Subgroups — C₃₁×#19258 #21476017

Order 7936.

738 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3169	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3109	C₂	1	2	yes	maximal, complemented
3	C₂×C₈×D₄×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#1677	C₂	1	4	yes	maximal, complemented
5	C₃₁×#1675	C₂	1	2	yes	maximal, complemented
6	C₃₁×#1667	C₂	1	2	yes	maximal, complemented
7	C₃₁×#1568	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#1551	C₂	1	2	yes	maximal, complemented
9	C₂³×C₈×C₃₁	—	2	1	no	—
10	C₃₁×#532	C₂²	1	2	yes	—
11	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
12	C₃₁×#500	C₂²	1	1	yes	characteristic, complemented
13	C₃₁×#493	C₂²	1	1	yes	characteristic, complemented
14	C₃₁×#486	C₂²	1	2	yes	complemented
15	C₃₁×#481	—	2	2	no	—
16	C₃₁×#476	C₂²	1	4	yes	—
17	C₃₁×#466	—	2	1	no	—
18	C₃₁×#466	—	2	1	no	—
19	C₃₁×#459	C₂²	1	4	yes	—
20	C₃₁×#447	—	2	2	no	—
21	C₃₁×#442	—	2	4	no	—
22	C₄×D₈×C₃₁	—	2	1	no	—
23	C₄×D₈×C₃₁	—	2	1	no	—
24	C₈×D₄×C₃₁	—	2	1	no	—
25	C₈×D₄×C₃₁	—	2	1	no	—
26	C₈×D₄×C₃₁	C₂²	1	2	yes	—
27	C₈×D₄×C₃₁	C₂²	1	2	yes	—
28	C₃₁×#432	C₂²	1	2	yes	—
29	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
30	C₂×C₃₁×C₂²⋊C₈	—	2	1	no	—
31	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
32	C₃₁×#335	C₂²	1	2	yes	complemented
33	C₃₁×#334	C₂²	1	2	yes	complemented
34	C₃₁×#333	C₂²	1	4	yes	complemented
35	C₃₁×#331	C₂²	1	4	yes	complemented
36	C₂×#41×C₃₁	—	2	2	no	—
37	C₂²×D₄×C₃₁	D₄	1	1	yes	characteristic
38	C₂³×C₄×C₃₁	—	2	1	no	—
39	C₂×D₈×C₃₁	—	2	4	no	—
40	C₂×D₈×C₃₁	—	2	1	no	—
41	C₂×D₈×C₃₁	—	2	1	no	—
42	C₂²×C₈×C₃₁	—	2	1	no	—
43	C₂²×C₈×C₃₁	—	2	2	no	—
44	C₂²×C₈×C₃₁	—	2	2	no	—
45	C₂²×C₈×C₃₁	—	4	4	no	—
46	C₂²×C₈×C₃₁	D₄	1	1	yes	characteristic
47	C₂²×C₈×C₃₁	D₄	1	1	yes	characteristic
48	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
49	C₃₁×#127	C₂³	1	2	yes	—
50	C₃₁×#124	—	2	2	no	—
51	C₃₁×#121	—	2	2	no	—
52	C₃₁×#121	—	2	2	no	—
53	C₄×D₄×C₃₁	—	2	1	no	—
54	C₄×D₄×C₃₁	—	2	2	no	—
55	C₄×D₄×C₃₁	—	2	2	no	—
56	C₄×D₄×C₃₁	—	2	1	no	—
57	C₄×D₄×C₃₁	D₄	1	2	yes	—
58	C₄×D₄×C₃₁	C₂³	1	2	yes	—
59	C₂×C₄⋊C₄×C₃₁	D₄	1	1	yes	characteristic
60	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
61	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
62	C₃₁×#107	—	2	1	no	—
63	C₃₁×#107	—	2	1	no	—
64	C₃₁×#106	—	2	4	no	—
65	C₃₁×C₄⋊C₈	—	2	1	no	—
66	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
67	C₃₁×C₄⋊C₈	C₂³	1	4	yes	—
68	C₃₁×#102	—	2	4	no	—
69	C₃₁×#102	—	2	2	no	—
70	C₃₁×#102	—	2	2	no	—
71	C₃₁×#102	—	2	4	no	—
72	C₃₁×C₂²⋊C₈	—	2	2	no	—
73	C₃₁×C₂²⋊C₈	—	2	2	no	—
74	C₃₁×C₂²⋊C₈	—	2	2	no	—
75	C₃₁×#97	—	2	2	no	—
76	C₄×C₈×C₃₁	D₄	1	1	yes	characteristic
77	C₄×C₈×C₃₁	D₄	1	1	yes	characteristic
78	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
79	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
80	C₂⁴×C₃₁	—	2	1	no	—
81	#41×C₃₁	—	8	4	no	—
82	C₂×Q₈×C₃₁	—	2	2	no	—
83	C₂×D₄×C₃₁	—	2	4	no	—
84	C₂×D₄×C₃₁	—	2	1	no	—
85	C₂×D₄×C₃₁	—	2	2	no	—
86	C₂×D₄×C₃₁	—	2	2	no	—
87	C₂×D₄×C₃₁	—	2	2	no	—
88	C₂×D₄×C₃₁	—	4	2	no	—
89	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
90	C₂²×C₄×C₃₁	—	2	1	no	—
91	C₂²×C₄×C₃₁	—	2	2	no	—
92	C₂²×C₄×C₃₁	—	2	2	no	—
93	C₂²×C₄×C₃₁	—	4	2	no	—
94	C₂²×C₄×C₃₁	—	4	2	no	—
95	C₂²×C₄×C₃₁	—	4	2	no	—
96	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
97	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₃₁	#41	1	1	yes	characteristic
99	D₈×C₃₁	—	4	2	no	—
100	D₈×C₃₁	—	4	8	no	—
101	D₈×C₃₁	—	4	2	no	—
102	C₂×C₈×C₃₁	—	2	2	no	—
103	C₂×C₈×C₃₁	—	2	4	no	—
104	C₂×C₈×C₃₁	—	2	2	no	—
105	C₂×C₈×C₃₁	—	4	1	no	—
106	C₂×C₈×C₃₁	—	4	4	no	—
107	C₂×C₈×C₃₁	—	4	2	no	—
108	C₂×C₈×C₃₁	—	4	4	no	—
109	C₂×C₈×C₃₁	C₂×D₄	1	1	yes	characteristic
110	C₂×C₈×C₃₁	C₂×D₄	1	1	yes	characteristic
111	C₂×C₈×C₃₁	C₂×D₄	1	1	yes	characteristic
112	C₂×C₈×C₃₁	C₂×D₄	1	1	yes	characteristic
113	C₄⋊C₄×C₃₁	—	2	1	no	—
114	C₄⋊C₄×C₃₁	—	2	2	no	—
115	C₄⋊C₄×C₃₁	—	2	2	no	—
116	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
117	C₂²⋊C₄×C₃₁	—	2	2	no	—
118	C₂²⋊C₄×C₃₁	—	2	2	no	—
119	C₂²⋊C₄×C₃₁	—	4	2	no	—
120	C₂²⋊C₄×C₃₁	—	4	2	no	—
121	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
122	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
123	C₄²×C₃₁	#41	1	1	yes	characteristic
124	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
125	#19258	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
126	C₂³×C₃₁	—	2	4	no	—
127	C₂³×C₃₁	—	2	2	no	—
128	C₂³×C₃₁	—	4	2	no	—
129	C₂³×C₃₁	—	4	2	no	—
130	C₂³×C₃₁	—	4	2	no	—
131	C₂³×C₃₁	#121	1	1	yes	characteristic
132	Q₈×C₃₁	—	8	2	no	—
133	D₄×C₃₁	—	2	4	no	—
134	D₄×C₃₁	—	2	2	no	—
135	D₄×C₃₁	—	4	4	no	—
136	D₄×C₃₁	—	4	2	no	—
137	D₄×C₃₁	—	4	2	no	—
138	D₄×C₃₁	—	8	2	no	—
139	D₄×C₃₁	—	8	4	no	—
140	D₄×C₃₁	#135	1	4	yes	—
141	C₂×C₄×C₃₁	—	2	2	no	—
142	C₂×C₄×C₃₁	—	2	2	no	—
143	C₂×C₄×C₃₁	—	2	1	no	—
144	C₂×C₄×C₃₁	—	2	1	no	—
145	C₂×C₄×C₃₁	—	2	2	no	—
146	C₂×C₄×C₃₁	—	4	4	no	—
147	C₂×C₄×C₃₁	—	4	2	no	—
148	C₂×C₄×C₃₁	—	4	2	no	—
149	C₂×C₄×C₃₁	—	4	2	no	—
150	C₂×C₄×C₃₁	—	4	2	no	—
151	C₂×C₄×C₃₁	—	8	4	no	—
152	C₂×C₄×C₃₁	#121	1	1	yes	characteristic
153	C₂×C₄×C₃₁	#121	1	1	yes	characteristic
154	C₂×C₄×C₃₁	#121	1	1	yes	characteristic
155	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
156	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
157	C₂×C₄×C₃₁	C₂×#41	1	1	yes	characteristic
158	C₈×C₃₁	—	2	1	no	—
159	C₈×C₃₁	—	2	1	no	—
160	C₈×C₃₁	—	2	1	no	—
161	C₈×C₃₁	—	4	4	no	—
162	C₈×C₃₁	—	4	2	no	—
163	C₈×C₃₁	AGL(1,ℤ/8)	1	2	yes	—
164	#3169	C₂×C₃₁	1	1	yes	characteristic, complemented
165	#3109	C₂×C₃₁	1	2	yes	complemented
166	C₂×C₈×D₄	C₂×C₃₁	1	1	yes	characteristic, complemented
167	#1677	C₂×C₃₁	1	4	yes	complemented
168	#1675	C₂×C₃₁	1	2	yes	complemented
169	#1667	C₂×C₃₁	1	2	yes	complemented
170	#1568	C₂×C₃₁	1	1	yes	characteristic, complemented
171	#1551	C₂×C₃₁	1	2	yes	complemented
172	C₂²×C₃₁	—	2	1	no	—
173	C₂²×C₃₁	—	2	1	no	—
174	C₂²×C₃₁	—	2	4	no	—
175	C₂²×C₃₁	—	4	8	no	—
176	C₂²×C₃₁	—	4	2	no	—
177	C₂²×C₃₁	—	4	2	no	—
178	C₂²×C₃₁	—	8	2	no	—
179	C₂²×C₃₁	—	8	2	no	—
180	C₂²×C₃₁	—	8	2	no	—
181	C₂²×C₃₁	#472	1	2	yes	—
182	C₂²×C₃₁	C₂×#121	1	1	yes	characteristic
183	C₄×C₃₁	—	2	1	no	—
184	C₄×C₃₁	—	2	1	no	—
185	C₄×C₃₁	—	2	1	no	—
186	C₄×C₃₁	—	2	1	no	—
187	C₄×C₃₁	—	4	2	no	—
188	C₄×C₃₁	—	8	2	no	—
189	C₄×C₃₁	C₂×#135	1	2	yes	—
190	C₄×C₃₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
191	C₄×C₃₁	#575	1	1	yes	characteristic
192	C₂³×C₈	—	2	1	no	—
193	#532	C₂²×C₃₁	1	2	yes	—
194	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
195	#500	C₂²×C₃₁	1	1	yes	characteristic, complemented
196	#493	C₂²×C₃₁	1	1	yes	characteristic, complemented
197	#486	C₂²×C₃₁	1	2	yes	complemented
198	#481	—	2	2	no	—
199	#476	C₂²×C₃₁	1	4	yes	—
200	#466	—	2	1	no	—
201	#466	—	2	1	no	—
202	#459	C₂²×C₃₁	1	4	yes	—
203	#447	—	2	2	no	—
204	#442	—	2	4	no	—
205	C₄×D₈	—	2	1	no	—
206	C₄×D₈	—	2	1	no	—
207	C₈×D₄	—	2	1	no	—
208	C₈×D₄	—	2	1	no	—
209	C₈×D₄	C₂²×C₃₁	1	2	yes	—
210	C₈×D₄	C₂²×C₃₁	1	2	yes	—
211	#432	C₂²×C₃₁	1	2	yes	—
212	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
213	C₂×C₂²⋊C₈	—	2	1	no	—
214	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
215	#335	C₂²×C₃₁	1	2	yes	complemented
216	#334	C₂²×C₃₁	1	2	yes	complemented
217	#333	C₂²×C₃₁	1	4	yes	complemented
218	#331	C₂²×C₃₁	1	4	yes	complemented
219	C₂×C₃₁	—	2	2	no	—
220	C₂×C₃₁	—	4	4	no	—
221	C₂×C₃₁	—	16	2	no	—
222	C₂×C₃₁	#3036	1	1	yes	characteristic
223	C₂×C₃₁	#3050	1	1	yes	characteristic
224	C₂×C₃₁	C₂×#472	1	1	yes	characteristic
225	C₂×#41	—	2	2	no	—
226	C₂²×D₄	D₄×C₃₁	1	1	yes	characteristic
227	C₂³×C₄	—	2	1	no	—
228	C₂×D₈	—	2	4	no	—
229	C₂×D₈	—	2	1	no	—
230	C₂×D₈	—	2	1	no	—
231	C₂²×C₈	—	2	1	no	—
232	C₂²×C₈	—	2	2	no	—
233	C₂²×C₈	—	2	2	no	—
234	C₂²×C₈	—	4	4	no	—
235	C₂²×C₈	D₄×C₃₁	1	1	yes	characteristic
236	C₂²×C₈	D₄×C₃₁	1	1	yes	characteristic
237	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
238	#127	C₂³×C₃₁	1	2	yes	—
239	#124	—	2	2	no	—
240	#121	—	2	2	no	—
241	#121	—	2	2	no	—
242	C₄×D₄	—	2	1	no	—
243	C₄×D₄	—	2	2	no	—
244	C₄×D₄	—	2	2	no	—
245	C₄×D₄	—	2	1	no	—
246	C₄×D₄	D₄×C₃₁	1	2	yes	—
247	C₄×D₄	C₂³×C₃₁	1	2	yes	—
248	C₂×C₄⋊C₄	D₄×C₃₁	1	1	yes	characteristic
249	C₂×C₂²⋊C₄	—	2	1	no	—
250	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
251	#107	—	2	1	no	—
252	#107	—	2	1	no	—
253	#106	—	2	4	no	—
254	C₄⋊C₈	—	2	1	no	—
255	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
256	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
257	#102	—	2	4	no	—
258	#102	—	2	2	no	—
259	#102	—	2	2	no	—
260	#102	—	2	4	no	—
261	C₂²⋊C₈	—	2	2	no	—
262	C₂²⋊C₈	—	2	2	no	—
263	C₂²⋊C₈	—	2	2	no	—
264	#97	—	2	2	no	—
265	C₄×C₈	D₄×C₃₁	1	1	yes	characteristic
266	C₄×C₈	D₄×C₃₁	1	1	yes	characteristic
267	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
268	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
269	C₃₁	#19258	1	1	yes	characteristic, direct product factor, Sylow
270	C₂⁴	—	2	1	no	—
271	#41	—	8	4	no	—
272	C₂×Q₈	—	2	2	no	—
273	C₂×D₄	—	2	4	no	—
274	C₂×D₄	—	2	1	no	—
275	C₂×D₄	—	2	2	no	—
276	C₂×D₄	—	2	2	no	—
277	C₂×D₄	—	2	2	no	—
278	C₂×D₄	—	4	2	no	—
279	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
280	C₂²×C₄	—	2	1	no	—
281	C₂²×C₄	—	2	2	no	—
282	C₂²×C₄	—	2	2	no	—
283	C₂²×C₄	—	4	2	no	—
284	C₂²×C₄	—	4	2	no	—
285	C₂²×C₄	—	4	2	no	—
286	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
287	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
288	C₂²×C₄	#41×C₃₁	1	1	yes	characteristic
289	D₈	—	4	2	no	—
290	D₈	—	4	8	no	—
291	D₈	—	4	2	no	—
292	C₂×C₈	—	2	2	no	—
293	C₂×C₈	—	2	4	no	—
294	C₂×C₈	—	2	2	no	—
295	C₂×C₈	—	4	1	no	—
296	C₂×C₈	—	4	4	no	—
297	C₂×C₈	—	4	2	no	—
298	C₂×C₈	—	4	4	no	—
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	C₂×C₈	C₂×D₄×C₃₁	1	1	yes	characteristic
303	C₄⋊C₄	—	2	1	no	—
304	C₄⋊C₄	—	2	2	no	—
305	C₄⋊C₄	—	2	2	no	—
306	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
307	C₂²⋊C₄	—	2	2	no	—
308	C₂²⋊C₄	—	2	2	no	—
309	C₂²⋊C₄	—	4	2	no	—
310	C₂²⋊C₄	—	4	2	no	—
311	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
312	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
313	C₄²	#41×C₃₁	1	1	yes	characteristic
314	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
315	C₂³	—	2	4	no	—
316	C₂³	—	2	2	no	—
317	C₂³	—	4	2	no	—
318	C₂³	—	4	2	no	—
319	C₂³	—	4	2	no	—
320	C₂³	C₃₁×#121	1	1	yes	characteristic
321	Q₈	—	8	2	no	—
322	D₄	—	2	4	no	—
323	D₄	—	2	2	no	—
324	D₄	—	4	4	no	—
325	D₄	—	4	2	no	—
326	D₄	—	4	2	no	—
327	D₄	—	8	2	no	—
328	D₄	—	8	4	no	—
329	D₄	C₃₁×#135	1	4	yes	—
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	2	1	no	—
333	C₂×C₄	—	2	1	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	4	4	no	—
336	C₂×C₄	—	4	2	no	—
337	C₂×C₄	—	4	2	no	—
338	C₂×C₄	—	4	2	no	—
339	C₂×C₄	—	4	2	no	—
340	C₂×C₄	—	8	4	no	—
341	C₂×C₄	C₃₁×#121	1	1	yes	characteristic
342	C₂×C₄	C₃₁×#121	1	1	yes	characteristic
343	C₂×C₄	C₃₁×#121	1	1	yes	characteristic
344	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
345	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
346	C₂×C₄	C₂×#41×C₃₁	1	1	yes	characteristic
347	C₈	—	2	1	no	—
348	C₈	—	2	1	no	—
349	C₈	—	2	1	no	—
350	C₈	—	4	4	no	—
351	C₈	—	4	2	no	—
352	C₈	C₃₁×AGL(1,ℤ/8)	1	2	yes	—
353	C₂²	—	2	1	no	—
354	C₂²	—	2	1	no	—
355	C₂²	—	2	4	no	—
356	C₂²	—	4	8	no	—
357	C₂²	—	4	2	no	—
358	C₂²	—	4	2	no	—
359	C₂²	—	8	2	no	—
360	C₂²	—	8	2	no	—
361	C₂²	—	8	2	no	—
362	C₂²	C₃₁×#472	1	2	yes	—
363	C₂²	C₂×C₃₁×#121	1	1	yes	characteristic
364	C₄	—	2	1	no	—
365	C₄	—	2	1	no	—
366	C₄	—	2	1	no	—
367	C₄	—	2	1	no	—
368	C₄	—	4	2	no	—
369	C₄	—	8	2	no	—
370	C₄	C₂×C₃₁×#135	1	2	yes	—
371	C₄	C₂×C₃₁×AGL(1,ℤ/8)	1	1	yes	characteristic
372	C₄	C₃₁×#575	1	1	yes	characteristic
373	C₂	—	2	2	no	—
374	C₂	—	4	4	no	—
375	C₂	—	16	2	no	—
376	C₂	C₃₁×#3036	1	1	yes	characteristic
377	C₂	C₃₁×#3050	1	1	yes	characteristic
378	C₂	C₂×C₃₁×#472	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₃₁
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₂×C₄²×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3169	C₂	semidirect
2. C₃₁×#3109	C₂	semidirect
3. C₂×C₈×D₄×C₃₁	C₂	semidirect
4. C₃₁×#1677	C₂	semidirect
5. C₃₁×#1675	C₂	semidirect
6. C₃₁×#1667	C₂	semidirect
7. C₃₁×#1568	C₂	semidirect
8. C₃₁×#1551	C₂	semidirect
12. C₃₁×#500	C₂²	semidirect
13. C₃₁×#493	C₂²	semidirect
14. C₃₁×#486	C₂²	semidirect
32. C₃₁×#335	C₂²	semidirect
33. C₃₁×#334	C₂²	semidirect
34. C₃₁×#333	C₂²	semidirect
35. C₃₁×#331	C₂²	semidirect
125. #19258	C₃₁	direct (N × H)
164. #3169	C₂×C₃₁	semidirect
165. #3109	C₂×C₃₁	semidirect
166. C₂×C₈×D₄	C₂×C₃₁	semidirect
167. #1677	C₂×C₃₁	semidirect
168. #1675	C₂×C₃₁	semidirect
169. #1667	C₂×C₃₁	semidirect
170. #1568	C₂×C₃₁	semidirect
171. #1551	C₂×C₃₁	semidirect
195. #500	C₂²×C₃₁	semidirect
196. #493	C₂²×C₃₁	semidirect
197. #486	C₂²×C₃₁	semidirect
215. #335	C₂²×C₃₁	semidirect
216. #334	C₂²×C₃₁	semidirect
217. #333	C₂²×C₃₁	semidirect
218. #331	C₂²×C₃₁	semidirect
269. C₃₁	#19258	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×#3169	2
C₃₁×#3109	2
C₂×C₈×D₄×C₃₁	2
C₃₁×#1677	2
C₃₁×#1675	2
C₃₁×#1667	2
C₃₁×#1568	2
C₃₁×#1551	2
#19258	31

Subgroups — C31×#19258 #21476017

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#19258 #21476017