Subgroups — C₃₁×#33650 #21490409

Order 7936.

588 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3058	C₂	1	1	yes	maximal, characteristic
2	C₃₁×#2913	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#2234	C₂	1	2	yes	maximal, complemented
4	C₃₁×#2234	C₂	1	2	yes	maximal, complemented
5	C₃₁×#2233	C₂	1	2	yes	maximal, complemented
6	C₃₁×#2232	C₂	1	2	yes	maximal, complemented
7	C₃₁×#2159	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#2158	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#2140	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₃₁×#357	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#2113	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×D₈×C₃₁	C₂²	1	1	yes	characteristic
13	C₂×C₃₁×#131	C₂²	1	1	yes	characteristic
14	C₃₁×#535	—	2	1	no	—
15	C₃₁×#520	—	2	1	no	—
16	C₂×C₃₁×M₃₂	C₂²	1	1	yes	characteristic
17	C₂²×C₁₆×C₃₁	C₂²	1	1	yes	characteristic
18	C₃₁×#469	—	2	2	no	—
19	C₃₁×#466	C₂²	1	2	yes	—
20	C₃₁×#466	C₂²	1	2	yes	—
21	C₃₁×#428	—	2	2	no	—
22	C₃₁×#428	—	2	1	no	—
23	C₃₁×#427	C₂²	1	1	yes	characteristic
24	C₃₁×#427	C₂²	1	1	yes	characteristic
25	C₃₁×#427	C₂²	1	2	yes	complemented
26	C₂×C₃₁×#107	C₂²	1	1	yes	characteristic
27	C₂×C₃₁×#107	C₂²	1	2	yes	complemented
28	C₃₁×#418	—	2	1	no	—
29	C₃₁×#367	C₂²	1	1	yes	characteristic, complemented
30	C₃₁×#367	C₂²	1	1	yes	characteristic, complemented
31	C₃₁×#367	C₂²	1	2	yes	complemented
32	C₃₁×#366	C₂²	1	1	yes	characteristic, complemented
33	C₃₁×#366	C₂²	1	1	yes	characteristic, complemented
34	C₃₁×#366	C₂²	1	2	yes	complemented
35	C₃₁×#357	C₂²	1	2	yes	—
36	C₃₁×#357	C₂²	1	2	yes	—
37	C₃₁×#357	C₂²	1	2	yes	—
38	C₃₁×#357	C₂²	1	2	yes	—
39	C₃₁×C₂²⋊C₁₆	C₂²	1	2	yes	complemented
40	C₃₁×C₂²⋊C₁₆	C₂²	1	2	yes	complemented
41	C₂×#41×C₃₁	D₄	1	1	yes	characteristic
42	C₂²×D₄×C₃₁	—	2	1	no	—
43	C₂×D₈×C₃₁	—	2	1	no	—
44	C₂×D₈×C₃₁	—	2	2	no	—
45	C₂×D₈×C₃₁	—	2	2	no	—
46	C₂×D₈×C₃₁	C₂³	1	2	yes	—
47	C₃₁×#131	—	2	2	no	—
48	C₃₁×#131	—	2	2	no	—
49	C₂×M₁₆×C₃₁	D₄	1	1	yes	characteristic
50	C₂×M₁₆×C₃₁	D₄	1	2	yes	—
51	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
52	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
53	C₃₁×#127	—	4	1	no	—
54	C₃₁×#124	—	4	1	no	—
55	C₃₁×#121	—	2	2	no	—
56	C₃₁×#121	—	2	2	no	—
57	C₃₁×#120	—	4	2	no	—
58	C₄×Q₈×C₃₁	—	4	1	no	—
59	C₄×D₄×C₃₁	—	4	2	no	—
60	C₄×D₄×C₃₁	—	4	1	no	—
61	C₃₁×#117	—	2	1	no	—
62	C₃₁×#117	—	2	1	no	—
63	C₃₁×#117	—	2	2	no	—
64	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
65	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
66	C₃₁×M₃₂	—	2	2	no	—
67	C₂×C₁₆×C₃₁	—	2	2	no	—
68	C₂×C₁₆×C₃₁	C₂³	1	1	yes	characteristic
69	C₂×C₁₆×C₃₁	C₂³	1	1	yes	characteristic
70	C₂×C₁₆×C₃₁	C₂³	1	2	yes	—
71	C₃₁×#107	—	2	1	no	—
72	C₃₁×#107	—	2	2	no	—
73	C₃₁×#107	C₂³	1	2	yes	—
74	C₃₁×#107	C₂³	1	1	yes	characteristic
75	C₃₁×#107	C₂³	1	1	yes	characteristic
76	C₃₁×#107	C₂³	1	1	yes	characteristic
77	C₃₁×#107	C₂³	1	1	yes	characteristic
78	C₃₁×#106	—	2	1	no	—
79	C₃₁×#106	—	2	1	no	—
80	C₃₁×#106	—	2	2	no	—
81	C₃₁×#102	—	2	2	no	—
82	C₃₁×#102	—	2	2	no	—
83	C₂⁴×C₃₁	—	4	1	no	—
84	#41×C₃₁	—	2	2	no	—
85	#41×C₃₁	—	2	2	no	—
86	C₂×Q₈×C₃₁	D₈	1	1	yes	characteristic
87	C₂×D₄×C₃₁	—	2	2	no	—
88	C₂×D₄×C₃₁	—	4	2	no	—
89	C₂×D₄×C₃₁	—	4	2	no	—
90	C₂×D₄×C₃₁	—	4	2	no	—
91	C₂×D₄×C₃₁	—	4	1	no	—
92	C₂×D₄×C₃₁	—	4	2	no	—
93	C₂×D₄×C₃₁	D₈	1	2	yes	—
94	C₂×D₄×C₃₁	D₈	1	1	yes	characteristic
95	C₂²×C₄×C₃₁	—	4	2	no	—
96	C₂²×C₄×C₃₁	—	4	1	no	—
97	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
98	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
99	D₈×C₃₁	—	2	2	no	—
100	D₈×C₃₁	—	2	2	no	—
101	D₈×C₃₁	—	4	2	no	—
102	M₁₆×C₃₁	—	2	2	no	—
103	M₁₆×C₃₁	—	2	4	no	—
104	C₂×C₈×C₃₁	—	2	2	no	—
105	C₂×C₈×C₃₁	—	2	2	no	—
106	C₂×C₈×C₃₁	C₂×D₄	1	2	yes	—
107	C₂×C₈×C₃₁	C₂×D₄	1	1	yes	characteristic
108	C₂×C₈×C₃₁	#41	1	2	yes	—
109	C₂×C₈×C₃₁	#41	1	2	yes	—
110	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
111	C₄⋊C₄×C₃₁	—	2	1	no	—
112	C₄⋊C₄×C₃₁	—	2	1	no	—
113	C₄⋊C₄×C₃₁	—	2	1	no	—
114	C₄⋊C₄×C₃₁	—	2	1	no	—
115	C₄⋊C₄×C₃₁	—	2	2	no	—
116	C₄⋊C₄×C₃₁	—	4	2	no	—
117	C₄⋊C₄×C₃₁	—	4	1	no	—
118	C₂²⋊C₄×C₃₁	—	4	2	no	—
119	C₂²⋊C₄×C₃₁	—	4	1	no	—
120	C₂²⋊C₄×C₃₁	—	4	1	no	—
121	C₂²⋊C₄×C₃₁	—	4	2	no	—
122	C₂²⋊C₄×C₃₁	—	4	2	no	—
123	C₄²×C₃₁	—	4	2	no	—
124	C₄²×C₃₁	—	4	1	no	—
125	C₄²×C₃₁	—	4	1	no	—
126	C₁₆×C₃₁	—	2	1	no	—
127	C₁₆×C₃₁	—	2	1	no	—
128	C₁₆×C₃₁	—	2	2	no	—
129	#33650	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
130	C₂³×C₃₁	—	4	2	no	—
131	C₂³×C₃₁	—	8	2	no	—
132	C₂³×C₃₁	—	16	1	no	—
133	C₂³×C₃₁	—	16	1	no	—
134	C₂³×C₃₁	C₂×D₈	1	2	yes	—
135	C₂³×C₃₁	C₂×D₈	1	1	yes	characteristic
136	Q₈×C₃₁	—	2	2	no	—
137	D₄×C₃₁	—	2	4	no	—
138	D₄×C₃₁	—	2	2	no	—
139	D₄×C₃₁	—	4	2	no	—
140	D₄×C₃₁	—	4	2	no	—
141	D₄×C₃₁	—	8	2	no	—
142	D₄×C₃₁	—	16	2	no	—
143	D₄×C₃₁	—	16	2	no	—
144	C₂×C₄×C₃₁	—	2	2	no	—
145	C₂×C₄×C₃₁	—	2	2	no	—
146	C₂×C₄×C₃₁	—	4	1	no	—
147	C₂×C₄×C₃₁	—	4	1	no	—
148	C₂×C₄×C₃₁	—	4	1	no	—
149	C₂×C₄×C₃₁	—	4	2	no	—
150	C₂×C₄×C₃₁	—	4	1	no	—
151	C₂×C₄×C₃₁	—	16	1	no	—
152	C₂×C₄×C₃₁	—	16	2	no	—
153	C₂×C₄×C₃₁	#123	1	2	yes	—
154	C₂×C₄×C₃₁	C₂×D₈	1	2	yes	—
155	C₂×C₄×C₃₁	C₂×D₈	1	1	yes	characteristic
156	C₂×C₄×C₃₁	#137	1	2	yes	—
157	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
158	C₈×C₃₁	—	2	2	no	—
159	C₈×C₃₁	#123	1	2	yes	—
160	C₈×C₃₁	C₂×#41	1	1	yes	characteristic
161	C₈×C₃₁	C₂×#41	1	1	yes	characteristic
162	#3058	C₂×C₃₁	1	1	yes	characteristic
163	#2913	C₂×C₃₁	1	1	yes	characteristic, complemented
164	#2234	C₂×C₃₁	1	2	yes	complemented
165	#2234	C₂×C₃₁	1	2	yes	complemented
166	#2233	C₂×C₃₁	1	2	yes	complemented
167	#2232	C₂×C₃₁	1	2	yes	complemented
168	#2159	C₂×C₃₁	1	1	yes	characteristic, complemented
169	#2158	C₂×C₃₁	1	1	yes	characteristic, complemented
170	#2140	C₂×C₃₁	1	1	yes	characteristic, complemented
171	C₂×#357	C₂×C₃₁	1	1	yes	characteristic, complemented
172	#2113	C₂×C₃₁	1	1	yes	characteristic, complemented
173	C₂²×C₃₁	—	2	1	no	—
174	C₂²×C₃₁	—	2	1	no	—
175	C₂²×C₃₁	—	2	2	no	—
176	C₂²×C₃₁	—	2	2	no	—
177	C₂²×C₃₁	—	2	2	no	—
178	C₂²×C₃₁	—	8	2	no	—
179	C₂²×C₃₁	—	8	2	no	—
180	C₂²×C₃₁	—	8	2	no	—
181	C₂²×C₃₁	—	16	4	no	—
182	C₂²×C₃₁	#480	1	2	yes	—
183	C₂²×C₃₁	C₂²×D₈	1	1	yes	characteristic
184	C₄×C₃₁	—	2	2	no	—
185	C₄×C₃₁	—	8	2	no	—
186	C₄×C₃₁	—	8	1	no	—
187	C₄×C₃₁	—	8	1	no	—
188	C₄×C₃₁	—	8	1	no	—
189	C₄×C₃₁	—	8	1	no	—
190	C₄×C₃₁	#480	1	2	yes	—
191	C₄×C₃₁	C₂×#123	1	1	yes	characteristic
192	C₄×C₃₁	C₂×#137	1	1	yes	characteristic
193	C₂²×D₈	C₂²×C₃₁	1	1	yes	characteristic
194	C₂×#131	C₂²×C₃₁	1	1	yes	characteristic
195	#535	—	2	1	no	—
196	#520	—	2	1	no	—
197	C₂×M₃₂	C₂²×C₃₁	1	1	yes	characteristic
198	C₂²×C₁₆	C₂²×C₃₁	1	1	yes	characteristic
199	#469	—	2	2	no	—
200	#466	C₂²×C₃₁	1	2	yes	—
201	#466	C₂²×C₃₁	1	2	yes	—
202	#428	—	2	2	no	—
203	#428	—	2	1	no	—
204	#427	C₂²×C₃₁	1	1	yes	characteristic
205	#427	C₂²×C₃₁	1	1	yes	characteristic
206	#427	C₂²×C₃₁	1	2	yes	complemented
207	C₂×#107	C₂²×C₃₁	1	1	yes	characteristic
208	C₂×#107	C₂²×C₃₁	1	2	yes	complemented
209	#418	—	2	1	no	—
210	#367	C₂²×C₃₁	1	1	yes	characteristic, complemented
211	#367	C₂²×C₃₁	1	1	yes	characteristic, complemented
212	#367	C₂²×C₃₁	1	2	yes	complemented
213	#366	C₂²×C₃₁	1	1	yes	characteristic, complemented
214	#366	C₂²×C₃₁	1	1	yes	characteristic, complemented
215	#366	C₂²×C₃₁	1	2	yes	complemented
216	#357	C₂²×C₃₁	1	2	yes	—
217	#357	C₂²×C₃₁	1	2	yes	—
218	#357	C₂²×C₃₁	1	2	yes	—
219	#357	C₂²×C₃₁	1	2	yes	—
220	C₂²⋊C₁₆	C₂²×C₃₁	1	2	yes	complemented
221	C₂²⋊C₁₆	C₂²×C₃₁	1	2	yes	complemented
222	C₂×C₃₁	—	2	2	no	—
223	C₂×C₃₁	—	4	2	no	—
224	C₂×C₃₁	—	16	2	no	—
225	C₂×C₃₁	C₂×#480	1	1	yes	characteristic
226	C₂×C₃₁	#3415	1	1	yes	characteristic
227	C₂×C₃₁	#3416	1	1	yes	characteristic
228	C₂×#41	D₄×C₃₁	1	1	yes	characteristic
229	C₂²×D₄	—	2	1	no	—
230	C₂×D₈	—	2	1	no	—
231	C₂×D₈	—	2	2	no	—
232	C₂×D₈	—	2	2	no	—
233	C₂×D₈	C₂³×C₃₁	1	2	yes	—
234	#131	—	2	2	no	—
235	#131	—	2	2	no	—
236	C₂×M₁₆	D₄×C₃₁	1	1	yes	characteristic
237	C₂×M₁₆	D₄×C₃₁	1	2	yes	—
238	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
239	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
240	#127	—	4	1	no	—
241	#124	—	4	1	no	—
242	#121	—	2	2	no	—
243	#121	—	2	2	no	—
244	#120	—	4	2	no	—
245	C₄×Q₈	—	4	1	no	—
246	C₄×D₄	—	4	2	no	—
247	C₄×D₄	—	4	1	no	—
248	#117	—	2	1	no	—
249	#117	—	2	2	no	—
250	#117	—	2	1	no	—
251	C₂×C₄⋊C₄	—	2	1	no	—
252	C₂×C₄⋊C₄	—	2	2	no	—
253	M₃₂	—	2	2	no	—
254	C₂×C₁₆	—	2	2	no	—
255	C₂×C₁₆	C₂³×C₃₁	1	1	yes	characteristic
256	C₂×C₁₆	C₂³×C₃₁	1	2	yes	—
257	C₂×C₁₆	C₂³×C₃₁	1	1	yes	characteristic
258	#107	—	2	1	no	—
259	#107	—	2	2	no	—
260	#107	C₂³×C₃₁	1	2	yes	—
261	#107	C₂³×C₃₁	1	1	yes	characteristic
262	#107	C₂³×C₃₁	1	1	yes	characteristic
263	#107	C₂³×C₃₁	1	1	yes	characteristic
264	#107	C₂³×C₃₁	1	1	yes	characteristic
265	#106	—	2	1	no	—
266	#106	—	2	1	no	—
267	#106	—	2	2	no	—
268	#102	—	2	2	no	—
269	#102	—	2	2	no	—
270	C₃₁	#33650	1	1	yes	characteristic, direct product factor, Sylow
271	C₂⁴	—	4	1	no	—
272	#41	—	2	2	no	—
273	#41	—	2	2	no	—
274	C₂×Q₈	D₈×C₃₁	1	1	yes	characteristic
275	C₂×D₄	—	2	2	no	—
276	C₂×D₄	—	4	2	no	—
277	C₂×D₄	—	4	2	no	—
278	C₂×D₄	—	4	2	no	—
279	C₂×D₄	—	4	1	no	—
280	C₂×D₄	—	4	2	no	—
281	C₂×D₄	D₈×C₃₁	1	2	yes	—
282	C₂×D₄	D₈×C₃₁	1	1	yes	characteristic
283	C₂²×C₄	—	4	2	no	—
284	C₂²×C₄	—	4	1	no	—
285	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
286	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
287	D₈	—	2	2	no	—
288	D₈	—	2	2	no	—
289	D₈	—	4	2	no	—
290	M₁₆	—	2	2	no	—
291	M₁₆	—	2	4	no	—
292	C₂×C₈	—	2	2	no	—
293	C₂×C₈	—	2	2	no	—
294	C₂×C₈	C₂×D₄×C₃₁	1	2	yes	—
295	C₂×C₈	C₂×D₄×C₃₁	1	1	yes	characteristic
296	C₂×C₈	#41×C₃₁	1	2	yes	—
297	C₂×C₈	#41×C₃₁	1	2	yes	—
298	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
299	C₄⋊C₄	—	2	1	no	—
300	C₄⋊C₄	—	2	1	no	—
301	C₄⋊C₄	—	2	1	no	—
302	C₄⋊C₄	—	2	1	no	—
303	C₄⋊C₄	—	2	2	no	—
304	C₄⋊C₄	—	4	2	no	—
305	C₄⋊C₄	—	4	1	no	—
306	C₂²⋊C₄	—	4	2	no	—
307	C₂²⋊C₄	—	4	1	no	—
308	C₂²⋊C₄	—	4	1	no	—
309	C₂²⋊C₄	—	4	2	no	—
310	C₂²⋊C₄	—	4	2	no	—
311	C₄²	—	4	2	no	—
312	C₄²	—	4	1	no	—
313	C₄²	—	4	1	no	—
314	C₁₆	—	2	1	no	—
315	C₁₆	—	2	1	no	—
316	C₁₆	—	2	2	no	—
317	C₂³	—	4	2	no	—
318	C₂³	—	8	2	no	—
319	C₂³	—	16	1	no	—
320	C₂³	—	16	1	no	—
321	C₂³	C₂×D₈×C₃₁	1	2	yes	—
322	C₂³	C₂×D₈×C₃₁	1	1	yes	characteristic
323	Q₈	—	2	2	no	—
324	D₄	—	2	4	no	—
325	D₄	—	2	2	no	—
326	D₄	—	4	2	no	—
327	D₄	—	4	2	no	—
328	D₄	—	8	2	no	—
329	D₄	—	16	2	no	—
330	D₄	—	16	2	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	2	2	no	—
333	C₂×C₄	—	4	1	no	—
334	C₂×C₄	—	4	1	no	—
335	C₂×C₄	—	4	1	no	—
336	C₂×C₄	—	4	2	no	—
337	C₂×C₄	—	4	1	no	—
338	C₂×C₄	—	16	1	no	—
339	C₂×C₄	—	16	2	no	—
340	C₂×C₄	C₃₁×#123	1	2	yes	—
341	C₂×C₄	C₂×D₈×C₃₁	1	2	yes	—
342	C₂×C₄	C₂×D₈×C₃₁	1	1	yes	characteristic
343	C₂×C₄	C₃₁×#137	1	2	yes	—
344	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
345	C₈	—	2	2	no	—
346	C₈	C₃₁×#123	1	2	yes	—
347	C₈	C₂×#41×C₃₁	1	1	yes	characteristic
348	C₈	C₂×#41×C₃₁	1	1	yes	characteristic
349	C₂²	—	2	1	no	—
350	C₂²	—	2	1	no	—
351	C₂²	—	2	2	no	—
352	C₂²	—	2	2	no	—
353	C₂²	—	2	2	no	—
354	C₂²	—	8	2	no	—
355	C₂²	—	8	2	no	—
356	C₂²	—	8	2	no	—
357	C₂²	—	16	4	no	—
358	C₂²	C₃₁×#480	1	2	yes	—
359	C₂²	C₂²×D₈×C₃₁	1	1	yes	characteristic
360	C₄	—	2	2	no	—
361	C₄	—	8	2	no	—
362	C₄	—	8	1	no	—
363	C₄	—	8	1	no	—
364	C₄	—	8	1	no	—
365	C₄	—	8	1	no	—
366	C₄	C₃₁×#480	1	2	yes	—
367	C₄	C₂×C₃₁×#123	1	1	yes	characteristic
368	C₄	C₂×C₃₁×#137	1	1	yes	characteristic
369	C₂	—	2	2	no	—
370	C₂	—	4	2	no	—
371	C₂	—	16	2	no	—
372	C₂	C₂×C₃₁×#480	1	1	yes	characteristic
373	C₂	C₃₁×#3415	1	1	yes	characteristic
374	C₂	C₃₁×#3416	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₃₁
prime radical	C₃₁×#3058	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₂×#41×C₃₁ ◁ C₂×C₃₁×#131 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃₁×#2913	C₂	semidirect
3. C₃₁×#2234	C₂	semidirect
4. C₃₁×#2234	C₂	semidirect
5. C₃₁×#2233	C₂	semidirect
6. C₃₁×#2232	C₂	semidirect
7. C₃₁×#2159	C₂	semidirect
8. C₃₁×#2158	C₂	semidirect
9. C₃₁×#2140	C₂	semidirect
10. C₂×C₃₁×#357	C₂	semidirect
11. C₃₁×#2113	C₂	semidirect
25. C₃₁×#427	C₂²	semidirect
27. C₂×C₃₁×#107	C₂²	semidirect
29. C₃₁×#367	C₂²	semidirect
30. C₃₁×#367	C₂²	semidirect
31. C₃₁×#367	C₂²	semidirect
32. C₃₁×#366	C₂²	semidirect
33. C₃₁×#366	C₂²	semidirect
34. C₃₁×#366	C₂²	semidirect
39. C₃₁×C₂²⋊C₁₆	C₂²	semidirect
40. C₃₁×C₂²⋊C₁₆	C₂²	semidirect
129. #33650	C₃₁	direct (N × H)
163. #2913	C₂×C₃₁	semidirect
164. #2234	C₂×C₃₁	semidirect
165. #2234	C₂×C₃₁	semidirect
166. #2233	C₂×C₃₁	semidirect
167. #2232	C₂×C₃₁	semidirect
168. #2159	C₂×C₃₁	semidirect
169. #2158	C₂×C₃₁	semidirect
170. #2140	C₂×C₃₁	semidirect
171. C₂×#357	C₂×C₃₁	semidirect
172. #2113	C₂×C₃₁	semidirect
206. #427	C₂²×C₃₁	semidirect
208. C₂×#107	C₂²×C₃₁	semidirect
210. #367	C₂²×C₃₁	semidirect
211. #367	C₂²×C₃₁	semidirect
212. #367	C₂²×C₃₁	semidirect
213. #366	C₂²×C₃₁	semidirect
214. #366	C₂²×C₃₁	semidirect
215. #366	C₂²×C₃₁	semidirect
220. C₂²⋊C₁₆	C₂²×C₃₁	semidirect
221. C₂²⋊C₁₆	C₂²×C₃₁	semidirect
270. C₃₁	#33650	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×#3058	2
C₃₁×#2913	2
C₃₁×#2234	2
C₃₁×#2233	2
C₃₁×#2232	2
C₃₁×#2159	2
C₃₁×#2158	2
C₃₁×#2140	2
C₂×C₃₁×#357	2
C₃₁×#2113	2
#33650	31

Subgroups — C31×#33650 #21490409

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#33650 #21490409