Subgroups — C₃₁×#20015 #21476774

Order 7936.

590 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3396	C₂	1	1	yes	maximal, characteristic
2	C₃₁×#3395	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3365	C₂	1	2	yes	maximal, complemented
4	C₃₁×#1709	C₂	1	1	yes	maximal, characteristic
5	C₃₁×#1682	C₂	1	2	yes	maximal, complemented
6	C₃₁×#1670	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#1668	C₂	1	1	yes	maximal, characteristic
8	C₃₁×#1640	C₂	1	2	yes	maximal, complemented
9	C₃₁×#1626	C₂	1	2	yes	maximal, complemented
10	C₈×Q₁₆×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×Q₁₆×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#559	C₂²	1	2	yes	—
13	C₃₁×#557	C₂²	1	2	yes	—
14	C₃₁×#495	—	2	1	no	—
15	C₃₁×#494	—	2	1	no	—
16	C₃₁×#494	C₂²	1	1	yes	characteristic
17	C₃₁×#493	C₂²	1	1	yes	characteristic
18	C₃₁×#488	—	2	2	no	—
19	C₃₁×#486	C₂²	1	2	yes	—
20	C₃₁×#486	C₂²	1	2	yes	—
21	C₃₁×#478	—	2	2	no	—
22	C₃₁×#475	C₂²	1	2	yes	—
23	C₃₁×#464	—	2	2	no	—
24	C₃₁×#463	—	2	2	no	—
25	C₃₁×#462	—	2	2	no	—
26	C₃₁×#462	C₂²	1	2	yes	—
27	C₃₁×#460	C₂²	1	2	yes	—
28	C₃₁×#460	C₂²	1	2	yes	—
29	C₈×Q₈×C₃₁	C₂²	1	2	yes	—
30	C₈×Q₈×C₃₁	C₂²	1	1	yes	characteristic
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×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
35	C₄×SD₁₆×C₃₁	—	2	2	no	—
36	C₄×D₈×C₃₁	—	2	1	no	—
37	C₃₁×#335	C₂²	1	1	yes	characteristic
38	C₃₁×#335	C₂²	1	1	yes	characteristic
39	C₃₁×#332	C₂²	1	2	yes	—
40	C₃₁×#331	C₂²	1	2	yes	—
41	C₃₁×Q₈⋊C₈	C₂²	1	1	yes	characteristic
42	C₃₁×Q₈⋊C₈	C₂²	1	2	yes	—
43	C₃₁×Q₈⋊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×Q₁₆×C₃₁	D₄	1	1	yes	characteristic
50	C₂×SD₁₆×C₃₁	—	2	2	no	—
51	C₂×SD₁₆×C₃₁	—	2	2	no	—
52	C₂×D₈×C₃₁	—	2	1	no	—
53	C₂×D₈×C₃₁	—	2	1	no	—
54	C₃₁×C₄⋊Q₈	—	2	2	no	—
55	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
56	C₃₁×#127	C₂³	1	2	yes	—
57	C₃₁×#125	—	2	2	no	—
58	C₃₁×#125	—	4	2	no	—
59	C₃₁×#124	—	2	2	no	—
60	C₃₁×#124	—	2	2	no	—
61	C₃₁×#123	—	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×Q₈×C₃₁	C₂³	1	1	yes	characteristic
67	C₄×D₄×C₃₁	—	2	2	no	—
68	C₄×D₄×C₃₁	—	2	2	no	—
69	C₃₁×#107	D₄	1	1	yes	characteristic
70	C₃₁×#107	D₄	1	1	yes	characteristic
71	C₃₁×#106	—	2	2	no	—
72	C₃₁×C₄⋊C₈	—	2	1	no	—
73	C₃₁×C₄⋊C₈	—	2	1	no	—
74	C₃₁×C₄⋊C₈	—	2	2	no	—
75	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
76	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
77	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
78	C₃₁×#103	—	2	2	no	—
79	C₃₁×#103	—	2	2	no	—
80	C₃₁×#103	D₄	1	1	yes	characteristic
81	C₃₁×#103	D₄	1	2	yes	—
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	—	2	2	no	—
87	C₃₁×#102	—	4	2	no	—
88	C₄×C₈×C₃₁	—	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	C₂×D₄	1	1	yes	characteristic
96	C₂×Q₈×C₃₁	C₂×D₄	1	2	yes	—
97	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
98	C₂×D₄×C₃₁	—	2	2	no	—
99	C₂×D₄×C₃₁	—	2	2	no	—
100	C₂×D₄×C₃₁	—	2	2	no	—
101	C₂²×C₄×C₃₁	—	4	2	no	—
102	Q₁₆×C₃₁	—	2	2	no	—
103	Q₁₆×C₃₁	—	2	2	no	—
104	Q₁₆×C₃₁	—	4	2	no	—
105	Q₁₆×C₃₁	—	8	1	no	—
106	Q₁₆×C₃₁	—	8	2	no	—
107	SD₁₆×C₃₁	—	4	4	no	—
108	SD₁₆×C₃₁	—	8	2	no	—
109	D₈×C₃₁	—	4	2	no	—
110	D₈×C₃₁	—	8	1	no	—
111	C₂×C₈×C₃₁	—	2	1	no	—
112	C₂×C₈×C₃₁	—	2	2	no	—
113	C₂×C₈×C₃₁	—	2	1	no	—
114	C₂×C₈×C₃₁	—	2	1	no	—
115	C₂×C₈×C₃₁	C₂×D₄	1	1	yes	characteristic
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	C₄⋊C₄×C₃₁	—	2	1	no	—
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	—	4	2	no	—
125	C₄⋊C₄×C₃₁	—	4	2	no	—
126	C₄⋊C₄×C₃₁	—	4	2	no	—
127	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
128	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
129	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
130	C₂²⋊C₄×C₃₁	—	4	2	no	—
131	C₂²⋊C₄×C₃₁	—	4	2	no	—
132	C₂²⋊C₄×C₃₁	—	4	2	no	—
133	C₄²×C₃₁	—	2	1	no	—
134	C₄²×C₃₁	—	2	2	no	—
135	C₄²×C₃₁	—	2	1	no	—
136	C₄²×C₃₁	—	4	2	no	—
137	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
138	#20015	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
139	C₂³×C₃₁	—	4	2	no	—
140	Q₈×C₃₁	—	2	1	no	—
141	Q₈×C₃₁	—	2	1	no	—
142	Q₈×C₃₁	—	2	2	no	—
143	Q₈×C₃₁	—	2	2	no	—
144	Q₈×C₃₁	—	2	1	no	—
145	Q₈×C₃₁	—	4	2	no	—
146	Q₈×C₃₁	—	4	2	no	—
147	Q₈×C₃₁	#135	1	2	yes	—
148	D₄×C₃₁	—	4	2	no	—
149	D₄×C₃₁	—	4	2	no	—
150	D₄×C₃₁	—	4	2	no	—
151	D₄×C₃₁	—	4	2	no	—
152	D₄×C₃₁	—	8	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	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	—	16	2	no	—
161	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
162	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
163	C₂×C₄×C₃₁	H(5,𝔽₂)	1	1	yes	characteristic
164	C₈×C₃₁	—	2	1	no	—
165	C₈×C₃₁	—	2	1	no	—
166	C₈×C₃₁	—	2	1	no	—
167	C₈×C₃₁	—	4	1	no	—
168	C₈×C₃₁	—	4	2	no	—
169	C₈×C₃₁	—	4	1	no	—
170	C₈×C₃₁	—	4	1	no	—
171	C₈×C₃₁	#135	1	2	yes	—
172	#3396	C₂×C₃₁	1	1	yes	characteristic
173	#3395	C₂×C₃₁	1	1	yes	characteristic, complemented
174	#3365	C₂×C₃₁	1	2	yes	complemented
175	#1709	C₂×C₃₁	1	1	yes	characteristic
176	#1682	C₂×C₃₁	1	2	yes	complemented
177	#1670	C₂×C₃₁	1	1	yes	characteristic, complemented
178	#1668	C₂×C₃₁	1	1	yes	characteristic
179	#1640	C₂×C₃₁	1	2	yes	complemented
180	#1626	C₂×C₃₁	1	2	yes	complemented
181	C₈×Q₁₆	C₂×C₃₁	1	1	yes	characteristic, complemented
182	C₈×Q₁₆	C₂×C₃₁	1	1	yes	characteristic, complemented
183	C₂²×C₃₁	—	8	2	no	—
184	C₂²×C₃₁	—	8	2	no	—
185	C₂²×C₃₁	—	8	2	no	—
186	C₂²×C₃₁	D₄²	1	1	yes	characteristic
187	C₄×C₃₁	—	2	2	no	—
188	C₄×C₃₁	—	2	1	no	—
189	C₄×C₃₁	—	4	1	no	—
190	C₄×C₃₁	—	4	2	no	—
191	C₄×C₃₁	—	4	1	no	—
192	C₄×C₃₁	—	4	2	no	—
193	C₄×C₃₁	—	4	1	no	—
194	C₄×C₃₁	—	8	2	no	—
195	C₄×C₃₁	C₂×#135	1	1	yes	characteristic
196	C₄×C₃₁	C₂×#135	1	1	yes	characteristic
197	C₄×C₃₁	#576	1	1	yes	characteristic
198	C₄×C₃₁	#578	1	1	yes	characteristic
199	#559	C₂²×C₃₁	1	2	yes	—
200	#557	C₂²×C₃₁	1	2	yes	—
201	#495	—	2	1	no	—
202	#494	—	2	1	no	—
203	#494	C₂²×C₃₁	1	1	yes	characteristic
204	#493	C₂²×C₃₁	1	1	yes	characteristic
205	#488	—	2	2	no	—
206	#486	C₂²×C₃₁	1	2	yes	—
207	#486	C₂²×C₃₁	1	2	yes	—
208	#478	—	2	2	no	—
209	#475	C₂²×C₃₁	1	2	yes	—
210	#464	—	2	2	no	—
211	#463	—	2	2	no	—
212	#462	—	2	2	no	—
213	#462	C₂²×C₃₁	1	2	yes	—
214	#460	C₂²×C₃₁	1	2	yes	—
215	#460	C₂²×C₃₁	1	2	yes	—
216	C₈×Q₈	C₂²×C₃₁	1	2	yes	—
217	C₈×Q₈	C₂²×C₃₁	1	1	yes	characteristic
218	C₈×Q₈	C₂²×C₃₁	1	1	yes	characteristic
219	C₄×Q₁₆	—	2	1	no	—
220	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
221	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
222	C₄×SD₁₆	—	2	2	no	—
223	C₄×D₈	—	2	1	no	—
224	#335	C₂²×C₃₁	1	1	yes	characteristic
225	#335	C₂²×C₃₁	1	1	yes	characteristic
226	#332	C₂²×C₃₁	1	2	yes	—
227	#331	C₂²×C₃₁	1	2	yes	—
228	Q₈⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
229	Q₈⋊C₈	C₂²×C₃₁	1	2	yes	—
230	Q₈⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
231	C₈²	C₂²×C₃₁	1	1	yes	characteristic
232	C₂×C₃₁	—	16	2	no	—
233	C₂×C₃₁	#3285	1	1	yes	characteristic
234	C₂×C₃₁	#3287	1	1	yes	characteristic
235	C₂×C₃₁	#3290	1	1	yes	characteristic
236	C₂×Q₁₆	—	2	2	no	—
237	C₂×Q₁₆	—	2	1	no	—
238	C₂×Q₁₆	—	2	1	no	—
239	C₂×Q₁₆	D₄×C₃₁	1	1	yes	characteristic
240	C₂×Q₁₆	D₄×C₃₁	1	1	yes	characteristic
241	C₂×SD₁₆	—	2	2	no	—
242	C₂×SD₁₆	—	2	2	no	—
243	C₂×D₈	—	2	1	no	—
244	C₂×D₈	—	2	1	no	—
245	C₄⋊Q₈	—	2	2	no	—
246	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
247	#127	C₂³×C₃₁	1	2	yes	—
248	#125	—	2	2	no	—
249	#125	—	4	2	no	—
250	#124	—	2	2	no	—
251	#124	—	2	2	no	—
252	#123	—	4	2	no	—
253	C₄×Q₈	—	2	2	no	—
254	C₄×Q₈	—	2	2	no	—
255	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
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	—	2	2	no	—
260	#107	D₄×C₃₁	1	1	yes	characteristic
261	#107	D₄×C₃₁	1	1	yes	characteristic
262	#106	—	2	2	no	—
263	C₄⋊C₈	—	2	1	no	—
264	C₄⋊C₈	—	2	1	no	—
265	C₄⋊C₈	—	2	2	no	—
266	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
267	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
268	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
269	#103	—	2	2	no	—
270	#103	—	2	2	no	—
271	#103	D₄×C₃₁	1	1	yes	characteristic
272	#103	D₄×C₃₁	1	2	yes	—
273	#103	D₄×C₃₁	1	1	yes	characteristic
274	#102	—	2	2	no	—
275	#102	—	2	2	no	—
276	#102	—	2	2	no	—
277	#102	—	2	2	no	—
278	#102	—	4	2	no	—
279	C₄×C₈	—	2	1	no	—
280	C₄×C₈	—	2	2	no	—
281	C₄×C₈	—	2	1	no	—
282	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
283	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
284	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
285	C₃₁	#20015	1	1	yes	characteristic, direct product factor, Sylow
286	C₂×Q₈	—	2	2	no	—
287	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
288	C₂×Q₈	C₂×D₄×C₃₁	1	2	yes	—
289	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
290	C₂×D₄	—	2	2	no	—
291	C₂×D₄	—	2	2	no	—
292	C₂×D₄	—	2	2	no	—
293	C₂²×C₄	—	4	2	no	—
294	Q₁₆	—	2	2	no	—
295	Q₁₆	—	2	2	no	—
296	Q₁₆	—	4	2	no	—
297	Q₁₆	—	8	1	no	—
298	Q₁₆	—	8	2	no	—
299	SD₁₆	—	4	4	no	—
300	SD₁₆	—	8	2	no	—
301	D₈	—	4	2	no	—
302	D₈	—	8	1	no	—
303	C₂×C₈	—	2	1	no	—
304	C₂×C₈	—	2	2	no	—
305	C₂×C₈	—	2	1	no	—
306	C₂×C₈	—	2	1	no	—
307	C₂×C₈	C₂×D₄×C₃₁	1	1	yes	characteristic
308	C₂×C₈	C₂×D₄×C₃₁	1	1	yes	characteristic
309	C₂×C₈	C₂×D₄×C₃₁	1	1	yes	characteristic
310	C₂×C₈	C₂×D₄×C₃₁	1	1	yes	characteristic
311	C₄⋊C₄	—	2	1	no	—
312	C₄⋊C₄	—	2	2	no	—
313	C₄⋊C₄	—	2	1	no	—
314	C₄⋊C₄	—	2	2	no	—
315	C₄⋊C₄	—	2	2	no	—
316	C₄⋊C₄	—	4	2	no	—
317	C₄⋊C₄	—	4	2	no	—
318	C₄⋊C₄	—	4	2	no	—
319	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
320	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
321	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
322	C₂²⋊C₄	—	4	2	no	—
323	C₂²⋊C₄	—	4	2	no	—
324	C₂²⋊C₄	—	4	2	no	—
325	C₄²	—	2	1	no	—
326	C₄²	—	2	2	no	—
327	C₄²	—	2	1	no	—
328	C₄²	—	4	2	no	—
329	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
330	C₂³	—	4	2	no	—
331	Q₈	—	2	1	no	—
332	Q₈	—	2	1	no	—
333	Q₈	—	2	2	no	—
334	Q₈	—	2	2	no	—
335	Q₈	—	2	1	no	—
336	Q₈	—	4	2	no	—
337	Q₈	—	4	2	no	—
338	Q₈	C₃₁×#135	1	2	yes	—
339	D₄	—	4	2	no	—
340	D₄	—	4	2	no	—
341	D₄	—	4	2	no	—
342	D₄	—	4	2	no	—
343	D₄	—	8	2	no	—
344	C₂×C₄	—	2	1	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	1	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	2	1	no	—
349	C₂×C₄	—	2	1	no	—
350	C₂×C₄	—	4	2	no	—
351	C₂×C₄	—	16	2	no	—
352	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
353	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
354	C₂×C₄	C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
355	C₈	—	2	1	no	—
356	C₈	—	2	1	no	—
357	C₈	—	2	1	no	—
358	C₈	—	4	1	no	—
359	C₈	—	4	2	no	—
360	C₈	—	4	1	no	—
361	C₈	—	4	1	no	—
362	C₈	C₃₁×#135	1	2	yes	—
363	C₂²	—	8	2	no	—
364	C₂²	—	8	2	no	—
365	C₂²	—	8	2	no	—
366	C₂²	D₄²×C₃₁	1	1	yes	characteristic
367	C₄	—	2	2	no	—
368	C₄	—	2	1	no	—
369	C₄	—	4	1	no	—
370	C₄	—	4	2	no	—
371	C₄	—	4	1	no	—
372	C₄	—	4	2	no	—
373	C₄	—	4	1	no	—
374	C₄	—	8	2	no	—
375	C₄	C₂×C₃₁×#135	1	1	yes	characteristic
376	C₄	C₂×C₃₁×#135	1	1	yes	characteristic
377	C₄	C₃₁×#576	1	1	yes	characteristic
378	C₄	C₃₁×#578	1	1	yes	characteristic
379	C₂	—	16	2	no	—
380	C₂	C₃₁×#3285	1	1	yes	characteristic
381	C₂	C₃₁×#3287	1	1	yes	characteristic
382	C₂	C₃₁×#3290	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	D₄²
commutator, Frattini, cosocle	C₄²	C₂⁴×C₃₁
prime radical	C₃₁×#493	C₂²
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
2. C₃₁×#3395	C₂	semidirect
3. C₃₁×#3365	C₂	semidirect
5. C₃₁×#1682	C₂	semidirect
6. C₃₁×#1670	C₂	semidirect
8. C₃₁×#1640	C₂	semidirect
9. C₃₁×#1626	C₂	semidirect
10. C₈×Q₁₆×C₃₁	C₂	semidirect
11. C₈×Q₁₆×C₃₁	C₂	semidirect
138. #20015	C₃₁	direct (N × H)
173. #3395	C₂×C₃₁	semidirect
174. #3365	C₂×C₃₁	semidirect
176. #1682	C₂×C₃₁	semidirect
177. #1670	C₂×C₃₁	semidirect
179. #1640	C₂×C₃₁	semidirect
180. #1626	C₂×C₃₁	semidirect
181. C₈×Q₁₆	C₂×C₃₁	semidirect
182. C₈×Q₁₆	C₂×C₃₁	semidirect
285. C₃₁	#20015	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×#3396	2
C₃₁×#3395	2
C₃₁×#3365	2
C₃₁×#1709	2
C₃₁×#1682	2
C₃₁×#1670	2
C₃₁×#1668	2
C₃₁×#1640	2
C₃₁×#1626	2
C₈×Q₁₆×C₃₁	2
#20015	31

Subgroups — C31×#20015 #21476774

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#20015 #21476774