—
287	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
288	C₂×D₄	—	4	2	no	—
289	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
290	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
291	C₂²×C₄	—	2	2	no	—
292	C₂²×C₄	—	2	1	no	—
293	C₂²×C₄	—	4	2	no	—
294	Q₁₆	—	8	4	no	—
295	SD₁₆	—	2	2	no	—
296	D₈	—	2	2	no	—
297	M₁₆	—	4	4	no	—
298	C₂×C₈	—	2	1	no	—
299	C₂×C₈	—	2	1	no	—
300	C₂×C₈	—	2	1	no	—
301	C₂×C₈	—	2	2	no	—
302	C₂×C₈	—	4	2	no	—
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	C₂×C₈	C₂×D₄×C₃₁	1	1	yes	characteristic
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	C₂×D₄×C₃₁	1	2	yes	—
315	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
316	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
317	C₂²⋊C₄	—	2	2	no	—
318	C₂²⋊C₄	—	2	1	no	—
319	C₂²⋊C₄	—	4	2	no	—
320	C₂²⋊C₄	—	4	2	no	—
321	C₂²⋊C₄	—	4	2	no	—
322	C₄²	—	2	1	no	—
323	C₄²	—	4	2	no	—
324	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
325	C₂³	—	2	2	no	—
326	C₂³	—	2	1	no	—
327	Q₈	—	2	1	no	—
328	Q₈	—	2	1	no	—
329	Q₈	—	8	2	no	—
330	Q₈	—	8	2	no	—
331	D₄	—	2	1	no	—
332	D₄	—	2	2	no	—
333	D₄	—	2	2	no	—
334	D₄	—	2	1	no	—
335	D₄	—	16	2	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	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	—	16	2	no	—
347	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
348	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
349	C₂×C₄	C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
350	C₈	—	2	2	no	—
351	C₈	—	2	1	no	—
352	C₈	—	2	1	no	—
353	C₈	—	4	2	no	—
354	C₈	—	4	1	no	—
355	C₈	—	4	1	no	—
356	C₈	C₃₁×#135	1	2	yes	—
357	C₈	C₃₁×#137	1	2	yes	—
358	C₂²	—	4	1	no	—
359	C₂²	—	4	2	no	—
360	C₂²	—	4	2	no	—
361	C₂²	—	4	1	no	—
362	C₂²	—	4	2	no	—
363	C₂²	—	4	1	no	—
364	C₂²	D₄²×C₃₁	1	1	yes	characteristic
365	C₄	—	2	1	no	—
366	C₄	—	4	1	no	—
367	C₄	—	4	2	no	—
368	C₄	—	4	1	no	—
369	C₄	—	4	1	no	—
370	C₄	—	8	2	no	—
371	C₄	—	8	2	no	—
372	C₄	C₂×C₃₁×#135	1	1	yes	characteristic
373	C₄	C₂×C₃₁×#137	1	1	yes	characteristic
374	C₄	C₃₁×#578	1	1	yes	characteristic
375	C₄	C₃₁×#578	1	1	yes	characteristic
376	C₂	—	8	1	no	—
377	C₂	—	8	2	no	—
378	C₂	C₃₁×#3276	1	1	yes	characteristic
379	C₂	C₃₁×#3283	1	1	yes	characteristic
380	C₂	C₃₁×#3292	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	D₄²
commutator, Frattini, cosocle	C₄²	C₂⁴×C₃₁
prime radical	C₃₁×#3341	C₂
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×#3380	C₂	semidirect
2. C₃₁×#3357	C₂	semidirect
4. C₃₁×#1713	C₂	semidirect
5. C₃₁×#1695	C₂	semidirect
6. C₃₁×#1676	C₂	semidirect
7. C₃₁×#1675	C₂	semidirect
8. C₃₁×#1634	C₂	semidirect
9. C₃₁×#1632	C₂	semidirect
10. C₃₁×#1589	C₂	semidirect
11. C₈×SD₁₆×C₃₁	C₂	semidirect
134. #19957	C₃₁	direct (N × H)
168. #3380	C₂×C₃₁	semidirect
169. #3357	C₂×C₃₁	semidirect
171. #1713	C₂×C₃₁	semidirect
172. #1695	C₂×C₃₁	semidirect
173. #1676	C₂×C₃₁	semidirect
174. #1675	C₂×C₃₁	semidirect
175. #1634	C₂×C₃₁	semidirect
176. #1632	C₂×C₃₁	semidirect
177. #1589	C₂×C₃₁	semidirect
178. C₈×SD₁₆	C₂×C₃₁	semidirect
284. C₃₁	#19957	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×#3380	2
C₃₁×#3357	2
C₃₁×#3341	2
C₃₁×#1713	2
C₃₁×#1695	2
C₃₁×#1676	2
C₃₁×#1675	2
C₃₁×#1634	2
C₃₁×#1632	2
C₃₁×#1589	2
C₈×SD₁₆×C₃₁	2
#19957	31

Subgroups — C31×#19957 #21476716

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#19957 #21476716